PHYSICS FORM ONE NOTES

Chapter One: Introduction to Physics

Introduction

Physics is the fundamental branch of science that explores the principles governing the behaviour of matter and energy in the universe. Physics deals with very large objects like planets and very small ones like atoms. It also covers various concepts, theories, and principles that provide insights into the natural world and its interactions. In this chapter, you will learn the concepts, theories, and principles of Physics. The competencies developed will enable you to apply the concepts, theories, and principles of Physics to solve daily life problems. You will also be able to relate physics with other branches of natural sciences.

Think

How could our life be without the interaction between matter and energy?

Concept of Physics

The universe is a totality of matter, energy, space, and time. The word universe originates from the Latin word ‘universus’ which means ‘all or everything’. It can therefore be referred to as everything surrounding us; within, near, far and beyond our planet, solar system, and galaxy in which our solar system belongs (the Milky Way Galaxy). We are part of the universe. Science is the major tool for studying and exploring the universe. It begins with inquiries such as what is the universe? What is its origin? What makes up the universe? How does it change with time? Why does the sky look blue? And why does iron turn red when heated? To answer such questions, the applications of theories, principles, and laws of science are required.

Physics falls under a broad category of natural science, which is divided into three main branches, namely physics, chemistry, and biology. Physics is the branch of science which deals with the study of matter, energy and their interactions.

The word physics originated from the Greek word ‘Physikos’ which means ‘nature’. Physics involves the study of physical and natural phenomena around us. Examples of these phenomena are the occurrence of eclipses, causes of sunset and sunrise, the formation of the rainbow, and volcanic eruption.

Figure 1.1: Natural phenomena

Physics is the branch of science that deals with the study of matter, energy and the mutual interactions between them. A person who studies physics is known as a Physicist.

In Physics, matter is studied in relation to its motion, as well as space and time. Matter is defined as any substance which has mass and occupies space. Physics as a subject uses concepts like force, energy, and mass to explain different phenomena. In doing so, students of physics get to learn more about matter, energy and how they interact with each other. Energy, for example, may take the form of heat, light, or electricity. Among the most important forms of energy today is electricity which can be generated in many ways including waterfalls and combustion of natural gas.

Figure 1.2: Kinyerezi power generation station

Task 1.1

Identify and observe real-life examples of physics concepts in your school and home environments. Record your observations and reflect on how these examples illustrate the concept learned in class.

Branches of Physics

Physics is known to be a fundamental subject among all branches of science. The content of physics is very broad and wide in such a way that it cannot be covered within a single domain. Therefore, physics is divided into several branches, each focusing on different aspects of the universe. Some of the major branches of physics are:

Mechanics

Mechanics is the branch of physics that deals with objects that are either stationary or in motion, the influence of forces acting on them and their impacts. Under this branch, aspects like linear, circular, and oscillatory motions of objects as well as fluids and their impacts are studied.

Heat

Heat is one among the forms of energy. Heat can be transferred from one point to another by either conduction, convection or radiation. This branch of physics describes the phenomena of matter when heat energy is supplied to it. These phenomena include the expansion of matter, changes of states of matter, and the anomalous expansion of water.

Light

Light is a form of energy that travels in a straight line. There are two types of light sources: Natural and artificial. The Sun is the primary or main source of natural light. We see different objects with the aid of light. Our eyes enable us to see objects when light falls on them.

Electromagnetism

Electromagnetism is the branch of physics that deals with the interaction between electric and magnetic fields. It has a wide range of applications in our daily life, including generation of electricity and fabrication of motors. Life could be difficult without electricity.

Astronomy

Astronomy deals with the study of the universe (cosmos) and everything contained in it. The word astronomy originates from two Greek words, ‘astron’ which means ‘star’ and ‘nomos’ which means ‘laws. The Greeks referred to it as the study of laws of stars. Astronomy seeks to answer inquiries such as how celestial objects like moons, planets, stars, and galaxies originate and change with time.

Geophysics

Geophysics is the branch of physics that deals with physical processes and physical properties of the Earth and its surroundings. It speculates the interior and exterior structure of the earth in terms of physical and chemical properties.

Electronics

Electronics is the basis of modern technology. It involves the study of circuits that are made of semiconductor components like, diode, transistor, and integrated circuits. Most of communication devices are made of semiconductor materials. Examples of devices that use the principles of electronics are television, radio, Light Emitting Diode (LED) lamps, mobile phones, cameras, printers, and computers.

Physics of the atom

This is a branch of physics which deals with the behaviour of particles that make up the atom and accompanying energy. We learn about radiation which is emitted by the atom during disintegration and how we can protect ourselves from harmful radiation.

Connection between Physics and other disciplines

Physics relates to many subjects in terms of either direct applications or the principles governing the working of instruments used in a given subject. Physics is closely related to chemistry, biology and mathematics. Physics is also related to earth sciences such as geology and meteorology. The relationships between physics and other subjects are discussed below.

Physics and chemistry

Chemistry principles are used to produce pesticides and insecticides, perfumes, and fertilizers. Then, physics principles are applied in packaging them so that they can be released in a controlled manner from compressed cylinders or sprays. Also, chemists use equipment designed and constructed using physics principles to achieve extraction of chemicals.

Figure 1.3: Pesticide and insecticide

Physics and biology

A number of instruments such as microscopes used in biology are designed and constructed using physics principles. Processes such as photosynthesis, conversion of matter into energy, and even the transfer of heat used in biology can be well explained by using laws of physics.

Physics and mathematics

Mathematics is a working tool of almost all disciplines. All branches of mathematics for instance, algebra, trigonometry, and vectors are applied to study physics. More often mathematical relations are used in expressing physics concepts. For instance, force, F is directly proportional to extension, e. This concept can be expressed mathematically as:

F ∝ e

F = ke

where k is a constant of proportionality. A graph of force, F against extension, e is shown in Figure 1.4.

Figure 1.4: Graph of force against extension

Physics and meteorology

Meteorology deals with the study of weather and climate. Meteorologists use an instrument like rain gauge which is designed and constructed using the principles of physics to measure rainfall. A wind vane uses physics principles to measure direction of the wind.

Figure 1.5: Instruments used in meteorology

Physics and astronomy

Astronomy deals with the study of objects that compose the physical universe. It involves the study of stars, planets, satellites, nebulae, galaxies as well as the distribution of matter and energy in space and time. Due to its complexity, astronomy uses principles, theories and laws of natural science, engineering, technology and mathematics (STEM). Therefore, physics plays a crucial role in astronomy. For example, the laws of planets and other objects present in the solar system are shown in Figure 1.6.

Figure 1.6: Solar system

Task 1.2

Search from different resources such as online sources then write short notes on how physics is related with other subjects apart from natural science.

Importance of studying physics

Generally, physics helps us to understand nature. The following are examples of its importance.

• The study of physics enables a person to answer questions about the physical properties of matter.
• Physics helps to answer questions like why some materials are attracted by magnets while others are not, why the sky looks blue, and why clouds look white.
• The study of physics enables us to acquire skills that are required in different professions such as engineering, technology, teaching, and architecture.
• The study of physics enables us to acquire knowledge and skills that are applied in designing and constructing different items which are useful in our daily lives. These include simple machines such as pulleys inclined planes, and complex ones like bicycles, escalators, and bulldozers.
• Physics is fun. It helps to understand the applications of physics principles in sports and games.
• Physics helps to understand the working principles of home appliances such as electric irons, grinders, vacuum flasks, thermos flasks, cooking stoves, televisions, and radios.

Contribution of Physics to the development of modern society

Discoveries in physics have led to various inventions that influence our lives. Electricity, motor vehicles, and electronics in general, are results of scientific and technological advancement. The study of how to control tiny particles like electrons and protons led to the discovery of electronics which in turn led to the production of devices like calculators and computers. Other applications of physics which can be experienced in daily life situations include the following:

At home

All tools and machinery that we use in our homes to simplify work are made by applying different laws of physics. These include crowbars, hammers, door handles, cutlery, hinges, and pulleys. For example, garden shear and sprayer are used when working in a home garden as shown in Figure 1.7.

Figure 1.7: Tools used for working at a home garden

Similarly, it would be difficult to get underground water to the surface without a pulley system or water pumps. Pulleys are used for drawing water from wells by applying a small force, F shown in Figure 1.8.

Figure 1.8: Drawing water from a deep well

Physicists have reduced the cost of electricity by applying physics principles to design and construct energy saving bulbs such as Compact Fluorescent Lamp (CFL) and Light Emitting Diodes (LED) shown in Figure 1.9.

Figure 1.9: Energy saving lamps

In hospital

Various machines are used in hospitals for the diagnosis and treatment of various diseases. These machines are designed and constructed using physics principles. Such machines include diagnostic X-ray and ultrasound machines. Figure 1.10 shows an ultrasound machine. Handling and using these machines is based on the knowledge and skills acquired in physics. This means that those who operate these machines must know physics.

Figure 1.10: Ultrasound machine

In addition, premature babies are nursed in incubators, shown in Figure 1.11(a), until they attain a safe weight and physical condition for them to survive on their own. The conditions in incubators are modified to the extent that they resemble a mother’s womb to support the survival of the babies. Syringes and needles for administering injections, feeding tubes and drip bottles, all apply physics principles. Figure 1.11(b) shows some tools used in the medical field.

Figure 1.11: Medical equipment

Sources of energy

Some processes and machines help us to obtain energy for our daily use. These machines make use of various laws of physics to give us different forms of energy. For example, batteries, generators and solar cells, shown in Figure 1.12, provide electrical energy. This energy is used in charging mobile phones, powering radios, and televisions. A car battery provides the energy needed in a car. When devices like bulbs are connected to these sources, they provide light energy for our daily use.

Figure 1.12: Sources of energy

Transport

Application of the laws of physics such as motion and frictional forces ensure vessels used in transportation like aeroplanes, trains, ships, cars and bicycles can move, brake and stop when necessary. Figure 1.13 shows transport vessels which operate because the laws related to friction, flotation, and balance are observed and applied accordingly.

Figure 1.13: Transport vessels

Remember that, if these laws are disobeyed, ships sink and trains derail. Ships and boats have refrigerators and air conditioners that function through the application of the laws of physics. Heat is removed from the fridges by the refrigerant and prevented from entering the fridge by using insulating materials such as a rubber strip attached to the fridge door.

Communication

Communication is important to human life as it keeps us informed of day-to-day happenings. Devices used in communication systems such as radio masts, telephones and satellite dishes shown in Figure 1.14, antenna and modems are used for accessing the internet, television, and radio signals using physics principles. Therefore, the knowledge of physics is essential in constructing these instruments.

Figure 1.14: Communication devices

Short messages (SMS) through mobile phones, electronic mail (emails), and fax messages from fax machines are also reliable means of communication. All these are the results of the application of the principles of physics. Figure 1.15 shows SMS, email and fax from the mobile phone, computer display and fax machine.

Figure 1.15: SMS, email and fax

Entertainment

Physics has enabled people to enjoy a variety of leisure activities as is evident in exercise machines (Used for walking, running or climbing while staying at the same place), bouncing castles, shown in Figure 1.16, and other sports and electronics equipments. Inflated balloons and bouncing castles are used to entertain children.

Figure 1.16: Equipment used for recreation

Music and pictures are recorded on tapes or compact disks commonly referred to as CDs. They are then listened to or watched on television using a Visual Compact Disk (VCD) player, Digital Video Disk (DVD) player or USB drive. The recording process utilises physics principles. Figure 1.17 shows a DVD player and other accessories including Compact Disk.

Figure 1.17: Recording instruments

Industry

Physics principles and laws have enabled industries to assemble, calibrate, and use highly accurate instruments. Physics can be applied in various industries such as construction, manufacturing, and automobile industries. Many instruments used in different industries apply the laws and principles of physics in their operation. Examples of these instruments are, sawmills used for cutting wood, cranes used for lifting heavy loads, and spanners used for tightening and loosening nuts and bolts.

In schools

In schools, equipment such as computers, photocopy machines, printers, projectors, language translating devices, telescopes, cameras, and binoculars, use the knowledge of physics.

In addition, instruments and apparatus used in school laboratories are made using the knowledge and skills acquired in physics. Examples of such apparatus and instruments are shown in Figure 1.18. Instruments should meet certain specifications or standards that are universally accepted. This is to enable the instrument to give the same standard or common measured value when used throughout the world.

Figure 1.18: Laboratory apparatus

Generally, physics is applied in many fields. It is an important discipline that enables experts to determine how structures like bridges, roads, and railways should be built to ensure safety.

Activity 1.1

Aim: To demonstrate applications of physics.

Materials: A plane mirror, a scale balance, different masses (5 g, 10 g, 15 g), flagpole

Procedure

Part I:

1. Look at your image in a plane mirror.
2. Observe how your face looks like.

Part II:

1. Prepare a scale balance.
2. Place a 10 g mass on one side and a 15 g mass on the other side of the scale balance.
3. Record your observations.
4. Now add a 5 g mass on the side with 10 g and observe what happens.

Part III:

1. Go out of the classroom and observe the top of the flagpole.
2. Look at the full length of the string used to hoist the flag and record your observations.

Questions

(a) How did your face look like?

(b) From your observation, explain what happened in step 4.

(c) What makes the scouts in your school able to raise the flag to the top of the pole?

Plane mirrors always form images of their observers. Therefore, a person looking at a mirror will see an image of himself or herself. A scale balance leans on the side that has more mass than the other. This is useful when measuring some items such as sugar and flour. A flag is raised to the top of a flagpole using a string that is rotated on a pulley. The string is then fastened at the bottom. All of these are applications of physics in daily life.

Theories and principles of Physics

The discipline of physics is built upon a foundation of theories and principles that have been developed and refined over centuries of scientific exploration. These theories and principles serve as the building blocks for understanding the laws and phenomena that govern the natural world. This means scientific exploration is a very important aspect of the development of physics. Therefore, in this section, we shall discuss the aspect of scientific investigation. Further, we will discuss the existing basic theories and principles of physics.

Basic principles of scientific investigations

The basic principles of scientific investigations form the foundation of the scientific method and guide researchers in conducting systematic and reliable experiments. These principles are essential for ensuring the accuracy, objectivity, and productivity of scientific findings.

The concept of scientific investigation

The scientific method is the basic skill needed in the world of science. Humans are always curious about why and how things happen in the world. The scientific method provides scientists with a well-structured platform to help find the answers to their questions.

Therefore, the scientific method is a set of steps used by scientists to investigate a problem or answer questions.

Basic steps of scientific investigation

Scientists including physicists are always looking for scientific evidence. A systematic search for evidence is recommended during and after experiments. The following are steps followed when carrying out a scientific investigation.

1. Problem identification

This is the first step in the scientific method. It is when one makes a puzzling observation.

An example of such an observation would be ‘What is the relationship between the length of the string to which the pendulum bob is attached and the time taken by the pendulum to complete a given number of oscillations? The following examples will help you to build competence on how to identify a problem.

Example 1.1

When a ball is released from the top of a ramp, it rolls down to the bottom. After several trials, you notice that the ball always stops at almost the same point. How can you identify the problem in this scenario?

Answer: The problem in this scenario is to explain why the ball consistently stops at almost the same point on the ramp during each trial. This issue could be related to factors such as friction, air resistance, or the ramp’s incline.

Example 1.2

A student conducts an experiment to measure the time taken for a pendulum to complete ten oscillations. However, the results are inconsistent as the measured time varies significantly between trials. What problem can be identified in this experiment?

Answer: The problem in this experiment is to identify the factors causing the inconsistency in the time measurements for the ten oscillations of pendulum. Key issues in this scenario may be variations in the starting angle, air resistance, or inaccuracies in the timing method.

2. Formulating a testable hypothesis

A hypothesis is a scientific assumption or prediction of the outcome. It is a suggestion of the answer to the question asked. To formulate a testable hypothesis in physics, we must make observations on a variety of events. For example, the length of the string to which the pendulum bob is attached affects the time taken by a pendulum to complete a given number of oscillations. The following examples may help you to formulate a testable hypothesis.

Example 1.3

You notice that when you rub a balloon against your hair, it becomes negatively charged, and you can make small pieces of paper stick to it. What testable hypothesis can you formulate to explain this phenomenon?

Answer: Hypothesis: If the balloon is rubbed against the hair, it will become charged and hence attract lightweight objects, like small pieces of paper, due to static electricity.

Example 1.4

During a solar eclipse, you observe that the temperature drops noticeably. Formulate a testable hypothesis to investigate this temperature change phenomenon.

Answer: Hypothesis: If a solar eclipse occurs, then there will be a decrease in temperature compared to normal conditions, due to the obstruction of the sun’s radiation towards the Earth’s surface.

Task 1.3

You notice that some metal objects left outside during a cold night feel much colder to the touch than other objects made of wood or plastic. Propose a testable hypothesis to explain this observation.

Fact

In science we never prove a hypothesis through a single experiment because there is a chance that you made an error somewhere along the way. What you can say is that, your results support or do not support the original hypothesis.

3. Conducting an experiment

Scientists particularly physicists experiments to study the causal relationships. This is done by manipulating one or more independent variables and measuring their effects on one or more dependent variables. There are three different types of variables, namely; dependent, independent, and controlled variables.

• Dependent variable; A variable which changes if the experimental condition changes. For example, the dependent variable is the time it takes for the pendulum bob to complete a given number of oscillations.
• Independent variable; A variable which does not change even when the experimental condition is changed. For example, the length of the pendulum bob is independent variable.
• Controlled variable; This is a variable that is kept constant during an experiment. For example, the number of oscillations is a controlled variable.

Designing Physics experiments

Designing an experiment involves creating a set of procedures to systematically test a hypothesis. This requires a strong understanding of the system under study. For valid conclusions, the selection of a representative sample and controlling any extraneous variables is important. To experiment, we need first to understand how to identify the experimental variables. The following examples will help you to build skills on how to identify the variables that need to be manipulated.

Example 1.5

A student is investigating how the height of a ramp affects the distance a toy car travels. The student changes the height of the ramp and measures the distance the car travels as shown in Figure 1.19. Identify the dependent, independent, and controlled variables in this experiment.

Figure 1.19

Answer

(a) Dependent variable: The distance travelled by the toy car.

(b) Independent variable: The height of the ramp.

(c) Controlled variables: The type of toy car used, the starting point of the car on the ramp, and the surface of the ramp.

Task 1.4

A student is investigating the relationship between the number of coils in a spring and the distance it compresses when a force is applied. They vary the number of coils and measure the compression distance. Determine the dependent, independent, and controlled variables in this experiment.

4. Data collection and analysis

Data collection involves recording what has been observed during the experiments. The observed results are tabulated (recorded in a table form) and ready for analysis. This involves plotting graphs and calculating mean, standard deviation, and errors. The results of the experiment can be recorded as shown in Table 1.1.

Table 1.1: Length of the string to which the pendulum bob is attached and time taken to complete number (n) of oscillations.

Number of observations	Length, l (m)	Time to complete (n) oscillations, t (s)	Period, T (s)	T^2 (s2)
			T = \frac{t}{n} (s)

Activity 1.2

Aim: Measurement of reaction time

Material needed: stopwatch

Procedure

1. Start the stopwatch and stop after 10 seconds.
2. Repeat the procedure for 5 observations.
3. Tabulate your observations

Table 1.2: Number of observations and Time (seconds)

Observation	Time (seconds)
First reading
Second reading
Third reading
Fourth reading
Fifth reading

Questions

(a) Do the observations yield the same results? Why?

(b) What should be done to improve the accuracy?

Measuring reaction time is an essential aspect of various scientific studies, sports performance analysis, and even everyday activities. It refers to the time it takes for a person to respond to a given stimulus. The stimulus can be visual, audio, or tactile, and the response can involve any action like pressing a button, vocalizing, or moving a body part.

5. Data presentation and interpretation

Data presentation involves the use of charts, graphs and mathematical formulae.

Drawing graphs in Physics

For all graphs plotted from experimental data, it is important to remember that you should not just connect the dots. Data do not always follow a line or curve perfectly. By obtaining several experimental data points any discrepancies in each data point can be removed. The data points plotted should be fitted by drawing the best line that describes the distribution of data points.

The graphs you plot must have the following features:

• The graph must have a clear descriptive title which outlines the relationship between dependent and independent variables with their appropriate units in brackets e.g A graph of temperature (°C) against time t (s).
• An appropriate scale is used for each axis so that the plotted points must occupy enough axis/space (work out the range of the data and the highest and lowest points). The scale must remain the same along the entire axis and should use easy intervals such as 10 s, 20 s and 50 s. Use graph paper for accuracy.
• Each axis must be labelled with what is shown on the axis and must include the appropriate units in brackets, e.g. Temperature (°C), time (s) and height (cm).
• The independent variable is generally plotted along the x-axis, while the dependent variable is generally plotted along the y-axis. Each point has an x and y co-ordinate and should be plotted with a symbol which can be easily seen, e.g., a cross or circle.
• A best fit line should be drawn to the graph. Do not start the graph at the origin unless there is a data point for (0,0), or if the best fit line runs through the origin.
• If there is more than one set of data drawn on a graph, a different symbol (and/or colour) must be used for each set and a key or legend must be included to define the symbols.
• Use line graphs when the relationship between the dependent and independent variables is continuous. For a line graph, you can draw a line of best fit with a ruler. Make sure the number of points are distributed fairly and evenly on each side of the line. Example of a graph of square of the period, T^2 (s^2) against length l (m) is shown in Figure 1.20.
• In an exponential graph, a best fit line should be drawn by using freehand.

After recording and analysing the data, you may look for possible trends or patterns and explain why they occur that way. For instance, physicists may notice that as the length of the string to which the bob is attached increases, the time to complete a given number of oscillations also increases. This pattern forms the basis on which evidence can be obtained.

Figure 1.20: Graph of square of period, T^2(s^2) against length, l (m)

6. Drawing a conclusion

A conclusion is a summary of the result of the experiment. It includes a statement that either proves or disapproves of the hypothesis. For instance, ‘the length of the string to which the pendulum bob is attached affects the time taken by a pendulum to complete a given number of oscillations’ proves our hypothesis. The experiment may be repeated to make sure the results obtained are reliable.

Example 1.6

A physics student conducts an experiment to investigate the relationship between the force applied to stretch a spring and the resulting displacement. The student collects the following data:

Table 1.3

Force applied (newtons, N)	Displacement (centimetre, cm)
1	2
2	4
3	6
4	8
5	10

(a) Based on the data, what conclusion can the student draw about the relationship between the force applied and the displacement of the spring?

Answer: The data shows that there is a direct relationship between the force applied to stretch the spring and the resulting displacement. As the force applied to the spring increases, the displacement also increases proportionally. This indicates that the displacement of the spring is directly proportional to the force applied.

(b) Plot the graph of force (y-axis) against displacement (x-axis)

Figure 1.21

7. Reporting results

Scientists communicate their results to others in a final scientific report. It is very important to communicate scientific findings to the public in the form of scientific publications, at scientific conferences, in articles, TV or radio programmes. The experimental results are presented in a specific format, so that others can read your work, understand it, and repeat the experiment. The structure of a good scientific report includes:

• Aim - Brief sentence describing the purpose of the experiment;
• Apparatus - List of the apparatus or equipment;
• Method - List of the steps followed to carry out the experiment;
• Results - Tables, graphs and observations about the experiment;
• Discussion - What your results mean; and
• Conclusion - Brief sentence concluding whether or not the aim was achieved.

Note: If your results do not support the hypothesis:

• do not leave out the experimental results;
• suggest possible reasons for the difference between your hypothesis and the experimental results; and
• suggest ideas for further investigations to find answer to the problem.

Figure 1.22: Scientific method flow chart

Task 1.5

Study the flow chart provided in Figure 1.22, then work on the following questions:

1. Once you formulate a research problem explain, why is it important to conduct background research before doing anything else?
2. What is the difference between a dependent, independent, and controlled variable and why is it important to identify them?
3. What is the difference between identifying a problem, a hypothesis, and a scientific theory?
4. Why is it important to repeat your experiment if the data do not fits the hypothesis?

Activity 1.3

In this activity, you are required to design your experiment. Use the information provided below and the scientific method flow chart shown in Figure 1.22 to design your scientific experiment. The following are basic steps to follow when designing your experiment.

1. Ask a question to which you want to find answer.
2. Write down your hypothesis.
3. Identify important variables of your investigation; those that are relevant and you can measure or observe.
4. Decide on the independent and dependent variables in your experiment and variables that must be kept constant.
5. Design the experiment that you will use to test your hypothesis:
   1. State the aim of the experiment.
   2. List all the apparatus (equipment) that will be used in your experiment.
   3. Write the method that will be used to test your hypothesis – in the correct sequence, with each step of the experiment numbered.
   4. Indicate how the results should be presented and what data are required.

Activity 1.4

Aim: To apply the scientific investigation method to test the accuracy of stopwatches.

Materials: Sellotape, table, pendulum bob, string, retort stand, analogue stopwatch, digital stopwatch

Procedure:

1. Arrange a simple pendulum system as shown in Figure 1.23.

Figure 1.23
2. Pull the bob slightly to one side then release it so that it swings back and forth.
3. Using analogue stopwatch, measure the time the pendulum takes to swing back and forth.
4. Record your observation for one complete oscillation.
5. Repeat steps 3 and 4 using the digital stopwatch instead of the analogue one.

Questions

With reference to the pendulum bob, use the scientific method outlined previously to investigate whether the digital stopwatch is more accurate than the analogue stopwatch in measuring the time taken to complete one oscillation. Briefly address the following:

(a) What was the hypothesis?

(b) What kind of an experiment can be used to test the hypothesis?

(c) What conclusion can be drawn from this experiment?

(d) After comparing the measurements, which stopwatch do you think is more accurate than the other? and

(e) Write a report explaining your experiment and conclusions.

The measurement from a digital stopwatch is more accurate than the one from an analogue stopwatch. The digital stopwatch therefore, gives a more precise measurement of time than the analogue one.

Task 1.6

1. Discuss the steps for carrying out experiments using scientific method.
2. Discuss the application of scientific investigation method for a simple pendulum.
3. Briefly explain the importance of forming hypothesis before doing an experiment.

Scientific theory

A theory in physics is a big idea or explanation that scientists come up with to describe how something in nature behaves. Think of it like a story that tries to explain why things happen the way they are observed. For example, the theory of gravity explains why things fall down when we drop them. It says that all objects with mass are attracted to each other, and that’s why we stay on the ground and do not float on air. Many theories explain various physical phenomena. In this section, we shall concentrate on the theory of gravity and its impact human beings.

Theory of gravity

The theory of gravity is the fundamental theory that explains the force of attraction between two objects that have mass. It says that objects with mass are attracted to each other. The force of attraction between such objects is referred to as the force of gravity. This force is very important for our daily activities. Activity 1.4, will help you to understand the impact of the force of gravity in our daily lives. All objects on the earth are attracted toward the earth because the earth is more massive than other objects.

Significance of the theory of gravity

1. It explains the arrangement and motion of planets, moon, and other celestial bodies in the solar system and beyond.
2. Helps to understand the tides and Earth’s motion around the sun.
3. Provide the basis for space exploration and satellite technology.
4. It influences our daily lives, from walking on the earth’s surface to the launching of spacecraft into space.

Laws of Physics

In physics, a law is a scientific statement that describes a physical phenomenon under certain conditions in nature. Physical laws provide important insight into the nature of the universe, and they are developed from several observations in nature. However, physical laws do not explain the mechanism by which a phenomenon occurs. Physical laws are applicable to all objects regardless of scenario but are only meaningful within certain contexts. Examples of physics laws are the Hooks law and the law of floatation.

Hooke’s law

Hooke’s law is a law of physics that explains the force needed to extend or compress a spring by distance x. It states that “provided the elastic limit is not exceeded, the extension is directly proportional to the force applied.”

The law of floatation

The law of floatation is a crucial principle for understanding why certain objects rise or submerge in fluids. It determines whether the object will float or sink based on its density relative to the surrounding medium. The law of floatation states that ‘a floating object displaces its own weight of fluid in which it floats’

Figure 1.24: Illustrates the law of floatation

Principles of physics

In physics, a principle is a general rule or explanation of how a specific physical phenomenon occurs. Essentially, a principle is a fundamental truth that forms a foundation for explaining a physical phenomenon in nature. In addition, principles describe some specific fundamental concepts. Developing a principle requires more explanations than the requirement for a physical law. It is for this reason; that physicists need to follow the method of scientific investigation when developing a physical principle. Examples of physics principles are Pascal’s principle, Archimede’s principle and the principle of conservation of energy.

Archimedes’ principle

Archimedes’ principle is a fundamental concept in fluid mechanics, named after Greek mathematician and scientist Archimedes. The principle explains the buoyant force experienced by an object immersed in a fluid, such as water or air. The principle states that “Any object partially or totally immersed in a fluid experiences an upthrust which is equal to the weight of the fluid displaced by the object”. Archimedes’ principle helps to understand why objects float or sink and has a practical application in various engineering and everyday scenarios.

Pascal’s principle

Pascal’s principle accounts for the transmission of pressure in fluid. Pascal’s principle states that “When pressure is applied at any point on the surface of a fluid contained in a closed container, the pressure is transmitted undiminished to all parts of the fluid and to the walls of the container”.

The principle of conservation of energy

The principle of conservation of energy emphasises that the total energy in a system is conserved. This principle allows us to analyse complex systems, predict their behaviour, and understand how energy flows and transforms, providing a fundamental framework for understanding the physical world. The principle states that ‘Energy can neither be created nor destroyed but it can be transformed from one form to another’

ICT corner

To build scientific literacy use simulations or visit (SGR) https://phet.colorado.edu select the simulation titled pendulum lab and simulation titled curve fitting, to help students collect data, drawing graph and choose the best line of fit.

Chapter summary

1. Physics is the study of the relationship between matter and energy.
2. People who study and work professionally in the field of physics are known as physicists.
3. Physicists use results from experiments to develop scientific laws that are normally expressed in the language of mathematics.
4. Physics is regarded as the ‘fundamental’ of natural sciences and it is related to other subjects. These subjects include, chemistry, biology, and mathematics.
5. Physics is applied in many areas of our lives. Some of the areas where it is evident are homes, hospitals, schools, communication, transport and industry.
6. Physics is important since it explains the behaviour of the universe while answering many questions. It is also important in:
   1. career development;
   2. manufacturing industries; and
   3. physics practicals.
7. The scientific method is a procedure used by scientists to investigate a problem or answer questions.
8. The scientific investigation method is divided into several steps, namely: problem identification, asking questions, formulating a testable hypothesis, performing an experiment, data collection and analysis, data presentation, data interpretation, and drawing a conclusion.
9. Physics uses theories, laws, and principles to describe the universe. These includes theory of gravity, Hooke's law, law of floatation, Pascal principle and the principle of conservation of energy.

Chapter Two: Measurement

Introduction

Measurement is a word used in everyday life. We measure a piece of land in hectares or acres, and the circumference of a playground using a tape measure. In physics, accurate and precise measurements enable the collection of useful experimental data that can be tested against theoretical predictions to enhance the development of physical theories. In this chapter, you will learn the concept of measurement of physical quantities, the basic apparatus/equipment used in measurement and how to use them. The competencies developed will enable you to deal with measurements in different context.

Think

How could our life be without measurement?

Concept of measurement

The word 'measurement' comes from the Greek word 'metron' which means 'limited proportion'. It is our common experience that, if you want to buy a trouser, the information that a shopkeeper first wants to know is the size of the trouser that fits your waist. If you do not know your size, he or she will take a tape and measure the size of your waist. The act of finding the size of a given quantity is referred to as measurement.

Measurement involves the process of assigning a numerical value and a unit to an observation or event. It is done by comparing the known and unknown quantities. For example, when you want to determine the length of a table, you use a ruler or a tape measure, which has predefined units, to compare with the table. The number of units that match the length of the table becomes the numerical value representing the length of the table. Every measurement has two parts which are:

1. A number or numerical part that gives the result of the comparison; and
2. A unit part which identifies the particular unit used to make the measurement.

In the unit part, the focus is on the standard unit (Systeme Internationale or International System Units-SI units) though, other units may also be used. For example, if the length of a playground is 100 m, '100' is the number part while 'm' is the unit part. Therefore, a meaningful measurement must have both a number and a unit.

A complete measurement that includes both number and unit parts is called a measurement of a physical quantity. For example, the measurement of 100 km, 2 kg or 10 s.

Physical quantity

A physical quantity is any measurable quantity. Physical quantities are divided into two categories, namely fundamental physical quantities and derived physical quantities.

Fundamental physical quantities

Fundamental physical quantities are quantities of measurement which cannot be expressed in terms of other quantities. These include; length, mass, time, temperature, amount of substance, electric current and luminous intensity. Among the measured fundamental physical quantities mass, length and time are the most common. Table 2.1 shows the fundamental physical quantities and their respective SI units.

Table 2.1: Fundamental physical quantities and their SI units

Physical quantity	SI unit	Unit symbol
Length	metre	m
Mass	kilogramme	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Vector and scalar quantities

The physical quantities can further be classified into either vector or scalar quantities.

Vector quantities

Vector quantities are those quantities that have both magnitude and direction. Examples of vector quantities are force, displacement, velocity and momentum.

Scalar quantities

Scalar quantities are those quantities that have magnitude but have no direction. Examples of scalar quantities are mass, distance, time, density, volume, pressure, speed, electric current, work, energy, and power.

For example, consider a car traveling at a speed of 100 kilometres per hour North. This describes the velocity of the car which is 100 kilometres per hour in the North direction. Velocity is a vector quantity. However, if the intention is to describe only the speed of the car and not the direction, the statement could be simply that the car is travelling at 100 kilometre per hour. Speed is a scalar quantity. Table 2.2 gives some of the vector and scalar quantities.

Table 2.2: Some of the vector and scalar quantities

Vector quantities	Scalar quantities
Force	Mass
Displacement	Distance
Acceleration	Time
Velocity	Electric current
Momentum	Density
Magnetic field	Pressure
Electric field	Work
	Energy
	Power
	Volume
	Area

Measurement of Length

Length is the most commonly measured quantity in daily life. Length is used to give the dimensions of an object or the distance between two points. Hence, distance is defined as the path taken by a particle in space between two points or objects. The distance around the surface of an object is called the perimeter. You can measure the distance ranging from small to large distances such as the distance from the earth to the sun. To cope with these differences, there are several other units obtained from the metre, namely, kilometre (km), centimetre (cm), millimetre (mm), micrometre (μm), nanometre (nm), picometre (pm) and femtometre (fm). Their equivalence is as follows:

• 1 km = 1000 m
• 1 m = 100 cm
• 1 cm = 10 mm
• 1 mm = 1000 μm
• 1 μm = 1000 nm
• 1 nm = 1000 pm
• 1 pm = 1000 fm

Table 2.3: Some of the units in comparison to the metre

Distance	Comparison with SI unit
1 kilometre (km)	1 000 m
1 centimetre (cm)	1/100 m
1 millimetre (mm)	1/1000 m
1 micrometre (μm)	1/1000 000 m
1 nanometre (nm)	1/1000 000 000 m

The length of an object is measured using specific instruments. The choice of an instrument to be used is determined by the following factors:

1. The desired degree of precision.
2. The size of the physical quantity to be measured.
3. The shape of the object.

Basic equipment/apparatus and their uses

The basic equipment or apparatus for measurements in physics serves as an essential foundation for conducting experiments and obtaining reliable data. This equipment includes measuring instruments such as rulers, callipers, and micrometres, which provide accurate length measurements, as well as balances to quantify mass. These tools enable physicists to explore fundamental principles, ensure precision in their measurements, and contribute significantly to the advancement of scientific knowledge.

Ruler

A ruler is a measuring instrument used to determine the length or distance of objects. It typically consists of a flat, rigid strip marked with units of measurement, enabling users to obtain precise measurements easily.

Classification of ruler

The rulers have been classified into two categories such as rigid rulers and the flexible rulers. Each category of ruler serves its purpose according to the length of measurement required, with varying levels of portability and application suitability.

Rigid Rules

Rigid rulers are solid and do not bend, providing consistent accuracy in measuring straight lines. Common types include metre ruler, 50 cm ruler and 30 cm ruler as discussed hereunder.

• Metre Rule: This rule has a length of 1 metre (100 centimetres). It is commonly made of wood, plastic, or metal and is primarily used for measuring longer distances, often in educational and professional settings like classrooms and workshops. Suitable for measuring larger objects and distances, making it ideal for geometry, craft projects, and mechanical work.
• A 50 cm Rule: It is sometimes referred to half metre rule because it has a length of 50 centimetres (0.5 meters). A 50 cm ruler is more compact than a metre ruler, often favoured for portability and ease of use in smaller projects. Commonly used in schools for drawing straight lines, measuring paper, and conducting small experiments. It is also popular among artists and designers.
• A 30 cm Rule: A 30 cm ruler is typically the smallest of the three categories and is often made from flexible materials or plastic. Ideal for students, it is commonly used for everyday tasks like measuring small items, drawing straight edges, and creating precise lines in artwork or homework assignments.

Figure 2.1: Classification of rulers

Flexible Ruler

Flexible rulers can bend and curve, making them suitable for measuring lengths that are not straight.

Tape Measure: This kind of flexible ruler typically extends anywhere from 1 metre to 10 meters or more. It consists of a long, flexible strip marked with measurements, often housed in a retractable case. It can easily bend around curves or objects and latch onto edges for precise measurements. Such a ruler is widely used in construction, tailoring, and DIY projects. It is also ideal for measuring curved surfaces, large distances, and irregular shapes where rigid rules might be ineffective.

Figure 2.2: Tape measures

Task 2.1

1. If asked to measure the length of a field, which type of instrument will you use? Why?
2. Place the following objects on the paper a pencil, a book and a matchstick. Mark the end points of each. Draw the line-segment connecting the points. Find the length of each object by measuring the distance between the points.

When taking a measurement, always ensure that your eye is perpendicular to the mark on the scale of the metre rule, as demonstrated in Figure 2.3, otherwise the value will have an error. An error caused by wrong positioning of the eye is known as parallax error. Such an error occurs when the measurement of the length an object is more or less than the true length, because of the eye being positioned at an angle to the measurement mark.

Figure 2.3: Reading from a metre rule

Care should be taken while using a metre rule so as to avoid damaging the ends. This is because the rule does not have an allowance (a short ungraduated portion) for wear at both ends. Suppose, you wish to measure the length of a table. The zero (0 cm) mark of the metre rule is aligned with one end of the table, as shown in Figure 2.4.

Figure 2.4: Measuring the length of a table

Since the metre rule does not extend beyond the end of the table, carefully mark the point on the table that corresponds to the end of the metre and then continue, as shown in Figure 2.5.

Figure 2.5: Reading to complete the length of the table

The actual length of the table is then given as: 100 cm + 40 cm = 140 cm. Therefore, the table has a length of 140 cm or 1.4 m.

In case the edge of a ruler is worn out, which is almost inevitable and the zero (0 cm) mark not clearly seen, it is advised to:

1. always start measuring from the mark more than zero; and
2. subtract the mark from the final reading.

Figure 2.6: Using a ruler with a worn-out edge

The length of the object is, 9.6 cm – 3.2 cm = 6.4 cm.

Task 2.2

Measure the length and width of the cover of your physics textbook to the nearest tenth of a centimetre. Record your results. Calculate the perimeter of the cover.

Perimeter = 2 times the length + 2 times the width = 2 (l + w)

Activity 2.1

Aim: To measure lengths of different objects.

Materials: metre ruler, tape measure, paper and pen

Procedure:

1. Walk around your school compound, identify the objects presented in Table 2.4.
2. Measure the lengths the objects provided and record in Table 2.4.

Table 2.4

Quantity to be measured	Measurement made
Width of your classroom
Height of your classroom door
Length of your laboratory floor
Width of your classroom window
Circumference of a ten litre bucket
Length of physics exercise book

Questions

1. Imagine your Physics teacher asks you to measure the length of a playing ground. Which type of instrument will you use? Why?
2. How can you apply the skills learnt in this activity in your daily life activities?

Callipers

Callipers are precision measuring instruments characterized by two adjustable arms or jaws designed to measure the dimensions of an object, such as its length, width, thickness, or diameter. The device can come in several types, including vernier, and digital callipers, each offering different methods for reading measurements, such as ruled scales or electronic displays. The accuracy of measurements taken with callipers depends significantly on the skills of the user and the proper application of the tool against the object being measured.

Vernier calliper

A vernier calliper is an instrument used to measure small lengths with a greater degree of accuracy than a metre rule. It is used to measure objects to the nearest hundredth of a centimetre, which means its accuracy is 0.01 cm. A vernier calliper has a fixed scale and a vernier scale. The fixed scale is also known as the main scale. The vernier scale slides along the fixed scale hence readings are taken from both scales. The fixed scale gives readings in centimetres and millimetres. The vernier scale gives readings in the hundredth of a centimetre. That is, the vernier scale gives the second decimal place of the measured value. Figure 2.7 show parts of a vernier calliper.

Figure 2.7: Parts of a vernier calliper

Digital calliper

As with the normal vernier calliper, the digital callipers also consist of mechanical parts like external jaws, internal jaws, stem, and screw lock and we cannot find the main scale, vernier scale because this is a digital vernier so there will be no use and necessity of main scale and vernier scale; instead, we can see the reference scale on the digital vernier calliper. This kind of calliper is automatic, so it certainly uses electrical and electronic parts for its working, therefore, the components that respond to the digital system are capacitance Sensors, LCD, copper plates, chips and battery as shown in Figure 2.8.

Figure 2.8: Parts of a digital calliper

The vernier scale is shorter scale than the main scale. 10 vernier divisions cover 9 main scale divisions. This is a length of 0.9 cm. When this is divided into 10 equal intervals, the result is the difference between the main scale division and the vernier scale division. This is known as Least Count.

Main scale division = \[ \frac{1 \, \text{cm}}{10} = 0.1 \, \text{cm} \]

Vernier scale division = \[ \frac{0.9 \, \text{cm}}{10} = 0.09 \, \text{cm} \]

Therefore, least count of a vernier calliper = (0.1 - 0.09) cm = 0.01 cm.

The vernier calliper has a set of jaws that can be used to measure the length thickness, and depth of objects as shown in Figure 2.9.

Figure 2.9: Measuring an external diameter using the outside (lower) jaws

At the top of a vernier calliper are two inner (upper) jaws that can be used to measure the internal diametre of a hollow object, shown in Figure 2.10. A stem that sticks out from the right side of the calliper is called a depth gauge or the depth probe. It can be adjusted to measure a depth of an object, as shown in Figure 2.11. The screw clamp visible on top of the calliper is tightened to secure the objects being measured so that the reading does not change while measuring.

Figure 2.10: Measuring the inner diameter using inside jaws

Figure 2.11: Measuring depth using the vernier calliper

How to read a vernier calliper

The following steps are taken when measuring length using a vernier calliper.

1. Close the jaws of the vernier calliper and look out for the zero mark (0 cm) differences.
2. Place the object to be measured between the jaws.
3. Slide the vernier along the main scale until it just touches the end of the object.
4. Use the screw clamp to secure the object in position, shown in Figure 2.12.

Figure 2.12: Measuring the diameter of a steel ball bearing

5. Read and record the reading on the main scale which is to the left of the zero cm mark of the vernier scale. This value is to the nearest tenth of a centimetre.
6. Observe along the vernier scale and record the mark which coincides with a mark on the main scale.
7. Read and note down the value on the vernier scale. This gives the digit in the hundredth place of the measurement.
8. Add the values in steps 4 and 6 to get your correct reading. Therefore, the length of the object = main scale reading + vernier scale reading.

Example 2.1

Using Figure 2.13, determine the diameter of the object that is placed between the jaws of the vernier calliper.

Figure 2.13

Solution

From Figure 2.13,

Main scale reading = 3.1 cm

Vernier scale reading = 2 divisions × 0.01 cm = 0.02 cm

Total reading = Main scale reading + Vernier scale reading

= 3.1 cm + 0.02 cm = 3.12 cm

The total reading = 3.12 cm

Therefore, the diameter of the object = 3.12 cm.

Example 2.2

The jaws of the vernier calliper make contact with the inner wall of the calorimetre without exerting any pressure and the zero scale of the vernier reading on the main scale as 3.4 cm, the 6th vernier scale division coinciding with a main scale division, and a vernier constant of 0.01 cm.

(a) How might the presence of a negative zero error in the vernier scale of the calliper impact the determination of the actual internal diameter of the calorimeter?

(b) Calculate the precise internal diameter of the calorimetre when we notice that the vernier scale has a negative zero error of -0.03 cm.

Solution

(a) To calculate the actual internal diameter of the calorimetre while accounting for the negative zero error in the vernier scale.

(b) Main scale reading = 3.4 cm

Least count (L.C) = 0.01 cm

Vernier coincidence = 6

Reading = Main scale Reading + Vernier coincidence × LC

= 3.4 cm + 6 × 0.01 cm

= 3.4 cm + 0.06 cm

= 3.46 cm

Corrected reading = reading – zero error

= 3.46 cm - (-0.03 cm)

= 3.46 cm + 0.03 cm

= 3.49 cm

Exercise 2.1

1. Draw both the main and vernier scales of a vernier calliper to show a reading of 0.36 cm.
2. What is the reading shown in Figure 2.14?
3. (a) What is the significance of the design of the vernier calliper and its readings when measuring the depth of the beaker, and how does the alignment of vernier scale divisions with the main scale affect the accuracy of the measurement? (b) In a scenario where a thin metallic strip on a vernier calliper descends from the upper edge to the lower edge and makes contact with the surface of a beaker, the main scale displays a reading of 6.4 cm, with a vernier constant of 0.1 mm, and the 4th vernier scale division aligns precisely with a main scale division. Determine the precise depth of the beaker, assuming there is no zero end error.

Activity 2.2

Aim: To measure the external diameter of a test tube using a vernier calliper.

Materials: Test tube and vernier calliper

Procedure

1. Close the jaws of the vernier calliper and observe the zero cm mark of the main and vernier scales. Record your observations.
2. Open the jaws and place the test tube between them.
3. Close the jaws gently until the test tube is held firmly. Record your observations.
4. Repeat steps 1 to 3 using other parts along the test tube.
5. Obtain three readings. Record your observations.

Questions

(a) Calculate the average of the readings obtained.

(b) Were the four obtained readings equal?

(c) Why was it important to take four readings and not one?

A test tube is cylindrical in shape. This means that its diameter is the same throughout. The readings obtained using the outside calliper jaws are equal in magnitude since the test tube is almost uniform in shape.

In an experiment, it is always best to obtain many readings so as to obtain an average result. Two or more readings offer an opportunity for the experimenter to compare and identify any pattern.

Task 2.3

Collect a variety of objects such as books, pencils, beakers, test tubes and other materials available at your physics laboratory. Use a vernier calliper to measure the thicknesses of the collected objects. The depth, internal and external diameters of the hollow objects should also be measured. Record your measurements in the following table:

Object	Dimension (cm)	Main scale reading (cm)	Vernier scale reading (cm)	Actual reading (cm)

A micrometre screw gauge

A micrometre screw gauge gives readings with better precision than the vernier calliper. Measurement can be obtained to the nearest thousandth of a centimetre. This is an accuracy of 0.001 cm. For this reason, it is usually used to measure the diameters of thin objects like wires and ball bearings. The micrometre screw gauge has different parts, as shown in Figure 2.15.

Figure 2.15: Parts of the micrometre screw gauge

A micrometre screw gauge consists of main scale (sleeve) and thimble scale. The main scale is marked in millimetres. The thimble scale is divided depending on the distance between two consecutive threads of the screw. This is called the pitch of the screw. If the pitch of the screw of the micrometre is 0.5 mm, then the thimble scale has 50 equal divisions. Otherwise, it has 100 divisions when the pitch is 1.0 mm. This means that when the thimble makes a complete turn, the spindle moves either forward or backward a distance of 0.5 mm or 1.0 mm respectively along the sleeve. When the spindle is completely closed onto the anvil, the thimble edge aligns with the zero mark on the sleeve scale. The thimble also has its zero-mark lying on the central line of the sleeve scale. Therefore, the gap between the spindle and the anvil equals the distance between the edge of the thimble and the zero mark on the main scale.

Measuring the diameter of a wire by micrometre screw gauge

The following are procedures for measuring the diameter of a wire using micrometre screw gauge.

1. Unscrew the thimble to create enough space to accommodate the wire between the spindle and the anvil.
2. Close the gap by rotating the thimble clockwise. Screw the ratchet knob until it clicks so as to show the correct setting.
3. Read and note down the value on the sleeve; that is the last mark must be visible to the left of the thimble. This value is to the nearest tenth of a millimetre. For example, in Figure 2.16, the value is 7.5 mm.
4. Read and note down the value on the thimble that is just below the reference line on the sleeve. This value is to the nearest hundredth of a millimetre (0.28 mm for Figure 2.16).
5. Add the values in steps 3 and 4. Therefore, for Figure 2.16,

Reading = Sleeve Scale Reading (SSR) + Thimble Scale Reading (TSR)

= SSR + TSR

= 7.50 mm + 0.28 mm = 7.78 mm

Figure 2.16: Micrometre screw gauge reading

Task 2.4

Diameter of a steel ball is measured using a vernier calliper which has divisions of 0.1cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given in the following table.

S/N	MS (cm)	VS division
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is -0.03 cm, calculate the average corrected diameter.

ICT corner

Visit https://phet.colorado.edu select the simulation involving measurements of various quantities like time, length

Chapter summary

1. Initially, approximations were used as a form of measurement. Advancement in science has made it possible to have appropriate instruments for each type of measurement.
2. Every measurement has the number part and the unit part. This complete measurement is called measurement of a physical quantity.
3. Fundamental quantities are the physical quantities which cannot be obtained from any other quantities. These quantities include length, mass, time, temperature, amount of substance, electric current and luminous intensity.
4. Fundamental physical quantities are measured using base units which are metre (m), kilogramme (kg), second (s), kelvin (K), mole (mol), Ampere (A) and Candella (cd).
5. The beam balance and digital balances are used to measure mass, while rulers, vernier callipers, micrometre screw gauges and tapes are used to measure length. On the other hand, time is measured using a stopwatch or a clock.
6. Derived quantities are obtained by dividing or multiplying two or more fundamental quantities. These quantities include weight, acceleration, velocity, volume and area. Their SI units are the newton, metre per second square, metre per second, cubic metre, and square metre, respectively.
7. There are three types of errors that emerge during measurements, namely:
   1. parallax error;
   2. zero error; and
   3. instrumental error.

Revision exercise 2

Section A

1. Choose the most correct answer
   1. To measure the length using a metre rule, wrong position of the eye leads to:
      1. parallax error.
      2. eye error.
      3. zero error.
      4. metre error.

Chapter Three: Introduction to Force

Introduction

The word force is often used in everyday situations. The interaction between two or more objects involves forces acting between them. Objects that are flying, hanging, balancing, moving, and spinning are all subjected to some kind of force. Almost every activity you do in daily life requires the application of force. This means, there are several types of forces with different effects. Generally, it is hard to imagine a world without forces. In this chapter, you will be introduced to different types of forces and their effects. The competencies developed will enable you to classify forces as well as effectively apply forces in your daily life.

Think

How could our life be without the existence of force?

Concept of force

If an object is at rest, it will remain in the state of rest unless some actions are performed to make it move. Similarly, if an object is in motion, it will require some actions to make it stop, otherwise it will keep moving. For example, for a cart at rest to move, it needs to be pushed or pulled. Similarly, a stationary car should be pulled or pushed to make it move. The action of pushing or pulling objects to accomplish an intended task involves force. Figure 3.1 shows pulling a cart and pushing a stationary car.

Figure 3.1: Pulling and pushing actions

A force can therefore be defined as a push or pull experienced by an object. It is usually described in terms of its magnitude and direction. The SI unit of force is newton, N. One newton is the amount of force required to give a mass of one kilogramme (1 kg) an acceleration of 1 m/s². Therefore, 1 N = 1 kg × 1 m/s².

Effects of forces

An object is stationary when all forces acting on it are balanced. If a new force is applied to the object, the forces become unbalanced. The result of unbalanced forces on an object can cause various effects including:

1. Change in the state of motion of an object
2. Change in the way the object moves
3. Change of shape or size of the object
4. Change of direction in which an object is moving

Activity 3.1

Aim: To demonstrate the effects of forces.

Materials: Carton of books, rubber bands, table and coil spring

Procedure

1. Move the carton of books from one end of the class to another without lifting it.
2. Stretch a rubber band until it is close to its breaking point.
3. Compress a coil spring between your hands.
4. Stretch the coil spring until it extends in length.

Question

In each case, what action makes an object change its shape or direction?

To move the carton of books, there is a need to either pull or push it. This means that a force has to be applied. The rubber band is pulled to stretch it while the spring is pushed to compress it. These activities demonstrate that pulling or pushing requires a force.

Determination of the magnitude of a force

A spring balance can be used to estimate the magnitude of force. It consists of a coiled spring fixed to a support at one end, with a hook at the other end as shown in Figure 3.2.

Figure 3.2: A spring balance

The body upon which the force acts is attached to the hook. The distance through which the spring is stretched is directly proportional to the magnitude of the force applied by the body. A pointer is attached to the spring and the magnitude of force is indicated on a calibrated scale. The larger the force, the more the spring is stretched and the higher the reading on the scale. The spring balance can be used to measure vertical and horizontal forces acting on a body, as shown in Figure 3.3 (a) and (b).

Figure 3.3: Spring balance used to measure forces

In Figure 3.3(a), the weight of the empty box is shown by the pointer on the spring balance. If you weigh the same empty box filled with sand the pointer will indicate a greater weight than that of the empty box. This is because the weight of sand adds to the weight of the box. To get the weight of sand you need to subtract the weight of the box from the weight of the empty box filled with sand.

Types of forces

Some forces in the environment occur naturally while others are derived from natural forces. The naturally occurring forces are known as fundamental forces while the derived forces are referred to as non-fundamental forces. The four fundamental forces are the force of gravity, electromagnetic force, strong force, and weak force. All other forces are derived from these fundamental forces. Examples of derived forces are elastic and frictional forces. Depending on the interaction between objects, all forces can be classified as non-contact or action-at-a-distance forces and contact forces.

Fundamental Forces

• Force of gravity
• Electromagnetic force
• Strong force
• Weak force

Contact Forces

• Frictional force
• Tensional force
• Normal force
• Air resistance
• Applied force
• Spring force

Force of gravity

The force of gravity is the force of attraction between objects which have mass. All objects having mass are pulled towards the earth's centre by the earth's force of gravity. It is because of the earth's force of gravity that bodies in the air move towards the earth's surface despite their sizes. For example, fruits fall from a tree because of the earth's gravitational force. Human beings can walk properly because of the earth's force of gravity. The magnitude of the gravitational force exerted on an object is referred to as the weight of an object. It is represented by the symbol w and measured in newton (N). The weight of an object is the product of its mass, m and acceleration due to gravity, g.

Weight is defined as an attractive force acting on an object due to gravity.

weight(w) = mass(m) × acceleration due to gravity(g)

w = mg

Where, w - Weight of object, m - Mass of object, g - Acceleration due to gravity

The weight of an object is equal to the gravitational force on it. The following are properties of the gravitational force:

1. It is always attractive.
2. It is the weakest force among the four fundamental forces.
3. It is a central force (gravitational force between two objects act along the line joining the centres of the objects).
4. It operates over very long distances.

Your weight on earth is the gravitational force that the earth exerts on you. Remember that gravity is an action-at-a-distance force, so even when you jump into the air, as shown in Figure 3.4, the earth still exerts its gravitational force on you. This is the force that prevents you from flying off on a spinning earth. The gravity force is also responsible for keeping a satellite in its orbit around the earth and planets in their orbits around the sun.

Figure 3.4: A boy jumping

Task 3.1

After learning about physical quantities, a student argues that mass and weight represents the same physical quantity. With reasons, support or oppose this argument.

It should be understood that, the weight of an object is related to its mass. For instance, on the earth's surface, an object with a weight of 1 N has also a mass of approximately 0.1 kg or 100 g. The ratio of weight (N) to mass (kg) gives approximately 10 N/kg which is always constant and is represented by "g".

So, g has two meanings:

1. It is the gravitational field strength of the earth (10 N/kg); and
2. It is the acceleration due to gravity (10 m/s²).

Near the earth's surface, there is a force of gravity of 10 newtons for each kilogram of mass (see Figure 3.5). Thus, the earth's force of gravity is 10 newtons per kilogram (10 N/kg).

Figure 3.5: Force of gravity acting on the bodies

Note: The acceleration due to gravity varies depending on the reference body. For example, the acceleration due to gravity on the moon g_m is equal to one-sixth of the acceleration due to gravity on the earth, g_e.

That is, g_m = 1/6 × g_e

If g_e = 10 N/kg, then g_m = 1/6 × 10 N/kg = 1.67 N/kg.

Thus, you would weigh less on the moon than on the earth, even though your mass remains constant.

Example 3.1

Assume a fixed mass rocket in Figure 3.6, moves from the earth to a planet X. If it weighs 10,000 N on the earth and 300 N on planet X, determine the acceleration due to gravity on planet X.

Figure 3.6

Solution

Let the weight on the earth be w_e.

So, the weight of the rocket on earth is w_e = m_e g_e

where m_e is the mass of the rocket on earth and g_e is the gravitational field strength on earth which is 10 N/kg.

m_e = w_e / g_e = 10,000 N / 10 N/kg = 1,000 kg

Weight of rocket on planet X, w_x, is w_x = m_x g_x

But m_x = m_e

w_x = m_x g_x

g_x = w_x / m_x = 300 N / 1,000 kg = 0.3 N/kg

Therefore, the acceleration due to gravity on planet X is 0.3 N/kg.

Activity 3.2

Aim: To measure a force using a spring balance.

Materials needed: Spring balance, various objects of different weights (e.g., small weights, books, fruits, etc.), table or any other hard flat surface, cushioned surface

Procedure

1. Place the table or hard flat surface at an appropriate area for the activity.
2. Vertically attach the spring balance securely to the hard surface.
3. Hang an object from the spring balance, allowing the spring to stretch.
4. Record the reading on the spring balance.
5. Repeat steps 3 and 4 for different objects.
6. Present all the measurements in tabular form.
7. Now, remove the spring from the hard surface and attach it to the cushioned surface.
8. Repeat steps 3 to 6 while observing the surface deformation.
9. Present your results using Table 3.1.

Table 3.1

Object	Spring readings	Difference in reading
	Hard surface	Cushioned surface
Book
Fruit
Stone
10 g mass
30 g mass

Questions

(a) How can you accurately measure the force of gravity using spring balance?

(b) Compare the readings on the spring balance when used on the cushioned surface and when the spring is attached to the hard surface. Account for the difference.

(c) How is the absorption and deformation of the cushioned surface affect the accuracy of the spring balance's readings?

The flat surface allows the spring balance to accurately measure the force of gravity, while the soft, cushioned surface interferes with the measurement as part of the force is absorbed by the surface when it deforms. This is why you feel less pain when you fall on a cushioned surface.

Electromagnetic force

This is a force that includes both electric and magnetic forces. It is relatively stronger than the force of gravity.

The following are examples of situations where electromagnetic forces are involved:

• In the formation of molecules of a substance. Atoms attract each other to form molecules. This is due to electromagnetic forces.
• If two parallel wires carrying current are placed near each other, the electromagnetic force acts on the wires.

Properties of electromagnetic force:

• It is either attractive or repulsive in nature
• It is a central force (originates from the centre or toward the centre)
• It is stronger than gravitational force
• It is a long-range force (operates over a very long distance)
• Its strength decreases as the distance between the objects increases
• Its direction depends on the charges of the objects involved

Strong force

This is a nuclear force that binds protons and neutrons together to form atomic nuclei. The action of strong force results in binding energy which can be felt when splitting a large nucleus into small fragments (fission) or combining two or more nuclei to form a bigger nucleus (fusion), as illustrated in Figure 3.7.

Figure 3.7: Nuclear fusion and fission

Properties of strong force:

• It is basically an attractive force
• It is a short-range force (operates in a distance ranging from 0.7 femtometre (fm) to 2.5 femtometre (fm))
• It is a non-central force (does not originate from the centre)
• It is stronger than gravitational force
• It does not depend on charges of objects

Weak force

This is a nuclear force which appears only in a certain nuclear process.

Properties of the weak force:

• It is much stronger than the gravitational force but weaker than the strong and electromagnetic forces
• It acts on a small range of about 0.001 fm to 0.01 fm

Exercise 3.1

1. Is an astronaut in space completely weightless? Explain your answer.
2. How much do you weigh on the earth? Would you weigh the same on the moon? Explain your answer.
3. Estimate your mass on the earth. If you are standing on the moon, do you think your mass on the moon will be the same? Discuss your answers.
4. Find the mass of a student who has a weight of 600 N.

Contact forces

These are forces which require physical contact to occur. They include: stretching, compression or restoring, attraction, repulsion, torsion, friction, viscous forces, and air resistance. These forces result from the interaction of fundamental forces. Each force has particular effects on the objects to which it acts. Hence, these forces are discussed based on their effects.

Frictional force

This is the force which opposes motion between two surfaces of objects in contact. Friction occurs when one surface of an object is resting or moving over another. Friction is a very common force. Whenever one object slides over another object, friction tries to stop the movement. For example, if a block is made to rest on a table, its weight acts on the table. But if the block is tied with a string and made to slide (pulled) as shown in Figure 3.8, there is some kind of resistance to the movement of the block. This is the work of friction.

Figure 3.8: Sliding a block on the table top

Frictional force occurs depending on the nature of the surfaces of bodies in contact. Friction produces heat, as is the case in matchsticks. Wear and tear of car tyres and shoe soles are caused by friction. For example, Figure 3.9 (a) shows new tyres and (b) shows worn tyres due to frictional force.

Figure 3.9: New and worn car tyres showing the effects of friction

Activity 3.4

Aim: To demonstrate frictional force.

Material: Wood blocks

Procedure

1. Rub the palms of your hands against each other. What do you feel?
2. Make tiny rails on the surfaces of the two wooden blocks.
3. Vigorously, rub the two blocks of wood against each other. What do you observe?

Questions

(a) Explain your observations.

(b) What is your conclusion?

When two objects in contact rub against each other, heat is produced. Frictional force, unlike other forces, produces heat.

Frictional force results to wastage of energy in the form of heat. In engines, friction can wear the moving parts resulting in poor performance of the engine.

Coefficient of friction

In activity 3.5, you noticed that more force is needed to pull the brick placed on the rough surface than when it is placed on the smooth surface. This is due to the existence of a large friction on a rough surface than on a smooth surface. In practice, no surface has no friction, rather, some surfaces have minimum friction while others have maximum friction. On rough surfaces, friction is more noticeable because the surface has maximum friction while on smooth surfaces the friction is minimal. The level of friction caused by a surface is expressed by the coefficient of friction.

The coefficient of friction is defined as the ratio of friction force to the normal reaction.

Coefficient of friction = friction force / normal reaction (weight)

Normal reaction = weight of an object = mg

Example 3.2

What is the coefficient of friction, which is calculated in the context of a brick with a mass of 8 kg being pulled on a rough surface with a friction force of 26 N? (take g = 10 N/kg)

Solution

Mass of a brick = 8 kg

Friction force = 26 N

Normal reaction = mg = 8 kg × 10 N/kg = 80 N

Coefficient of friction = friction force / normal reaction (weight) = 26 N / 80 N = 0.325

Therefore, the coefficient of friction between the brick and the surface is 0.325.

Stretching and compressional forces

Stretching force is the force exerted on an object when its two ends are pulled apart. On the other hand, compressional force is the force exerted on the body when its two ends are pushed towards each other. Stretching and compressional forces are important in dealing with elastic materials, such as rubber bands, springs, wire and ropes. Figures 3.11 (a) and (b) show stretching forces on a rubber band and compressional force on a spring.

Figure 3.11: Stretching and compressional forces

Elastic (Restoring) force

Some materials tend to restore their original shapes and sizes when a force acting on them is removed. Such materials are said to be elastic materials. Examples of elastic materials are rubber bands and springs. As one stretches or compresses an elastic material, such as a spring, it resists the change in shape. The material exerts a counter force in the opposite direction to the stretching or compressing force. This force is called elastic force. As soon as the stretching or compressing force is removed, the elastic force causes the material to return to its original shape. Hence, the elastic force is also called a restoring force. Figure 3.12 illustrates the deformation and restoration of a spring.

Figure 3.12: Restoring force of a spring

Air resistance

Air resistance is the force that resists the movement of an object through the air. Air resistance is an example of fluid resistance or fluid force. It is the force exerted on an object moving through a fluid (liquid or gas). This force depends on the:

1. Size and shape of the object
2. Speed of the object
3. Density of the fluid

Air resistance is most noticeable in objects moving at high speeds or objects with large surface areas. For instance, a runner has to exert force to oppose the force of a blowing wind. On the contrary, if the runner moves along the direction of the wind, the wind provides the force that increases his or her speed. Air resistance slows down many moving objects such as a car and even cyclists, as shown in Figure 3.13 (a). However, air resistance is advantageous to parachutists since it acts against the force of gravity on the parachute and slows its downward motion, as shown in Figure 3.13 (b).

Figure 3.13: Effect of air resistance

Viscous force

Viscous force is the resistance force provided by a fluid when it is subjected to a tangential force. The force acts to oppose the flow of the fluid past the object. From day-to-day observations, water has a smaller viscous force than cooking oil. On the other hand, honey has a larger viscous force than cooking oil.

The measure of resistance of the fluid to its flow past a surface is referred as the viscosity of the fluid. Thus, honey has a higher viscosity than water. Figure 3.15 shows how one can visually compare the viscosity of different fluids.

Figure 3.15: Comparison of water and honey viscosity

Task 3.2

Discuss why engineers spend much time trying to reduce fluid resistance in cars, ships, and planes.

Tensional force

Tension is the force exerted on an object by a stretched material. It is the force that is transmitted through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends. The tension force is directed along the length of the wire and pulls outwards along the two ends of the rope. Figure 3.16 shows the tension force along the stretched cable wire.

Figure 3.16: Tension force along the cable wire

Buoyant force

Buoyant force is the force that causes objects to float. It is the force exerted on an object that is partly or totally immersed in a fluid. Buoyant force is caused by differences in pressure acting on opposite ends sides of an object immersed in a static fluid as shown in Figure 3.17. This is the reason why an object feels lighter when immersed in a fluid but heavier just above the surface of the fluid.

Figure 3.17: Buoyant force

Normal force

This is a support force exerted upon an object which is in contact with another stable object. The normal force is also called reaction force and it acts perpendicular (at right angle) to the surface in contact. For example, if a book is resting on a table, then the table is exerting an upward force on the book in order to support the weight of the book, as shown in Figure 3.18.

Figure 3.18: A normal force

When a person leans against a wall, the wall supports the person by pushing him or her away perpendicular to the wall.

Torsional force

This is the force produced on a solid object when it is twisted. It is an elastic force since the object returns to its original shape when the force is removed. An example of torsional force is observed in twisting a rubber or a ruler, as illustrated in Figures 3.19.

Figure 3.19: Illustration of torsional force

Task 3.3

1. Discuss the four types of contact forces and the properties of each type. State their uses in everyday life.
2. Hang two balloons on a wall side by side and allow them to touch each other. Rub each one of them with a dry cloth. What happens? Explain.
3. Place a bar magnet on a smooth table and then bring another bar magnet near it. What happens? Explain.
4. Starting with two bar magnets parallel to each other, rotate one bar magnet by 90° and bring it near the first magnet. What happens? Explain.

Chapter summary

1. A force is a push or pull experienced by an object. It results from the interaction between two objects.
2. Forces can cause a change in the:
   1. speed or direction of an object's motion
   2. shape and size of an object
   3. way an object moves
3. Some forces act through physical contact between two objects while others act at a distance.
4. Force is measured in newtons (N).
5. A spring balance can be used to measure various forces, including weight.
6. Weight is a measure of the gravitational force exerted on an object.
7. There are four fundamental forces, namely:
   1. gravitational force
   2. electromagnetic force
   3. the strong force
   4. the weak force
8. Forces produce several effects when in action. These include stretching, compressing, bending and rotating or turning.
9. Friction is a resistance force that an object encounters when resting or moving over another object.
10. A compressional force is the force which when applied to an object result in a decrease of its size.

Revision exercise 3

Section A

1. Choose the most correct answer
   1. A force acting on an object causes some properties of the object to change. Which of the list contains properties that can be changed by the action of force?
      1. Mass, motion, and shape
      2. Mass, motion and size
      3. Mass, shape, and size
      4. Motion, shape and size

Chapter Four: Density and Relative Density

Introduction

Density is an important concept for scientists and engineers because it is useful in determining the characteristics of a material. Engineers must think of the density of the materials before marine and air transport vessels can be designed and built so that they will float. For example, aluminium alloy as one of the materials used in aircraft construction substituted steel because aluminium is less dense than steel. In this chapter, you will learn the concept of density, how to determine the densities of solids and liquids, the concept of relative density and the determination of the relative density of solids and liquids. The competencies developed are useful in designing and constructing of models for marine and air transport vessels so that they will float. Moreover, you will acquire skills in identifying the purity of a substance and estimating the composition of different types of mixtures.

Think

How can the concept of density be used in designing marine and air transport vessels?

Concept of density

Suppose you measure the mass of three blocks made up of glass, iron and wood whose size are identical shown in Figure 4.1. You will find that the masses of all blocks are different although their volumes are similar.

Figure 4.1: Blocks of glass, iron, and wood

The iron block will have a greater mass than the glass block which has a greater mass than the wooden block. The difference in mass arises from the way the particles of the blocks are packed together. This suggests that a comparison of the mass of a substance and its volume leads to an important physical quantity called density. This quantity is the measure of how the constituent particles of a substance are packed in a unit volume. If particles are closely packed in a small volume of a substance, the substance is said to have high density and vice versa. Figure 4.2 shows high and low density substances.

Figure 4.2: Concept of density

Thus, density is the extent to which the particles of a substance are closely packed in a particular substance. The more compact the particles are in a particular substance, the higher the density of that substance.

Density is the mass of a substance divided by its volume. The symbol used for density is the Greek letter, ρ (rho).

Density, ρ = mass (m) of substance / volume (V) of the same substance
ρ = m/V

The SI unit of density is kg/m³. Another unit used for expressing density is g/cm³.

Density-Mass-Volume Triangle

Figure 4.3: Density-mass-volume triangle

The relationship between the density, mass, and volume of a substance can easily be remembered by the density-mass-volume triangle. From the triangle:

• To find density (ρ): cover ρ, you get m/V
• To find mass (m): cover m, you get ρ × V
• To find volume (V): cover V, you get m/ρ

Density is an intrinsic property of matter since it is independent of the number of particles contained in the materials. The densities of common substances are given in Table 4.1.

Table 4.1: Densities of common substances

Solids
Substance	Density (kg/m³)
Aluminium	2,700
Copper	8,800
Gold	19,300
Iron	7,800
Lead	11,300
Glass	2,500
Ice (0 °C)	920

Table 4.1 (continued): Densities of common substances

Liquids
Substance	Density (kg/m³)
Seawater	1,030
Water (4 °C)	1,000
Water (20 °C)	998
Gasoline/petrol	700

Table 4.1 (continued): Densities of common substances

Gases (at standard conditions)
Substance	Density (kg/m³)
Air	1.225
Carbon dioxide	1.98
Hydrogen	0.820
Helium	0.178

Activity 4.1

Aim: To determine the mass to volume ratio for given objects.

Materials: Vernier calliper, beam balance, three identical blocks of different materials (for instance, aluminium, copper, and iron, respectively)

Figure 4.4: Aluminium, copper, and iron blocks

Procedure

1. Measure the length, height and width of each object.
2. Measure the mass of each block.
3. Record all observations using the following table.

Table 4.2

Substance	Length (cm)	Height (cm)	Width (cm)	Mass (g)	Volume (cm³)	m/V
Aluminium
Copper
Iron

Questions

(a) Compare the mass to volume ratio of each substance.

(b) Are they different or the same? Why?

(c) What physical quantity does the ratio represent?

Example 4.1

What would be the density of a glass block calculated based on its dimensions of 0.12 m × 0.04 m × 0.10 m and a mass of 1.2 kg?

Solution

Density = mass / volume

Volume of the block = 0.12 m × 0.04 m × 0.10 m = 0.00048 m³

Mass of the block = 1.2 kg

Density of block, ρ = m/V = 1.2 kg / 0.00048 m³ = 2,500 kg/m³

Therefore, the density of the block is 2,500 kg/m³.

Example 4.2

Using Table 4.1, calculate the mass of the glass that has the same volume as 5.4 g of aluminium.

Solution

Density of aluminium = 2,700 kg/m³ = 2.7 g/cm³

Mass of aluminium = 5.4 g

Density of glass = 2.5 g/cm³

Required: Mass of the glass

From the formula of density, V = m/ρ

The volume of aluminium will be: V = 5.4 g / 2.7 g/cm³ = 2 cm³

This volume is the same as that of glass,

Thus, m_g = ρ_g × V_g

where m_g is the mass of glass, ρ_g is the density of the glass, and V_g is the volume of the glass.

Then, m_g = 2.5 g/cm³ × 2 cm³ = 5 g

Therefore, the mass of glass is 5 g.

Determination of density of a substance

A technique used in the determination of density of a substance depends on the properties of the substance. For a given substance, the appropriate method for measuring its mass and volume must be used. Once the measured values of mass and volume are known, the density of a substance can be calculated.

It is important to note that different techniques are used to determine the density of solids, liquids and gases.

Determination of density of solid

The density of a solid object can be determined using techniques that depend on the shape of the object under observation. The shape of the object may be regular or irregular. For the case of regular shape, one needs to measure its mass and dimensions. The density is then calculated using the formula ρ = m/V, where volume is calculated using the dimensions of the objects. If the shape of the object is irregular, its volume can be measured using the measuring cylinder or eureka can as discussed in Chapter Two of this book.

Activity 4.2

Aim: To determine the density of regular shaped objects.

Materials: Wood blocks, glass block, textbooks, ruler and test tube

Procedure

1. Measure and record the length, height and width of each object.
2. Measure and record the mass of each object.
3. Calculate the volume of each object using a proper formula.
4. For each object calculate its density.
5. Report your results in a tabular form.

Question

Compare the densities of different objects.

Example 4.3

In a physics exercise, a student was given a rectangular shaped block to find its density and predict using a standard density table the type of material composing the block. The student measures the mass and dimensions of the block and obtained 150 g and 3 cm × 4 cm × 5 cm, respectively. What possible conclusion did the student make?

Solution

Mass = 150 g

Volume = 3 cm × 4 cm × 5 cm = 60 cm³

Density = Mass / Volume = 150 g / 60 cm³ = 2.5 g/cm³ or 2,500 kg/m³

This value is the same as the density of glass (see Table 4.1). Therefore, the block is made of glass.

Task 4.1

Suppose, you have a wooden block, metre ruler, and a beam balance and you want to determine the density of the wooden block:

(a) What information do you need in order to calculate the density of the wooden block?

(b) How would you obtain such information using the available resources?

Density of insoluble granules

Determination of the density of small insoluble particles such as sand grains is also possible. Unlike other solids, granules must be held in some type of container while being measured. This could be realised by using a density bottle.

A density bottle has a precisely measured volume, usually 25 ml, 50 ml, or 100 ml and a tight-fitting stopper with a small hole to allow excess liquid to escape. It is mostly used in studying and analysing the relative densities of two immiscible liquids. Figure 4.5 shows parts of a density bottle.

Figure 4.5: Density bottle

The following steps are to be followed when using a density bottle to measure the density of insoluble granules such as sand:

1. Measure the mass of the empty density bottle with its stopper; record as m_0.
2. Remove the stopper, add a small amount of sand to the bottle and replace the stopper. Measure the mass of the bottle containing sand and its stopper; record this mass as m_1.
3. The difference between m_1 and m_0 gives the mass of the sand. Mass of sand = (m_1 - m_0).
4. Remove the stopper, add water into the bottle until the bottle is full, replace the stopper.
5. Measure the mass of the bottle containing water and sand as m_2.
6. The difference between m_2 and m_1 gives the mass of the water added to the bottle. Mass of water is (m_2 - m_1).
7. Since the density of water is 1 g/cm³, the volume added to the bottle is given in cm³, which is numerically equal to the mass of the water in grammes.

Volume of water (V_w) = mass of water (m_w) / density of water (ρ_w)
V_w = m_w / ρ_w = m_w / 1 g/cm³ = (m_2 - m_1) g / 1 g/cm³ = (m_2 - m_1) cm³

Therefore, the volume of water is in cm³.

8. Since the only materials in the bottle are water and sand, the sum of their volumes must be equal to the volume of the bottle.

Volume of bottle = volume of sand + volume of water
Volume of sand = volume of bottle - volume of water
V_sand = V_bottle - V_water

9. Use the formula to calculate the density of sand. That is,

ρ_sand = m_sand / V_sand
ρ_sand = m_sand / (V_bottle - V_water)
Therefore, ρ_sand = (m_1 - m_0) / [V_bottle - (m_2 - m_1)]

Density of a liquid

The density of a liquid can also be calculated if its mass and volume are known. Thus, the density of a liquid can be determined through the following steps:

1. Measure an empty beaker; record it as m_0.
2. Using a burette, run out a known volume (V) of the liquid into the beaker and measure the mass; record it as m_1.
3. Subtract m_0 from m_1 to get the mass of the liquid, that is, mass of liquid = (m_1 - m_0).
4. Calculate the density of the liquid by dividing mass obtained in step (3) by the known volume of liquid, that is;

Density of liquid = Mass of a liquid / Volume of a liquid
= (m_1 - m_0) g / V cm³

Example 4.5

In an experiment to determine the density of liquid Y, a Form One student obtained the following results: Mass of beaker = 500 g and Mass of beaker + liquid (25 cm³) = 600 g. What did the student obtain as the density of liquid Y?

Solution

Volume of liquid Y = 25 cm³

Mass of empty beaker = 500 g

Mass of beaker + liquid Y = 600 g

Mass of liquid = (600 - 500) g = 100 g

Density of liquid, ρ = Mass of liquid / Volume of liquid = 100 g / 25 cm³ = 4 g/cm³

Therefore, density of liquid Y is 4 g/cm³.

Relative density of a substance

It is common practice to express the density of a substance such as solid, liquid and gas (air) in relation to the density of water. The ratio between density of substance to the density of water is called relative density, R.D.

Relative density is the ratio between density of substance to the density of water.

R.D = Density of substance / Density of water
= Mass of substance / Mass of equal volume of water

The relative density has no unit, since it is expressed as the ratio of the same quantity.

Relative density is also known as the specific gravity (S.G). It indicates how many times a substance is denser compared to water. A substance is denser than water if its relative density is larger than 1 and the substance is less dense than water if its relative density is less than 1.

Example 4.6

An object has a density of 7 g/cm³. Calculate its relative density, (R.D).

Solution

Density of object = 7 g/cm³

R.D = Density of substance / Density of water = 7 g/cm³ / 1 g/cm³ = 7

Therefore, relative density of the object is 7.

Identification of Gemstones

Density helps in identifying gemstones such as gold and diamond by comparing their densities with known values.

Geology and Mineralogy

Geologists use density to determine the mineral content of rocks and other samples.

Building Materials

Density is considered during the selection of appropriate building materials for construction.

Marine and Air Vessels

Density is crucial in designing vessels that can float, such as ships and aircraft.

Swimming Equipment

Density considerations are important in designing swimming and diving equipment.

Purity Determination

Relative density can be used to determine the purity of substances and estimate mixture compositions.

ICT corner

Visit https://phet.colorado.edu select the simulation titled "Density and buoyancy" to help students visualise and demonstrate the concept of density of a substance.

Chapter summary

1. Density of a substance is expressed as the mass of the substance per unit volume. Its SI unit is the kilogram per cubic metre, kg/m³. It can be expressed mathematically as ρ = m/V.
2. The determination of the density of a solid depends on the shape of a particular solid. That is, whether the solid has a regular or irregular shape.
3. The density of solids is generally higher than the density of liquids.
4. Relative density of a substance is the ratio of the substance's density to the density of water. It has no units since it is a ratio of the same quantity.
5. A relative density bottle is used to determine relative density of liquids.
6. Density is used in designing various structures for ships and aircraft.
7. Density is considered during the selection of building materials and design of swimming equipment.

Revision exercise 4

Section A

1. Choose the most correct answer.
   1. A group of Form One students conducted an experiment to determine the density of wood. They measure the masses and volumes of different sized samples of a type of wood. Furthermore, they plotted the graph based on the data collected shown in Figure 4.11. Which graph depict their results?
      

      Figure 4.11
      1. Graph showing direct proportion between mass and volume
      2. Graph showing inverse proportion between mass and volume
      3. Graph with curved line
      4. Graph with no clear relationship

Chapter Five: Sinking and Floating

Introduction

Sinking and floating is a fundamental phenomenon with practical applications in a wide range of fields, including ship building, marine engineering, and even understanding the behaviour of gases in the atmosphere. Archimedes' principle and the law of floatation are important laws of physics that explain the nature and mechanism of sinking and floating. Understanding these concepts is essential for designing stable and buoyant structures that can navigate fluid environments effectively. In this chapter, the concept of sinking and floating, Archimedes' principle and the law of floatation will be discussed. Competencies developed will enable you to efficiently use the phenomenon of floating and sinking in your daily activities.

Think

What objects are naturally sink but can be molded to make them float?

Concept of sinking and floating

When an object is placed in water, it either sinks (goes down into the water) or floats (stays on the surface of the water). Figure 5.1 (a) shows a sealed empty plastic bottle floats on water because its weight is less than the upthrust exerted on it by water.

Figure 5.1: Sinking and floating

While the sand-filled bottle shown in Figure 5.1 (b) sinks because its weight is larger than the upthrust acting on the bottle. Therefore, floating is the tendency of an object suspended in water to stay on the surface of the water. On the other hand, sinking is the tendency of an object to go to the lower level of water.

Whether an object floats or sinks in a fluid depends on its relative size, weight, and the upthrust acting on the object. If the weight of the object is greater than the upthrust, the object moves downward and therefore sinks. If the weight of an object is less than the upthrust, the object will stay on the surface of the fluid and therefore float. The action of weight and the upthrust on an object in the fluid is shown in Figure 5.2.

Figure 5.2: Forces acting on a body submerged in a liquid

In Chapter Two, it was shown that when an object is immersed in a fluid, it displaces a volume of the fluid equal to the volume of the body. It is also shown in the previous section that the upthrust acting on the immersed object depends on the volume of the object and the density of the liquid in which it is immersed. Therefore, sinking and floating can also be explained in terms of the density of the object and that of the fluid.

Object Floats When:

• Density of object < Density of fluid
• Weight of object < Upthrust
• Object stays on surface

Object Sinks When:

• Density of object > Density of fluid
• Weight of object > Upthrust
• Object goes to bottom

If the object's density is greater than that of the fluid, the object will sink. The object floats if its density is less than that of the fluid. Ships and boats float on water because their average density is less than the density of water. Inflated balloons float in air because their average densities is less than the density of air. Metallic objects, such as spoons and coins, sink in water because they have higher average densities than the density of water.

Task 5.1

The density of aluminium foil is 2.7 times that of water. Take a piece of foil, shape it into a ball, and place it in water, will it submerge? Explain the factors that determine whether it sinks or floats, and discuss any possible methods to make it sink.

Activity 5.1

Aim: To demonstrate sinking and floating of objects.

Materials: Various objects of different shapes and sizes (examples are metal spoon, plastic bottle cap, wooden block, rubber ball, Aluminium foil, toy boat), large container filled with water (a basin or a bucket) and paper pencil.

Procedure

1. Predict which object will sink and which one will float. Record your results.
2. Fill the container with water.
3. Wear sanitary gloves, and gently put an object in the water at a time. Observe if it sinks or floats.
4. Repeat the step 3 for every object at your disposal.

Questions

(a) What do you notice about the objects that sank?

(b) What do you notice about the objects that floated?

(c) Were there any surprising results or objects that didn't behave as you predicted?

(d) In terms of density compare the objects that sank and those which floated.

Conditions for floating

For an object to float, the upthrust exerted by the surrounding fluid must be greater than the objects weight. Upthrust depends on the volume of the submerged part of the object and the density of the surrounding fluid. Thus, when an object is placed in a fluid, the greater the submerged volume of the object, the greater the upthrust.

A ship is normally built with a large hollow space. Typically, the ship has a large volume which allows it to displace a large volume of water, resulting into a large upthrust equalising the weight of the ship. If the hollow space is filled with air, the average density of the ship material and air is less than the density of water and so, the ship floats. Therefore, the following conditions must be satisfied for an object to float in water:

1. The volume of the submerged part of the object must be large enough to displace a large volume of water.
2. The average density of the object must be less than the density of the fluid in which it floats
3. The upthrust due to water must be greater or equal to the total weight of the object.

Task 5.2

Some water bodies such as the dead sea are known to have abnormally high concentrations of salt. Discuss why a human body sinks in the normal oceans but floats on the dead sea.

Concept of upthrust

Task 5.3

Hold a stone in one hand and sense its weight. Tie the same stone using a string and submerge it in water. Hold the string and try to pull it. What do you feel about its weight?

Consider a cork being held at the bottom of a beaker that contains a liquid, as shown in Figure 5.3 (a). When the cork is released, it immediately rises to the surface of the liquid, as shown in Figure 5.3(b).

Figure 5.3: Upthrust in water

The rising of the cork shows that, while inside the liquid, an upward force acts on it. Since this force is greater than the weight of the cork, it is pushed up to the surface of the liquid. An upward force acting on an object that is totally or partially immersed in a fluid is called an upthrust or buoyant force. Upthrust enables an object to float or feel lighter in a fluid.

When one is swims in water, his or her weight is balanced by the upthrust acting on the body. Water vessels, like ships and boats, float and sail on water due to this force, otherwise, they would sink. The tendency or ability of an object to float on a fluid suspended on it is called buoyancy and the upward force exerted by a fluid on that object is called upthrust (buoyant force). Buoyancy is the force that determines whether an object will sink, float, or remain suspended in a fluid. This concepts was best described by Archimedes, who famously shouted "Eureka!" when he discovered the phenomenon.

Apparent weight of an object

If one attempts to lift an object in a swimming pool and then, attempts to lift the same object outside of the pool, it feels much lighter in the pool than when outside. This is the effect of upthrust. When a body is totally or partially immersed in a fluid, it experiences an upthrust exerted by the fluid. The upthrust is equal to the weight of the fluid displaced by the immersed object. Because of upthrust, an object that is submerged in the fluid appears to weigh less than its actual weight in air. The weight of the submerged object is known as apparent weight, while its weight in air is referred to as the actual weight. The difference between the weight and the apparent weight of an object is referred to as the apparent loss in weight.

Apparent loss in weight = Actual weight – Apparent weight of body in fluid
= Weight of the displaced fluid
= Upthrust
Thus, Upthrust = Apparent loss in weight

Activity 5.2

Aim: To determine the apparent loss in weight of objects immersed in water.

Materials: Measuring cylinder, spring balance, solid objects such as stones, water, string

Procedure

1. Tie the stone using a string and measure its weight in air using a spring balance as shown in Figure 5.4. Record this weight as w_1.
2. Fill a measuring cylinder with water to about 30 ml of its volume.
3. Lower the stone suspended at the end of the spring balance into the water. It should be partially immersed. Note the reading on the spring balance as w_2 and the level of liquid in the measuring cylinder.
4. Lower the stone such that it is totally immersed in the water, as shown in Figure 5.4 and record this weight as w_3.
5. Remove the stone, dry and re-weight it in air. Record this weight as w_4.
6. Calculate the apparent loss in weight of the stone and record it as w_L.
7. Repeat steps 1 to 6 for other objects, one at a time.

Figure 5.4: Measuring weight in air and water

Questions

(a) What do you notice about the values w_1, w_2, w_3, w_4, and w_L?

(b) What is your conclusion about the weight of the stone?

In Activity 5.2, you have learnt that, the weight of an object in air (w_1) is larger than its weight when it is submerged in water (w_2). That is, there is an apparent loss in weight (w_L) which is the difference between the weight in air and the weight in liquid. Thus,

Apparent loss in weight = weight in air – weight in water
w_L = w_1 - w_2 or w_L = w_1 - w_3

Note that the apparent loss in weight is equal to the upthrust exerted on the object by water.

Archimedes' Principle

If an object is immersed in water, it displaces some of the water. The relationship between the upthrust acting on a body and the weight of the displaced fluid, when the body is partially or totally immersed in the fluid was discovered by a Greek scientist known as Archimedes. This relationship is explained by Archimedes' principle, which is referred to as the law of buoyancy.

Archimedes' principle states that: "Any object partially or totally immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced by the object".

It is important to note that the weight of an object acts downwards while the upthrust exerted by the displaced fluid acts upwards.

Verification of Archimedes' principle

To verify the Archimedes' principle, perform the following activity.

Activity 5.3

Aim: To verify the Archimedes' Principle.

Materials: Beaker, eureka can, spring balance, measuring cylinder, stone, water and digital balance.

Figure 5.5: Setup for verifying Archimedes' principle

Procedure

1. Measure the weight of the stone in the air using a spring balance and record its weight.
2. Using a digital balance, measure the mass of a dry empty measuring cylinder, and record its mass.
3. Pour water into a eureka can up to its spout level.
4. Place the measuring cylinder under the spout of the eureka can.
5. Weigh the stone when it is totally immersed in water and record its weight. Wait until all the displaced water overflows into the measuring cylinder.
6. Weigh the measuring cylinder containing the displaced water. Record its weight.

Questions

(a) Determine the mass of the displaced water.

(b) Calculate the weight of the displaced water.

(c) Calculate the upthrust exerted by water on the stone.

(d) How does the upthrust relate to the weight of the displaced water?

(e) Using the results from this activity and your own words, state the Archimedes' principle.

In Activity 5.3, you observed that upthrust is equal to the weight of the displaced fluid. This observation verifies Archimedes' principle, which applies to objects of all densities. It is important to note that upthrust depends on the weight of the fluid displaced.

Example 5.1

In an experiment to study the behaviour of the weight of an object a student finds that the weight of the object is 4.9 N in air and its weight when completely submerged in water is reduced to 3.1 N. Calculate the upthrust.

Solution

Weight of the object in air = 4.9 N

Weight of the object in water = 3.1 N

Upthrust = weight of an object in air - weight of an object in water

= 4.9 N - 3.1 N = 1.8 N

Therefore, upthrust acting on the object is 1.8 N.

Factors affecting upthrust

According to Archimedes' principle, an object submerged in a fluid experiences an upthrust that is equal to the weight of the fluid displaced. That is,

Upthrust (U) = Weight of displaced fluid (w_f)

But, Weight of the fluid displaced (w_f) = mass (m_f) × acceleration due to gravity (g)

Mass of the fluid (m_f) = density of the fluid (ρ_f) × volume of the displaced fluid (V_f)

m_f = ρ_f V_f

In Chapter Four, you learned that the volume of the displaced fluid is equivalent to the volume of the immersed object. That is,

Volume of the fluid displaced (V_f) = volume of object (V_o)

Since, V_f = V_o

m_f = ρ_f V_o

U = m_f g

Thus, U = ρ_f V_o g

That is, upthrust = density of the fluid × volume of the object × g

Hence, upthrust is affected by:

1. The volume of the immersed object
2. The density of the fluid in which the object is immersed
3. The acceleration due to gravity

Law of Floatation

The previous sections have established that a body can float on a fluid if certain conditions are satisfied. This leads us to the law of floatation which states that:

A floating body displaces its own weight of the fluid in which it floats.

Applications of sinking and floating in everyday life

Ships and Boats

Designed with hollow spaces to increase volume and decrease average density, allowing them to float despite being made of dense materials like steel.

Submarines

Use ballast tanks to control buoyancy by taking in or expelling water, allowing them to sink or rise as needed.

Hot-air Balloons

Rise because heated air inside the balloon is less dense than the cooler surrounding air, creating upward buoyant force.

Life Jackets

Provide additional buoyancy by displacing more water, increasing the upthrust to keep people afloat.

Hydrometers

Instruments that measure liquid density by how deeply they sink, used in brewing, winemaking, and battery testing.

Swimming and Diving

Understanding buoyancy helps swimmers float and divers control their depth using buoyancy control devices.

ICT corner

Visit https://phet.colorado.edu select the simulation titled "Density and buoyancy" to help students visualise and demonstrate the concept of density and buoyancy.

Chapter summary

1. An object immersed partially or totally in a fluid (liquid or gas) experiences an upward force called the buoyant force or upthrust.
2. The buoyant force causes the object to have an apparent weight that is less than its weight in the air. Apparent loss in weight = weight in air – weight in a fluid.
3. Archimedes' principle states that 'The upthrust on a body is equal to the weight of fluid displaced by the object. That is, upthrust = weight of displaced fluid.
4. The density and relative density of solid and liquid can be determined using Archimedes' principle.
5. An object floats or sinks depending on its density and the density of the fluid in which it is placed.
6. An object will float if it displaces a weight of fluid equal to its own weight. In other words, an object will float if its density is less than the density of the fluid in which it is immersed.
7. Hot-air balloons, submarines, ships and weather balloons can be made to float by altering their volume to make them less dense than the fluid in which they float.
8. A hydrometer is a device used to measure the relative density of different liquids. It works on the principle that the hydrometer sinks until it displaces a volume of liquid that has the same weight as itself. The hydrometer sinks further in low density liquids than in high-density liquids.

Revision exercise 5

Section A

1. Choose the most correct answer:
   1. The same body is immersed in liquid A and then, in liquid B. The extent to which the body sinks in liquid B is less than in liquid A. What conclusion can be drawn from such an observation? The density of:
      1. the liquid A is more than that of liquid B.
      2. the liquid B is more than that of liquid A.
      3. the solid body is less than that of the liquid in both cases.
      4. the liquid A is the same as that of liquid B.

Chapter Six: Mechanical Properties of Matter

Introduction

Study of mechanical properties of matter plays a significant role in physics and engineering. When constructing houses, bridges, and fly-overs, the proper selection of materials, based on their properties, is required. In this chapter, the concepts involving elasticity, adhesion and cohesion, surface tension and capillarity will be discussed. The competencies developed will enable you to analyse and apply the properties of different materials found in your environment.

Think

What are the mechanical properties of materials used in constructing bridges?

Concept of elasticity

If you stretch and release a rubber band, it will return to its original shape and size. If you compress and release a coil spring, it will resume its original length and shape. When a rubber band is stretched, we say it is deformed because it is not in its original shape. A coil spring is also deformed when compressed. The ability of objects to return to its original shape after deformation is called elasticity. Thus, elasticity is the ability of a deformed body to return to its original shape and size when the forces causing the deformation are removed. A body with this ability is said to be elastic.

Figure 6.1: Elastic materials

Relationship between tension and extension of an elastic material

When a metal is subjected to a force it undergoes deformation. The force that causes this deformation is referred to as tension, while the extent of deformation is known as extension. Elastic materials undergo deformation when tension is applied but regain their original shape when the tension is released. Materials which cannot exhibit elasticity are known as inelastic materials. Examples of elastic materials include a rubber band and strings. A good example of inelastic material is the glass.

Elastic Materials

• Return to original shape after deformation
• Examples: Rubber bands, springs
• Follow Hooke's Law within elastic limit

Inelastic Materials

• Do not return to original shape
• Examples: Glass, clay
• Permanent deformation occurs

To a great extent, most materials exhibit elastic behaviour. However, there is a limit of how much the material can deform and be able to regain its original shape. This limit is known as the elastic limit. Different materials have different elastic limits. If a material is deformed beyond the elastic limit, it behaves as plastic. Such a deformation is known as plastic deformation. Therefore, if the elastic limit is not exceeded, there is a definite relationship between tension and extension of elastic materials. This relationship can be realized by performing Activity 6.1.

Activity 6.1

Aim: To investigate the relationship between tension applied to an elastic material and extension.

Materials: Coil spring, pointer, slotted masses, mass holder, metre rule, retort stand and clamp

Procedure

1. Hang a coil spring on a retort stand as shown in Figure 6.2.
2. Attach the pointer at the free end of the spring and hang the mass holder.
3. Place a metre rule adjacent to the apparatus so that the position of the pointer can be measured.
4. Measure and record the position of the pointer when there is no mass placed on the holder as X_0.
5. Place a 50 g mass as shown in Figure 6.3 on the holder, measure and record the pointer position as X_1.
6. Repeat the experiment with masses of 100 g, 150 g and 200 g. Record the respective pointer positions as X_2, X_3 and X_4.
7. Tabulate the results of your observation in Table 6.1.

Figure 6.2: Experimental setup for elasticity

Table 6.1: Experimental results

Mass (g) on holder	Force on spring (N) F = (m × g)/100	Extension (cm) e = X_i - X_0	F/e (N/cm)
50
100
150
200

Questions

(a) Comment on the values of F/e

(b) What is the relationship between tension and extension?

(c) Plot a graph of force (F) against extension (e) of the spring.

(d) Give an explanation for the shape of the graph.

(e) Use the graph to determine the constant of proportionality in this case.

Graph of Tension Against Extension

Figure 6.4: Relationship between tension and extension of a stretched spring

Certain observations can be made from the graph in Figure 6.4. For the portion between O and A, the tension (force) is directly proportional to the extension of the spring. This is in accordance with Hooke's law, which explains the relationship between the force applied on an elastic material and the extension produced.

Hooke's Law

Hooke's law states that: "Provided the elastic limit is not exceeded, the extension is directly proportional to the force applied".

The elastic limit is the maximum point beyond which the material cannot return to its original shape when the deformation force is removed. If the elastic limit is exceeded the material experiences plastic deformation. From the graph, in Figure 6.4, point B is the elastic limit and the part between points B and C, the spring undergoes plastic deformation, whereby it remains deformed even after the load is removed. The spring will continue to increase in length until a certain maximum tension is reached. Beyond this tension, the spring will finally break. In the elastic region, the ratio of the applied force (F) to the distance stretched (e) is called the elastic force constant, k. Hence, k = F/e.

The SI unit of k is N/m.

Exercise 6.1

1. A force of 40 N is applied to the spring with a spring constant of 100 N/m. What is the resulting displacement of the spring?
2. A rubber band has an original length of 20 cm and is stretched to a length of 25 cm. What is the percentage change in length of the rubber band?
3. A spring has a spring constant of 80 N/m. If the spring is compressed by 30 cm, what is the resulting force applied to the spring?

Applications of elasticity in daily life

At Home

• Rubber gaskets that seal refrigerator doors
• Clothing with elastic components
• Springs in furniture
• Rubber bands for holding things together
• Toys like balloons and balls

In Transport

• Hoses, belts and shock-absorbing springs for vehicles
• Rubber tyres
• Support cables for bridges
• Suspension systems

In Industry

• Steel beams used in construction
• Conveyor belts
• Measuring instruments and weights
• Insulation against vibration and sound
• Mechanical control devices

Task 6.1

Identify some elastic objects in your environment and explain how the concept of elasticity has made them useful in your daily life.

Adhesion and cohesion

If you pass through a grass field in the morning you will notice some drops of water stuck on grass leaves. Water drops are formed by the molecules that stick together because of cohesive forces. On the other hand, drops of water stick to the grass leaves because of the adhesive forces between water molecules and grass molecules. Thus, cohesion and adhesion are the two important concepts in explaining molecular interactions.

Cohesion

Force of attraction between molecules of the same type

• Water molecules sticking to other water molecules
• Mercury forming spherical drops
• Responsible for surface tension

Adhesion

Force of attraction between molecules of different kinds

• Water sticking to glass surfaces
• Glue sticking surfaces together
• Ink sticking to paper

Both cohesion and adhesion play important roles in explaining various physical phenomena. For example, solids are known to have definite shapes because of the strong cohesive forces among their molecules which are in fixed positions and close together. Water wets glass surfaces since adhesive forces between water and glass molecules are stronger than cohesive forces between water molecules. Conversely, mercury does not wet glass surfaces since cohesion between its molecules is stronger than adhesion between mercury and glass molecules. Furthermore, cohesion and adhesion explain why liquids form meniscus when poured into glass tubes as shown in Figure 6.5.

Figure 6.5: Shapes of menisci of mercury and water

Mercury forms a convex meniscus because of the stronger cohesion between its molecules compared to the adhesion between glass and mercury molecules. Water forms concave meniscus because adhesive forces between water and glass molecules are stronger than cohesion between water molecules.

Activity 6.2

Aim: To observe the adhesion and cohesion.

Materials: Water, glycerine, glass slides, cylinders and droppers

Procedure

1. Pour about 50 ml of glycerine and water into separate cylinders and carefully observe the meniscus of each liquid.
2. Using a dropper, place a drop of glycerine on glass slide and note down your observation.
3. Use another dropper to place a drop of water on another glass slide and note your observation.

Questions

(a) Compare the menisci of water with glycerine.

(b) What did you observe when drops of glycerine and water were placed on separate glass slides?

(c) Explain your observations.

The meniscus of water curves upwards forming a concave shape while the meniscus of glycerine curves downwards forming a convex shape. When each of these liquids is dropped on a glass slide, the water spreads further unlike glycerine. This is because glycerine has a high cohesive force among its particles. A drop of glycerine on a glass slide remains almost spherical because the cohesive force is stronger than adhesive force.

Applications of adhesion and cohesion

• Adhesive tapes and glue: Used to stick different objects together using adhesive effects
• Water purification: Adhesion helps to remove harmful materials such as bacteria from drinking water
• Friction: Adhesive forces are the source of friction between surfaces
• Water transport in plants: Cohesion supports water transport in plants and animals through capillary action
• Tissue repair: Animals and plants use cohesion of tissue to repair damage
• Viscosity: Cohesion is responsible for viscosity in fluids
• Writing: Ink sticks on paper because adhesive forces between ink and paper are greater than the cohesive forces in the molecules of ink

Task 6.2

Think of your daily life, paying attention to situations where cohesion and adhesion are involved. Discuss how these concepts are crucial to your daily activities.

Surface tension

Liquid surfaces have a tendency of shrinking into the minimum surface area. This tendency leads to surface tension.

Surface tension is defined as the property of the surface of a liquid that allows it to resist an external force due to the cohesive nature of its molecules.

This allows the liquid surface to behave like a fully stretched elastic skin. Small insects such as water striders and items like plastic, paper clips float on the surface of water, shown in Figures 6.6 and 6.7, because of the surface tension of water.

Figure 6.6: Water strider walking on water

Figure 6.7: Paper clip floating on the surface of water

Mechanism of surface tension

Surface tension is caused by cohesive forces between liquid molecules. Taking an example of water in a glass, the molecules at the surface of water do not have neighbouring water molecules above them, as shown in Figure 6.8. Consequently, these molecules cohere more strongly to the water molecules directly associated with them, that is the molecules that are next to and below them. Because of the stronger cohesive force between water molecules, it is more difficult to move an object through the surface than to move it when it is completely submerged.

Figure 6.8: Surface tension mechanism

This resistance to an external force due to cohesive forces between molecules is called surface tension.

Activity 6.3

Aim: To demonstrate the surface tension in water.

Materials: Needle, water, trough, paper clip, chalk powder, liquid detergent and razor blades

Procedure

1. Fill the trough with water.
2. Gently place the needle, razor blade and paper clip on the water surface.
3. Observe what happens.
4. Sprinkle some chalk powder on the water surface.
5. Note down your observations.
6. Add a little detergent such as soap to the water in the trough and observe what happens.

Questions

(a) What did you observe when the needle, paper clip, razor blade and chalk powder were gently placed on the water surface?

(b) What did you observe when some detergent was sprinkled on the water?

When the needle, paper clip, and razor blade were placed on the surface of the water, they all floated on top, as shown using a razor blade in Figure 6.9. This demonstrates surface tension.

Figure 6.9: Razor blade floating on water due to surface tension

Applications of surface tension

• Insect locomotion: Water striders and other insects can walk on water due to surface tension
• Cleaning action of soaps: Soaps and detergents reduce surface tension, allowing them to penetrate fabrics
• Formation of droplets: Surface tension causes liquids to form spherical droplets
• Capillary action: Surface tension helps in the rise of liquids in narrow tubes
• Medical applications: Surface tension principles are used in various medical tests and procedures
• Industrial processes: Used in coating processes, emulsion formation, and foam stability

Capillarity

Capillarity, also known as capillary action, is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. This phenomenon occurs due to the interplay between cohesive and adhesive forces.

Figure 6.10: Capillary action in different diameter tubes

When a narrow tube (capillary tube) is placed in a liquid, the liquid may rise or fall in the tube depending on the relative strengths of adhesion and cohesion:

• If adhesive forces are stronger than cohesive forces, the liquid rises in the tube (e.g., water in glass)
• If cohesive forces are stronger than adhesive forces, the liquid is depressed in the tube (e.g., mercury in glass)

Applications of capillarity

• Water transport in plants: Capillary action helps water move from roots to leaves
• Ink in fountain pens: Capillary action draws ink to the nib
• Paper towels and sponges: Absorb liquids through capillary action
• Wicking in candles: Melted wax moves up the wick through capillary action
• Soil moisture movement: Water moves through soil via capillary action
• Medical tests: Used in blood and urine tests where liquids move through test strips

Chapter summary

1. Elasticity is the ability of a material to return to its original shape after deformation when the deforming force is removed.
2. Hooke's Law states that the extension of an elastic material is directly proportional to the applied force, provided the elastic limit is not exceeded.
3. The elastic limit is the maximum stress that a material can withstand without permanent deformation.
4. Adhesion is the force of attraction between molecules of different substances, while cohesion is the force of attraction between molecules of the same substance.
5. Surface tension is the property of liquid surfaces that allows them to resist external forces due to cohesive forces between molecules.
6. Capillarity is the ability of liquids to flow in narrow spaces without external assistance, resulting from the interplay between adhesion and cohesion.
7. These mechanical properties have numerous practical applications in daily life, industry, and technology.

Revision exercise 6

Section A

1. Choose the most correct answer:
   1. Which of the following best describes elasticity?
      1. The ability to stretch without breaking
      2. The ability to return to original shape after deformation
      3. The resistance to change in shape
      4. The ability to absorb energy
   2. According to Hooke's Law:
      1. Force is inversely proportional to extension
      2. Force is directly proportional to extension
      3. Force is proportional to the square of extension
      4. There is no relationship between force and extension

Section B

2. Differentiate between adhesion and cohesion, giving two examples of each.
3. Explain why water forms a concave meniscus while mercury forms a convex meniscus in glass tubes.
4. A spring extends by 5 cm when a force of 10 N is applied. Calculate the spring constant.
5. Describe an experiment to demonstrate surface tension.

Section C

6. Discuss the importance of understanding mechanical properties of matter in engineering and construction.
7. Explain how capillary action is important for plant survival.
8. Design an experiment to investigate the relationship between the diameter of capillary tubes and the height to which water rises.

Chapter Eight: Linear Motion

Introduction

Motion is a fundamental concept in physics that describes how objects change their position over time. Linear motion, specifically, deals with objects moving along a straight path. Understanding motion helps us analyze everything from a car traveling on a road to a ball thrown in the air. In this chapter, you will learn about the concepts of motion, distance, displacement, speed, velocity, acceleration, equations of linear motion, and motion under gravity. The competencies developed will enable you to analyze and solve problems related to moving objects in various contexts.

Think: How would our daily activities be affected if we couldn't predict the motion of objects?

Concept of Motion

Motion refers to the change in position of an object with respect to time and its surroundings. An object is said to be in motion if its position changes relative to a reference point. For example, a car moving on a road is in motion relative to the trees on the roadside.

Distance and Displacement

Distance is the total path length traveled by an object, regardless of direction. It is a scalar quantity measured in meters (m). Displacement, on the other hand, is the straight-line distance between the initial and final positions of an object, along with the direction. It is a vector quantity measured in meters (m).

Example 8.1

A student walks 4 km east and then 3 km north. Calculate:

(a) The total distance traveled

(b) The displacement

Solution:

(a) Distance = 4 km + 3 km = 7 km

(b) Displacement = √(4² + 3²) = √(16 + 9) = √25 = 5 km, northeast

Speed and Velocity

Speed is the rate of change of distance with time. It is a scalar quantity measured in meters per second (m/s). Velocity is the rate of change of displacement with time. It is a vector quantity measured in meters per second (m/s).

Average speed = Total distance / Total time
Average velocity = Total displacement / Total time

Example 8.2

A car travels 120 km in 2 hours. Calculate its average speed.

Solution:

Average speed = Total distance / Total time = 120 km / 2 h = 60 km/h

Acceleration

Acceleration is the rate of change of velocity with time. It is a vector quantity measured in meters per second squared (m/s²).

Acceleration (a) = Change in velocity / Time taken = (v - u) / t
Where:
v = final velocity
u = initial velocity
t = time

Example 8.3

A car accelerates from 20 m/s to 30 m/s in 5 seconds. Calculate its acceleration.

Solution:

a = (v - u) / t = (30 m/s - 20 m/s) / 5 s = 10 m/s / 5 s = 2 m/s²

Equations of Linear Motion

The following equations describe the motion of objects moving with constant acceleration:

1. v = u + at
2. s = ut + ½at²
3. v² = u² + 2as
4. s = ½(u + v)t

Where:
u = initial velocity
v = final velocity
a = acceleration
s = displacement
t = time

Example 8.4

A car starts from rest and accelerates uniformly at 4 m/s² for 10 seconds. Calculate:

(a) The final velocity

(b) The distance traveled

Solution:

Given: u = 0 m/s, a = 4 m/s², t = 10 s

(a) v = u + at = 0 + (4)(10) = 40 m/s

(b) s = ut + ½at² = 0 + ½(4)(10)² = 2 × 100 = 200 m

Motion Under Gravity

Objects moving under the influence of gravity experience a constant acceleration. On Earth, this acceleration is approximately 9.8 m/s² downward, often rounded to 10 m/s² for simplicity in calculations.

Example 8.5

A ball is dropped from a height of 80 m. Calculate:

(a) The time taken to reach the ground

(b) The velocity with which it hits the ground

Solution:

Given: u = 0 m/s, s = 80 m, a = 10 m/s²

(a) s = ut + ½at² → 80 = 0 + ½(10)t² → 80 = 5t² → t² = 16 → t = 4 s

(b) v = u + at = 0 + (10)(4) = 40 m/s

Activity 8.1

Aim: To measure the speed of a moving object

Materials: Stopwatch, measuring tape, toy car, ramp

Procedure:

1. Set up a ramp and mark two points A and B at a known distance apart.
2. Release the toy car from the top of the ramp.
3. Start the stopwatch when the car passes point A and stop it when it passes point B.
4. Record the time taken and calculate the speed.
5. Repeat the experiment three times and calculate the average speed.

Questions:

(a) Why is it important to repeat the experiment multiple times?

(b) How does the angle of the ramp affect the speed of the car?

Task 8.1

Observe different types of motion in your environment (e.g., people walking, vehicles moving, birds flying). Classify them as uniform motion, accelerated motion, or decelerated motion. Record your observations and share them with your classmates.

Chapter Summary

1. Motion is the change in position of an object with respect to time.
2. Distance is the total path length traveled, while displacement is the straight-line distance between initial and final positions with direction.
3. Speed is the rate of change of distance, while velocity is the rate of change of displacement.
4. Acceleration is the rate of change of velocity with time.
5. The equations of linear motion describe the relationship between displacement, velocity, acceleration, and time for objects moving with constant acceleration.
6. Objects moving under gravity experience a constant acceleration of approximately 10 m/s² downward.
7. Understanding motion helps us analyze and predict the behavior of moving objects in various situations.

Chapter Nine: Work, Energy, and Power

Introduction

Work, energy, and power are fundamental concepts in physics that help us understand how forces cause changes in our world. From lifting objects to operating machines, these concepts explain the transfer and transformation of energy in various forms. In this chapter, you will learn about work, different forms of energy, energy transformations, and power. The competencies developed will enable you to analyze energy usage in daily life and understand the principles behind various machines and devices.

Think: How would our daily lives be different without the ability to transfer and transform energy?

Concept of Work

In physics, work is done when a force causes an object to move in the direction of the force. Work is only done when there is movement in the direction of the applied force.

Work (W) = Force (F) × Distance (d) × cosθ
W = F × d × cosθ

Where:
W = Work done (in joules, J)
F = Force applied (in newtons, N)
d = Distance moved in the direction of force (in meters, m)
θ = Angle between the force and direction of motion

Example 9.1

A person pushes a box with a force of 50 N over a distance of 10 m in the same direction as the force. Calculate the work done.

Solution:

W = F × d = 50 N × 10 m = 500 J

Concept of Energy

Energy is the capacity to do work. It exists in various forms and can be transformed from one form to another. The SI unit of energy is the joule (J).

Forms of Energy

Kinetic Energy

Energy possessed by moving objects

KE = ½ × m × v²

Potential Energy

Stored energy due to position

PE = m × g × h

Chemical Energy

Energy stored in chemical bonds

Heat Energy

Energy due to temperature differences

Light Energy

Energy carried by light waves

Electrical Energy

Energy from moving electric charges

Example 9.2

Calculate the kinetic energy of a 2 kg object moving at 5 m/s.

Solution:

KE = ½ × m × v² = ½ × 2 kg × (5 m/s)² = ½ × 2 × 25 = 25 J

Energy Transformations

Energy can change from one form to another. The total energy in a closed system remains constant according to the law of conservation of energy.

Common Energy Transformations

Chemical → Electrical → Light + Heat (Battery in a flashlight)

Potential → Kinetic (Falling object)

Electrical → Kinetic (Electric motor)

Light → Chemical (Photosynthesis)

Concept of Power

Power is the rate at which work is done or energy is transferred. It measures how quickly work is completed.

Power (P) = Work done (W) / Time taken (t)
P = W / t

The SI unit of power is the watt (W), where 1 watt = 1 joule/second.

Example 9.3

A student does 600 J of work in 10 seconds. Calculate the power.

Solution:

P = W / t = 600 J / 10 s = 60 W

Different Units of Power

Unit	Symbol	Equivalent in Watts
Watt	W	1 J/s
Kilowatt	kW	1,000 W
Megawatt	MW	1,000,000 W
Horsepower	hp	746 W

Activity 9.1

Aim: To demonstrate energy transformations

Materials: Battery, wires, small bulb, switch

Procedure:

1. Connect the battery, wires, bulb, and switch to make a simple circuit.
2. Close the switch and observe what happens.
3. Identify the energy transformations taking place.
4. Touch the bulb carefully after it has been on for a while and note your observation.

Questions:

(a) What forms of energy are produced when the circuit is closed?

(b) Why does the bulb become warm after being on for some time?

(c) What is the original source of energy in this system?

Activity 9.2

Aim: To calculate the power of different activities

Materials: Stopwatch, stairs, weighing scale

Procedure:

1. Measure your mass using the weighing scale.
2. Measure the height of a flight of stairs.
3. Time how long it takes to run up the stairs.
4. Calculate the work done and power developed.
5. Repeat walking up the stairs and compare the power.

Questions:

(a) Why is more power developed when running compared to walking?

(b) How could you increase the power developed in this activity?

Task 9.1

Identify five different appliances in your home and complete the following table:

Appliance	Energy Input	Useful Energy Output	Waste Energy Output
Example: Electric bulb	Electrical energy	Light energy	Heat energy
1.
2.
3.
4.
5.

Task 9.2

Investimate the power ratings of different electrical appliances in your home. Create a table showing the appliance, its power rating in watts, and estimate how much it would cost to run each appliance for one hour (assuming electricity costs Tsh 200 per kWh).

Chapter Summary

1. Work is done when a force causes displacement in the direction of the force (W = F × d).
2. Energy is the capacity to do work and exists in various forms including kinetic, potential, chemical, heat, light, and electrical energy.
3. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
4. Kinetic energy is the energy of moving objects (KE = ½mv²).
5. Potential energy is stored energy due to position (PE = mgh).
6. Power is the rate of doing work or transferring energy (P = W/t).
7. The SI unit of work and energy is the joule (J), while the SI unit of power is the watt (W).
8. Understanding work, energy, and power helps us analyze and improve the efficiency of machines and processes in daily life.

Chapter Ten: Simple Machines

Introduction

Simple machines are basic mechanical devices that make work easier by changing the magnitude or direction of a force. They are the building blocks of more complex machines and have been used since ancient times. In this chapter, you will learn about different types of simple machines, their mechanical advantage, velocity ratio, efficiency, and applications in daily life. The competencies developed will enable you to identify simple machines in your environment and understand how they make work easier.

Think: How would we perform everyday tasks without simple machines like levers, pulleys, and inclined planes?

What are Simple Machines?

Simple machines are devices that require the application of a single force to do work. They make tasks easier by:

• Changing the magnitude of a force
• Changing the direction of a force
• Changing the speed of work
• Transferring force from one point to another

Types of Simple Machines

There are six basic types of simple machines:

1. Lever

A rigid bar that rotates around a fixed point called a fulcrum.

Mechanical Advantage = Effort Arm / Load Arm

Examples: Seesaw, crowbar, scissors, bottle opener

2. Pulley

A wheel with a grooved rim that a rope or cable passes through.

Mechanical Advantage = Number of supporting ropes

Examples: Flagpole, window blinds, crane systems

3. Inclined Plane

A sloping surface that reduces the force needed to lift objects.

Mechanical Advantage = Length / Height

Examples: Ramps, stairs, sloping roads

4. Wheel and Axle

A larger wheel attached to a smaller axle that rotate together.

Mechanical Advantage = Radius of wheel / Radius of axle

Examples: Doorknob, steering wheel, water faucet

5. Screw

An inclined plane wrapped around a cylinder.

Mechanical Advantage = Circumference / Pitch

Examples: Screws, bolts, jar lids, spiral staircase

6. Wedge

Two inclined planes joined back to back.

Mechanical Advantage = Length / Thickness

Examples: Knife, axe, doorstop, needle

Key Concepts

Mechanical Advantage (MA)

The ratio of the load (output force) to the effort (input force).

MA = Load (L) / Effort (E)

Velocity Ratio (VR)

The ratio of the distance moved by the effort to the distance moved by the load.

VR = Distance moved by effort / Distance moved by load

Efficiency

The ratio of useful work output to work input, expressed as a percentage.

Efficiency = (Work output / Work input) × 100%
Efficiency = (MA / VR) × 100%

Example 10.1

A machine requires an effort of 50 N to lift a load of 200 N. Calculate the mechanical advantage.

Solution:

MA = Load / Effort = 200 N / 50 N = 4

This means the machine multiplies the effort by 4 times.

Example 10.2

An inclined plane is 6 m long and 2 m high. Calculate its mechanical advantage.

Solution:

MA = Length / Height = 6 m / 2 m = 3

Detailed Study of Each Simple Machine

Levers

Levers are classified into three classes based on the relative positions of the fulcrum, load, and effort:

Class	Fulcrum Position	Mechanical Advantage	Examples
First Class	Between load and effort	Can be >1, =1, or <1	Seesaw, scissors, crowbar
Second Class	At one end, load between fulcrum and effort	Always >1	Wheelbarrow, bottle opener, nutcracker
Third Class	At one end, effort between fulcrum and load	Always <1	Tweezers, fishing rod, human arm

Pulleys

Pulleys are classified into three types:

• Fixed Pulley: Changes direction of force only (MA = 1)
• Movable Pulley: Multiplies force (MA = 2)
• Block and Tackle: Combination of fixed and movable pulleys (MA = number of supporting ropes)

Activity 10.1

Aim: To investigate the mechanical advantage of different levers

Materials: Meter rule, spring balance, standard masses, fulcrum stand

Procedure:

1. Set up a first-class lever using a meter rule as the lever and a stand as the fulcrum.
2. Place a 100 g mass (load) on one side of the fulcrum.
3. Use a spring balance to measure the effort needed to balance the load at different distances from the fulcrum.
4. Record your observations and calculate the mechanical advantage for each setup.
5. Repeat for second-class and third-class lever arrangements.

Questions:

(a) Which class of lever gave the highest mechanical advantage?

(b) How does the position of the fulcrum affect the mechanical advantage?

(c) Why are third-class levers useful even though they have MA < 1?

Activity 10.2

Aim: To demonstrate the working of different pulley systems

Materials: Pulleys, string, spring balance, masses

Procedure:

1. Set up a single fixed pulley and measure the effort needed to lift a known load.
2. Set up a single movable pulley and measure the effort needed.
3. Set up a block and tackle system with multiple pulleys.
4. Compare the mechanical advantages of each system.

Questions:

(a) What advantage does a fixed pulley provide?

(b) How does a movable pulley reduce the effort needed?

(c) What is the relationship between the number of pulleys and mechanical advantage?

Compound Machines

Compound machines are made by combining two or more simple machines. Most modern machines are compound machines.

Examples of Compound Machines

• Bicycle: Lever (brakes), wheel and axle (wheels), pulley (chain system)
• Car jack: Lever and screw
• Scissors: Two first-class levers and a wedge
• Clock: Wheel and axle, lever, screw

Task 10.1

Identify and list at least ten simple machines in your home or school environment. For each machine, identify:

1. The type of simple machine
2. Its class (for levers)
3. How it makes work easier
4. What would be different if it weren't available

Task 10.2

Design a simple machine that could help solve a problem in your community. Your design should include:

• A clear description of the problem
• A sketch of your machine
• Identification of the simple machines used
• Explanation of how it works
• Estimation of its mechanical advantage

Chapter Summary

1. Simple machines are basic devices that make work easier by changing the magnitude or direction of a force.
2. The six simple machines are: lever, pulley, inclined plane, wheel and axle, screw, and wedge.
3. Mechanical Advantage (MA) is the ratio of load to effort and indicates how much a machine multiplies force.
4. Velocity Ratio (VR) is the ratio of distance moved by effort to distance moved by load.
5. Efficiency measures how well a machine converts input work to useful output work.
6. Levers are classified into three classes based on the relative positions of fulcrum, load, and effort.
7. Pulleys can be fixed, movable, or combined in block and tackle systems.
8. Compound machines combine two or more simple machines to perform complex tasks.
9. Simple machines are found everywhere in daily life and have been essential to human technological development.

Chapter Eleven: Light Energy

Introduction

Light is a form of energy that enables us to see the world around us. It travels in straight lines and exhibits various interesting properties and behaviors. From the colors of a rainbow to the formation of shadows, light plays a crucial role in our daily lives. In this chapter, you will learn about the nature of light, its properties, reflection, refraction, and the formation of images by mirrors and lenses. The competencies developed will enable you to understand optical phenomena and apply this knowledge in practical situations.

Think: How would our world be different if light didn't travel in straight lines or if we couldn't see colors?

Nature of Light

Light is a form of electromagnetic radiation that can be detected by the human eye. It exhibits both wave-like and particle-like properties.

Sources of Light

• Natural Sources: Sun, stars, fireflies
• Artificial Sources: Light bulbs, candles, LEDs
• Luminous Objects: Emit their own light
• Non-luminous Objects: Reflect light from other sources

Properties of Light

• Travels in straight lines
• Can be reflected
• Can be refracted
• Can be dispersed
• Travels very fast (300,000 km/s in vacuum)

Rectilinear Propagation of Light

Light travels in straight lines. This property explains:

• Formation of shadows
• Eclipses
• Working of pinhole cameras

Example 11.1

Explain why we can see a light source through a straight pipe but not through a bent pipe.

Solution:

Light travels in straight lines. In a straight pipe, light can travel directly from the source to our eyes. In a bent pipe, the light rays cannot bend to reach our eyes.

Reflection of Light

Reflection occurs when light bounces off a surface. There are two main types of reflection:

Type	Surface	Image Formation	Examples
Regular Reflection	Smooth, polished	Clear images	Mirrors, still water
Diffuse Reflection	Rough, uneven	No clear images	Paper, walls, wood

Laws of Reflection

1. The incident ray, reflected ray, and normal all lie in the same plane
2. Angle of incidence (i) = Angle of reflection (r)

Reflection Diagram

Incident ray → Normal → Reflected ray

Angle i = Angle r

Types of Mirrors

Plane Mirrors

• Flat reflecting surface
• Images are virtual and erect
• Image size equals object size
• Image is laterally inverted
• Image distance equals object distance

Spherical Mirrors

• Concave Mirror: Curved inward
• Convex Mirror: Curved outward
• Used in various optical devices
• Form real or virtual images

Refraction of Light

Refraction is the bending of light when it passes from one medium to another due to change in speed.

Refractive index (n) = Speed of light in vacuum / Speed of light in medium

Laws of Refraction

1. The incident ray, refracted ray, and normal all lie in the same plane
2. Snell's Law: n₁sinθ₁ = n₂sinθ₂

Examples of Refraction:

• Straw appearing bent in water
• Twinkling of stars
• Formation of rainbows
• Working of lenses

Lenses

Lenses are transparent materials with curved surfaces that refract light to form images.

Lens Type	Shape	Light Behavior	Image Formation	Uses
Convex Lens	Thicker in center	Converges light	Real or virtual images	Magnifying glass, cameras
Concave Lens	Thinner in center	Diverges light	Always virtual images	Spectacles, peepholes

Dispersion of Light

Dispersion is the separation of white light into its constituent colors.

Visible Spectrum

Red - Orange - Yellow - Green - Blue - Indigo - Violet

(ROY G BIV)

Rainbow Formation: Raindrops act as prisms that disperse sunlight into the colors of the spectrum.

Activity 11.1

Aim: To demonstrate the rectilinear propagation of light

Materials: Three cardboards with small holes, candle, stands

Procedure:

1. Set up three cardboards with small holes in a straight line.
2. Place a candle at one end.
3. Look through the holes from the other end.
4. Observe if you can see the candle flame.
5. Move one cardboard slightly and observe what happens.

Questions:

(a) Why can you see the flame when the holes are aligned?

(b) What happens when one cardboard is moved out of alignment?

(c) What does this tell us about how light travels?

Activity 11.2

Aim: To study reflection in plane mirrors

Materials: Plane mirror, protractor, ruler, pins, drawing board

Procedure:

1. Place a plane mirror vertically on a drawing board.
2. Draw a line along the mirror's reflecting surface.
3. Place two pins in front of the mirror (object pins).
4. Locate the images of the pins by placing two other pins (image pins).
5. Measure the angles of incidence and reflection.

Questions:

(a) What is the relationship between the angle of incidence and reflection?

(b) How does the image distance compare to the object distance?

(c) What are the characteristics of the image formed?

Activity 11.3

Aim: To demonstrate dispersion of light

Materials: Glass prism, white screen, sunlight or bright light source

Procedure:

1. Allow a narrow beam of white light to fall on a glass prism.
2. Observe the light coming out of the prism.
3. Place a white screen to catch the spectrum.
4. Note the sequence of colors formed.

Questions:

(a) What colors do you observe in the spectrum?

(b) Which color is deviated the most? Which the least?

(c) What does this tell us about white light?

Human Eye and Vision

The human eye is a natural optical instrument that uses refraction to form images on the retina.

Parts of the Eye:

• Cornea: Transparent front part that refracts light
• Lens: Further refracts light to focus on retina
• Retina: Light-sensitive layer where images form
• Iris: Controls amount of light entering
• Pupil: Opening that allows light to enter

Task 11.1

Investigate the uses of different types of mirrors and lenses in your environment. Create a table showing:

Device/Application	Type of Mirror/Lens	Purpose	How it Works
Example: Car side mirror	Convex mirror	Wide field of view	Diverges light to show larger area
1.
2.
3.
4.
5.

Task 11.2

Design a simple periscope or kaleidoscope using mirrors and cardboard. Your design should include:

• A labeled diagram showing light path
• List of materials needed
• Step-by-step construction procedure
• Explanation of how it works using principles of reflection

Chapter Summary

1. Light is a form of energy that travels in straight lines at very high speed.
2. Light exhibits rectilinear propagation, which explains shadows and pinhole cameras.
3. Reflection occurs when light bounces off surfaces, following the laws of reflection.
4. Plane mirrors form virtual, erect images that are laterally inverted.
5. Spherical mirrors (concave and convex) form different types of images based on object position.
6. Refraction is the bending of light when it passes between different media.
7. Lenses use refraction to form images - convex lenses converge light, concave lenses diverge light.
8. Dispersion is the separation of white light into its constituent colors (spectrum).
9. The human eye is a natural optical instrument that forms images using refraction.
10. Understanding light properties helps us design optical instruments and explain natural phenomena.

Chapter Twelve: Sound Energy

Introduction

Sound is a form of energy that we experience through our sense of hearing. It plays a crucial role in communication, entertainment, and our understanding of the environment. From music to warning signals, sound helps us interpret the world around us. In this chapter, you will learn about the production, propagation, and properties of sound, as well as how we hear and use sound in various applications. The competencies developed will enable you to understand acoustic phenomena and apply this knowledge in daily life situations.

Think: How would our world be different if sound couldn't travel through air, or if we couldn't control the volume of sounds around us?

Nature of Sound

Sound is a mechanical wave that results from vibrating objects and requires a medium (solid, liquid, or gas) to travel through.

Production of Sound

• Produced by vibrating objects
• Vibrations create pressure waves
• Examples: Vocal cords, guitar strings, speakers
• No vibration = No sound

Propagation of Sound

• Requires a material medium
• Cannot travel through vacuum
• Travels as longitudinal waves
• Speed depends on the medium

Sound Wave Propagation

Compression → Rarefaction → Compression

Characteristics of Sound Waves

Amplitude

• Maximum displacement from equilibrium
• Determines loudness
• Measured in decibels (dB)
• Greater amplitude = Louder sound

Frequency

• Number of vibrations per second
• Determines pitch
• Measured in Hertz (Hz)
• Higher frequency = Higher pitch

Wavelength

• Distance between successive compressions
• Inversely related to frequency
• Measured in meters (m)
• λ = v/f (wavelength = speed/frequency)

Speed of sound (v) = Frequency (f) × Wavelength (λ)

Speed of Sound in Different Media

Medium	Speed (m/s)	Reason
Air (20°C)	343	Particles far apart
Water	1,480	Particles closer together
Steel	5,100	Particles very close
Wood	3,300-4,500	Depends on type

Audible, Infrasonic, and Ultrasonic Sounds

Frequency Ranges

Type	Frequency Range	Human Perception	Examples
Infrasonic	Below 20 Hz	Cannot hear	Earthquakes, elephant communication
Audible	20 Hz - 20,000 Hz	Can hear	Human speech, music
Ultrasonic	Above 20,000 Hz	Cannot hear	Dolphin communication, medical imaging

Reflection of Sound (Echo)

Sound waves can bounce off surfaces, creating echoes. This principle is used in various applications.

Distance to reflecting surface = (Speed of sound × Time) ÷ 2

Example 12.1

A person claps hands and hears an echo after 3 seconds. If the speed of sound is 340 m/s, how far is the reflecting surface?

Solution:

Distance = (340 m/s × 3 s) ÷ 2 = 510 m

Human Ear and Hearing

The human ear is a remarkable organ that detects and interprets sound waves.

Parts of the Ear:

• Outer Ear: Collects sound waves (pinna and ear canal)
• Middle Ear: Amplifies sound (eardrum and ossicles)
• Inner Ear: Converts sound to nerve signals (cochlea)

Applications of Sound

Medical Applications

• Ultrasound imaging
• Breaking kidney stones
• Physical therapy
• Hearing aids

Industrial Applications

• Sonar for navigation
• Quality control testing
• Cleaning delicate equipment
• Distance measurement

Entertainment & Communication

• Music and audio systems
• Telephones and radios
• Public address systems
• Musical instruments

Noise Pollution

Unwanted or excessive sound that can have harmful effects on human health and the environment.

Source	Sound Level (dB)	Effects
Whisper	30	Comfortable
Normal conversation	60	Comfortable
Heavy traffic	85	Hearing damage over time
Rock concert	110	Risk of immediate damage
Jet engine	140	Pain and immediate damage

Activity 12.1

Aim: To demonstrate that sound requires a medium to travel

Materials: Bell jar, vacuum pump, electric bell, battery

Procedure:

1. Place an electric bell inside a bell jar.
2. Connect the bell to a battery so it rings.
3. Listen to the sound clearly.
4. Use a vacuum pump to remove air from the bell jar.
5. Observe what happens to the sound as air is removed.

Questions:

(a) What happens to the sound as air is removed from the jar?

(b) Why does the sound become fainter?

(c) What conclusion can you draw about sound propagation?

Activity 12.2

Aim: To study the relationship between length and pitch

Materials: Ruler, string, weights, retort stand

Procedure:

1. Set up a string suspended from a retort stand with a weight at the end.
2. Pluck the string and listen to the pitch.
3. Change the length of the vibrating string by moving the point of suspension.
4. Pluck the string again and note the change in pitch.
5. Record your observations for different lengths.

Questions:

(a) What happens to the pitch when the string length increases?

(b) What happens to the pitch when the string length decreases?

(c) How do musical instruments use this principle?

Activity 12.3

Aim: To measure the speed of sound

Materials: Two wooden blocks, stopwatch, measuring tape

Procedure:

1. Stand at least 100 meters from a large building or cliff.
2. Clap two wooden blocks together loudly.
3. Start the stopwatch when you clap and stop it when you hear the echo.
4. Record the time taken for the echo to return.
5. Calculate the speed of sound using the formula.
6. Repeat several times and take average.

Questions:

(a) Why is it important to stand far from the reflecting surface?

(b) How accurate is your measurement compared to the known value?

(c) What factors might affect your results?

Task 12.1

Investigate sound pollution in your school or neighborhood. Create a report that includes:

• Identification of major noise sources
• Estimation of noise levels (using reference table)
• Times when noise is most problematic
• Effects on people in the area
• Suggestions for reducing noise pollution

Task 12.2

Design and construct a simple musical instrument that can produce different pitches. Your project should include:

• A working instrument made from local materials
• Explanation of how it produces sound
• How different pitches are created
• Demonstration of playing a simple tune

Chapter Summary

1. Sound is a form of energy produced by vibrating objects and requires a medium to travel.
2. Sound travels as longitudinal waves consisting of compressions and rarefactions.
3. The characteristics of sound include amplitude (loudness), frequency (pitch), and wavelength.
4. Speed of sound depends on the medium and is fastest in solids, followed by liquids, then gases.
5. Human hearing range is approximately 20 Hz to 20,000 Hz.
6. Sound can be reflected (echo), absorbed, or transmitted when it encounters obstacles.
7. The human ear converts sound waves into nerve signals that the brain interprets.
8. Sound has numerous applications in medicine, industry, communication, and entertainment.
9. Noise pollution is excessive or unwanted sound that can harm human health and the environment.
10. Understanding sound properties helps us design better acoustic environments and protect our hearing.

Chapter Thirteen: Magnetism

Introduction

Magnetism is a fundamental force of nature that has fascinated humans for centuries. From ancient compasses to modern electric motors, magnetic principles have been crucial to technological development. Magnets are found in numerous everyday devices and play a vital role in many industrial processes. In this chapter, you will learn about magnetic materials, properties of magnets, magnetic fields, and the Earth's magnetism. The competencies developed will enable you to understand magnetic phenomena and apply this knowledge in practical situations.

Think: How would navigation be different without magnets? What modern devices wouldn't work if magnetism didn't exist?

What is Magnetism?

Magnetism is a physical phenomenon produced by the motion of electric charge, resulting in attractive and repulsive forces between objects.

Magnetic Materials

• Ferromagnetic: Strongly attracted to magnets (iron, nickel, cobalt)
• Paramagnetic: Weakly attracted to magnets (aluminum, platinum)
• Diamagnetic: Weakly repelled by magnets (copper, silver, gold)
• Non-magnetic: No interaction with magnets (wood, plastic, paper)

Natural vs Artificial Magnets

• Natural Magnets: Found in nature (magnetite/lodestone)
• Artificial Magnets: Man-made magnets
• Permanent Magnets: Retain magnetism
• Temporary Magnets: Lose magnetism easily

Properties of Magnets

Magnetic Poles

• Every magnet has two poles: North and South
• Poles cannot be isolated
• Like poles repel, unlike poles attract
• Magnetic strength is greatest at poles

Magnetic Force

• Invisible force field around magnets
• Decreases with distance
• Can act through some materials
• Follows inverse square law

Magnetic Field

• Region around magnet where force acts
• Shown by magnetic field lines
• Lines never cross each other
• Direction from North to South pole

N S

↔

N S

Magnetic Field Pattern

Field lines emerge from North pole and enter South pole

Magnetic Poles and Their Behavior

Pole Combination	Force	Description
North - North	Repulsion	Like poles push away from each other
South - South	Repulsion	Like poles push away from each other
North - South	Attraction	Unlike poles pull toward each other

Magnetic Field Lines

Magnetic field lines are imaginary lines that show the direction and strength of a magnetic field.

Properties of Magnetic Field Lines:

• Never intersect each other
• Form continuous closed loops
• Direction is from North to South outside the magnet
• Closer lines indicate stronger magnetic field
• Density decreases with distance from magnet

Earth's Magnetism

The Earth behaves like a giant magnet with magnetic poles near the geographic poles.

Magnetic Elements

• Magnetic Declination: Angle between geographic and magnetic meridian
• Magnetic Inclination: Angle with horizontal (dip angle)
• Horizontal Component: Component of Earth's magnetic field

Evidence of Earth's Magnetism

• Compass needle alignment
• Aurora phenomena
• Magnetic rock orientation
• Animal migration patterns

Making and Destroying Magnets

Method	Process	Result
Single Touch Method	Stroke object with one pole of magnet	Weak magnet
Double Touch Method	Stroke with both poles from center outward	Stronger magnet
Electrical Method	Place in solenoid with DC current	Strong permanent magnet
Destroying Magnetism	Heating, hammering, or AC current	Loss of magnetic properties

Applications of Magnets

Everyday Applications

• Compasses for navigation
• Magnetic door catches
• Refrigerator magnets
• Magnetic toys and games
• Credit card strips

Industrial Applications

• Electric motors and generators
• Magnetic separation
• MRI machines in medicine
• Magnetic levitation trains
• Speakers and microphones

Electromagnetic Applications

• Transformers
• Relays and switches
• Electric bells
• Induction cookers
• Magnetic cranes

Electromagnetism

When electric current flows through a conductor, it produces a magnetic field around it.

Magnetic field around straight conductor follows Right-Hand Rule

Factors Affecting Electromagnet Strength:

• Number of turns in the coil
• Current flowing through the coil
• Nature of the core material
• Cross-sectional area of the core

Example 13.1

How can you increase the strength of an electromagnet?

Solution:

To increase the strength of an electromagnet, you can:

• Increase the number of turns in the coil
• Increase the current flowing through the coil
• Use a soft iron core
• Wind the coil more tightly

Activity 13.1

Aim: To identify magnetic and non-magnetic materials

Materials: Bar magnet, various objects (iron nail, copper wire, aluminum foil, steel spoon, plastic ruler, wood, nickel coin)

Procedure:

1. Bring a bar magnet close to each object one by one.
2. Observe if there is any attraction.
3. Record which objects are attracted and which are not.
4. Classify the materials as magnetic or non-magnetic.

Questions:

(a) Which materials were attracted to the magnet?

(b) Which materials showed no attraction?

(c) What common property do magnetic materials share?

Activity 13.2

Aim: To study the properties of magnetic poles

Materials: Two bar magnets, thread, stand

Procedure:

1. Suspend one magnet from a stand using thread.
2. Bring the North pole of the second magnet close to the North pole of the suspended magnet.
3. Observe what happens.
4. Repeat with South-South and North-South combinations.
5. Record your observations.

Questions:

(a) What happens when like poles are brought together?

(b) What happens when unlike poles are brought together?

(c) What law of magnetism do these observations demonstrate?

Activity 13.3

Aim: To make a simple electromagnet

Materials: Iron nail, insulated copper wire, battery, paper clips, switch

Procedure:

1. Wrap the copper wire tightly around the iron nail (30-40 turns).
2. Connect the ends of the wire to a battery through a switch.
3. Close the switch to complete the circuit.
4. Bring the nail close to paper clips and observe.
5. Open the switch and observe what happens.
6. Try increasing the number of turns and observe the effect.

Questions:

(a) When does the nail become magnetic?

(b) What happens when the circuit is broken?

(c) How does increasing the number of turns affect the strength?

Task 13.1

Investigate the uses of magnets in your home and school. Create a table showing:

Device/Application	Type of Magnet Used	Purpose	How it Works
Example: Refrigerator door	Permanent magnet	Keep door closed	Attraction between magnet and metal strip
1.
2.
3.
4.
5.

Task 13.2

Design and construct a simple magnetic compass. Your project should include:

• A working compass that points North-South
• Explanation of how it works using Earth's magnetism
• Testing in different locations
• Comparison with commercial compass

Chapter Summary

1. Magnetism is a fundamental force with attractive and repulsive properties.
2. Materials can be classified as ferromagnetic, paramagnetic, diamagnetic, or non-magnetic.
3. Every magnet has two poles (North and South) and like poles repel while unlike poles attract.
4. Magnetic field lines show the direction and strength of magnetic fields.
5. The Earth behaves as a giant magnet with magnetic poles near the geographic poles.
6. Magnets can be made by stroking, electrical methods, or induction.
7. Magnetism can be destroyed by heating, hammering, or using AC current.
8. Electromagnets are temporary magnets created by electric current flowing through a coil.
9. Magnets have numerous applications in daily life, industry, and technology.
10. Understanding magnetism helps us develop new technologies and understand natural phenomena.

Chapter Fourteen: Static Electricity

Introduction

Static electricity is a fascinating phenomenon that we encounter in our daily lives, from the shock we feel when touching a metal object after walking on carpet to the way a balloon sticks to a wall after being rubbed on hair. This form of electricity involves stationary electric charges and their effects. In this chapter, you will learn about electric charges, charging methods, conductors and insulators, and the applications of static electricity. The competencies developed will enable you to understand and explain common electrostatic phenomena.

Think: Why do you sometimes get a shock when touching metal objects? How can a balloon stick to a wall without any glue?

What is Static Electricity?

Static electricity refers to the buildup of electric charge on the surface of objects. These charges remain stationary until they find a path to discharge.

Basic Concepts

• Electric charge: Fundamental property of matter
• Two types: Positive and negative
• Like charges repel, unlike charges attract
• Measured in Coulombs (C)

Charge Carriers

• Protons: Positive charge
• Electrons: Negative charge
• Neutrons: No charge
• Atoms are normally neutral

Charge Interactions

+

REPEL

+

-

REPEL

-

+

ATTRACT

-

Methods of Charging

Charging by Friction

• Rubbing two different materials
• Electrons transfer from one to another
• Example: Rubbing balloon on hair
• Materials gain opposite charges

Charging by Conduction

• Direct contact between objects
• Charge transfers through touch
• Both objects get same type of charge
• Example: Touching charged rod to metal sphere

Charging by Induction

• No direct contact needed
• Charged object influences nearby objects
• Objects get opposite charges
• Example: Bringing charged rod near electroscope

Triboelectric Series

Materials listed from those that tend to lose electrons (positive) to those that tend to gain electrons (negative):

Material	Charge Tendency
Rabbit fur	Most positive
Glass	Positive
Human hair	Positive
Nylon	Slightly positive
Cotton	Neutral
Wood	Neutral
Amber	Negative
Rubber	Negative
PVC	Most negative

Conductors and Insulators

Property	Conductors	Insulators
Charge Flow	Easy flow of electrons	Very difficult flow
Electron Mobility	Free electrons available	Electrons tightly bound
Examples	Metals (copper, aluminum)	Rubber, plastic, glass
Charging Method	Conduction works well	Friction works well
Charge Distribution	Spread throughout	Remains localized

Electroscope

An electroscope is a device used to detect the presence and type of electric charge.

Working Principle:

• Consists of a metal rod with thin metal leaves
• When charged, leaves repel each other
• Degree of separation indicates charge amount
• Can identify charge type using known charges

Lightning and Thunder

Lightning is a dramatic natural example of static electricity discharge.

Formation Process

• Air currents cause charge separation in clouds
• Positive charges gather at top
• Negative charges gather at bottom
• When voltage is high enough, discharge occurs

Thunder

• Result of rapid air expansion
• Caused by intense heat from lightning
• Sound travels slower than light
• Distance = Time difference × 340 m/s

Example 14.1

If you see lightning and hear thunder 5 seconds later, how far away is the storm?

Solution:

Distance = Speed of sound × Time = 340 m/s × 5 s = 1,700 meters (1.7 km)

Applications of Static Electricity

Industrial Applications

• Electrostatic precipitators (air pollution control)
• Photocopiers and laser printers
• Spray painting (electrostatic painting)
• Sandpaper manufacturing

Everyday Applications

• Static cling in clothing
• Balloon sticking to walls
• Dust attraction to TV/computer screens
• Static electricity in hair

Safety Applications

• Lightning rods
• Static grounding straps
• Antistatic materials
• Humidity control

Dangers and Safety Measures

Hazard	Risk	Prevention
Lightning strikes	Injury or death, fire	Lightning rods, indoor shelter
Fuel handling	Fire or explosion	Grounding, bonding
Electronics damage	Component failure	ESD protection, grounding
Industrial processes	Dust explosions	Humidity control, grounding

Activity 14.1

Aim: To demonstrate charging by friction

Materials: Balloon, wool cloth, small pieces of paper, running water tap

Procedure:

1. Inflate a balloon and tie it closed.
2. Rub the balloon vigorously with a wool cloth for 30 seconds.
3. Bring the charged balloon close to small pieces of paper.
4. Observe what happens.
5. Bring the charged balloon close to a thin stream of running water.
6. Record your observations.

Questions:

(a) What happened to the paper pieces when the charged balloon approached?

(b) What happened to the water stream?

(c) Explain these observations using concepts of static electricity.

Activity 14.2

Aim: To investigate conductors and insulators

Materials: Electroscope, various materials (metal rod, plastic comb, glass rod, copper wire, rubber band, aluminum foil)

Procedure:

1. Charge the electroscope by touching it with a charged rod.
2. Touch each material to the electroscope in turn.
3. Observe if the leaves collapse or remain separated.
4. Record which materials allow charge to flow away.
5. Classify the materials as conductors or insulators.

Questions:

(a) Which materials caused the leaves to collapse quickly?

(b) Which materials had little effect on the leaves?

(c) What property determines whether a material is a conductor or insulator?

Activity 14.3

Aim: To demonstrate charging by induction

Materials: Two metal spheres on insulated stands, charged rod

Procedure:

1. Place two metal spheres touching each other on insulated stands.
2. Bring a negatively charged rod close to one sphere (but don't touch).
3. While the rod is nearby, separate the two spheres.
4. Remove the charged rod.
5. Test the charge on each sphere using an electroscope.
6. Record your observations.

Questions:

(a) What type of charge did each sphere acquire?

(b) Why were the spheres charged even though the rod never touched them?

(c) How is this method different from charging by conduction?

Task 14.1

Investigate static electricity phenomena in your daily life. Create a report that includes:

• At least five different examples of static electricity you observe
• Explanation of how each example occurs
• Materials involved in each case
• Ways to increase or decrease the static effects
• Safety considerations for each situation

Task 14.2

Design and construct a simple electroscope using local materials. Your project should include:

• A working electroscope that can detect charge
• Explanation of how it works
• Demonstration of detecting different types of charges
• Testing with various charged objects
• Suggestions for improving its sensitivity

Chapter Summary

1. Static electricity involves stationary electric charges on object surfaces.
2. There are two types of electric charges: positive and negative.
3. Like charges repel each other, unlike charges attract each other.
4. Charging can occur by friction, conduction, or induction.
5. Conductors allow easy flow of charge, while insulators resist charge flow.
6. An electroscope is used to detect and identify electric charges.
7. Lightning is a natural discharge of static electricity from clouds.
8. Static electricity has many practical applications in industry and daily life.
9. Proper safety measures are necessary when dealing with static electricity.
10. Understanding static electricity helps explain many common phenomena and enables technological applications.