WORK, ENERGY AND POWER

Keywords

• Elastic potential energy
• Gravitational potential energy
• Hooke’s law
• Kinetic energy
• Restoring force

By the end of this chapter, you will be able to:

1. Know that the sun is our major source of energy, and different forms of energy. know that energy can be changed from one form to another, and understand the law of conservation of energy
2. Understand positive and negative effects of solar energy.
3. Understand the difference between renewable and non – renewable energy resources with respect to Uganda.
4. Know and use the relationship between works done, force, distance moved and time taken. (
5. Understand that an object may have energy due to its motion or its position, and change between kinetic and positional potential energy.
6. Know the mathematical relationship between positional potential energy and kinetic energy, and use it in calculations.
7. Understand the meaning of machines and explain how simple machines simplify work.
8. Understand the principles behind the operation of simple machines.

1.1 Concept of work, energy and power

Usually in daily life, to sustain our lives, we must do something so that we get all the needs of life. People normally engage in different activities to earn a living. It is from these activities that work is done. One can say that writing notes in your notebook is doing work. Other activities where work is done in daily life include lifting blocks on a construction site , carrying an object from one point to another , digging on a farm , and many other daily activities we do at home and at school .

From what you already know from your primary school science, one must apply a force to do some work. Therefore, when a force acts upon an object and causes it to move from one place to another, it is said that work is done upon the object.

Work, W, is defined as the product of force and distance moved by its point of application in the direction of the force.

W = F x d, where F is force and d is distance

The SI unit of work is the joule (abbreviated J), force is measured in newtons, N, and distance is measured in meters, m.

 Did you know that the joule is the amount of work done when a force of one newton moves its point of application through a distance of one metre?

Activity 1.1 investigating work

Figure 1.1: People doing communal work

The picture in Figure 1.1 was taken in a certain village in Eastern Uganda. Men and women were digging a trench where piped water would pass.

 Basing on your clear analysis of the picture:

(a) Is there any indicator that these people did some work? Explain your reasoning. (

b) Even from (a) above, how do you know that work is done?

c) Discuss any three scenarios where you (or your friend) performed work.

(d) In daily life, we always do work either for payment or for personal satisfaction. Explain why you think it is important to study work in Physics.

 Example 1.1

(a) How much work is performed when a 50kg crate is pushed through a distance of 15m with a force of 20N, as shown in Figure 1.2?

Answer Using the formula W = F xd – 20N x 15m – 300J

Work against gravity

When a body is lifted vertically upwards, work is done against gravitational force. The gravitational force acting on the body is the weight of the body defined by weight, W – mg, where m is the mass of the body and g is the acceleration due to gravity.

Therefore, the work done to lift a body of mass, m, through a vertical distance, d, is given by:

Work done = weight of body x distance = > Work done = mgd .

Example 1.2

 A crane lifts a heavy stone of 2200kg from a deep hole through a vertical height of 7m from the bottom of the hole. Calculate the work done by the crane.

Answer

Work = weight of the stone x height of the hole

 = mgh

 = (22,000kg) (10ms “) x 7 (m)

= 154,000J

Activity 1.2 Determining work done

Key Question: How is work done?

What you need

• Spring balance, mass hanger, masses of 100g, smooth surface and a metre rule.

 What to do

1. You may attempt this activity as a class or in groups.
2. Place a mass hanger on a smooth table. Attach a spring Energy and balance.
3. Attach / fix the spring balance to the object and pull it while applying a constant force using your hands. Make sure that force is applied parallel to the table.
4. From the spring balance, record the force in newtons that was used to make the object move. (h) In groups, explain what happens to the work done when the force changes.
5. Also, record the distance moved in metres.
6. Calculate the work done, W, by the force you applied.
7. Repeat procedures (a) to (f) for different masses up to 400g and record your observations.
8. In groups, explain what happens to the work done when the force changes

Assessment 1.1

(a) List some situations in which you have seen people at work.

(b)In groups, discuss a situation where work is mechanical.

(c)A learner in a certain secondary school pulls a box of books of mass 50kg. The box is displaced through a distance of 3 metres in the direction of force. What is the work done?

(d) A crane is a machine used to lift heavy objects. One day, it lifts a mass of 500kg through a distance of 12m. Calculate the work done by the crane.

 (e)Present your findings.

1.2 Concept of Energy

 In daily life, one must have energy in order to perform any activity. It is not possible to do anything without energy. Normally we say that we do not have energy to mean that you are not capable of performing any duty. The fact is you can be alive without energy though one may have less energy. Therefore, in order to survive, we need energy. This means that we must have sources of energy and we will discuss some of these sources in this chapter.

Activity 1.3 Discovering energy sources.

In groups, discuss how the following services provide energy as illustrated below

 Figure 1.3: Showing sources of energy.

Study Figure 1.3 and answer the following questions:

(a) What is the major source of energy for all living things indicated in Figure 1.3? Explain your response.

b) What do plants use the energy from the sun for?

c) Imagine that the sun goes down for 7 days, would life be possible? If yes, explain how. If not explain why not and how long you think life would be possible. By

(d) Other than the major source of energy indicated in Figure 1.3, what are other sources of energy in real life?

(e) Are the sources explained in (d) above natural sources or artificial sources or both? Explain how you were able to differentiate the two kinds of sources.

 DID YOU KNOW?

The sun is our single greatest source of energy and that “one hour’s worth of energy from the sun could power the earth for a whole year “?

Energy can be defined as the capacity to do work. It has the same units as work and heat, i.e. joule (J).

There are two kinds of energy sources, namely primary sources and secondary sources?

1.3 Renewable and Non – renewable Energy Sources

Many substances and organisms store energy which can then be used later. We call them energy sources. Energy sources have energy that is stored within them and can be used to make something happen. For example, energy stored in petrol can be used to make a car move.

Since the dawn of humanity people have used different sources of energy to survive , e.g. , wood for cooking and heating , wind and water for milling grain , and solar for lighting fires .

Activity 1.4 Answering questions about renewable and non-renewable energy sources

In groups, interpret the picture shown in Figure 1.4 and answer the questions that follow

Figure 1.4: Energy web

(a) What are some of the energy sources indicated in Figure 1.4?

b) What scientific name can be given to energy sources that:

1. Can be reused?
2. Cannot be reused?

c) Discuss the advantages of those that can be reused over those that cannot be reused. Hydrogen Secondary Energy Sources Energy

d)You have the following energy sources: Biomass, natural gas, hydro energy, oil, coal, thermal, wind, and solar energy.

On a chart, group these energy sources into renewable and non – renewable energy sources. You can use arrow diagrams.

Activity 1.5 Demonstrating renewable and non – renewable energy sources

What you need

• Polyethylene paper, dried wood, paraffin, source of heat, Manila paper.

What to do

 (a) In groups, burn Manila paper, dried wood and polyethylene paper with paraffin (one at a time).

(b) Observe and discuss the reactions that take place as you burn any of the materials mentioned above.

c) Report your findings on a poster. In your report, include the effects of renewable and non – renewable energy in the environment.

 (d) Discuss ways of conserving energy for the future.

 (e) You may pin your poster in your Physics lab after presenting it to the class for discussion.

In most villages in Uganda, wood is the most commonly used source of energy. This leads to massive destruction of forests and the environment.

The differences between renewable and non – renewable energy sources can be summarized in the table below:

Renewable	Non – renewable
Can be replaced by a natural process in a short period of time or can be recycled.	These are natural resources that either cannot be replaced or may take millions of years to replace by natural processes for example coal and oil.
Can be reused or recycled and used multiple times.	Cannot be reused or recycled.
Some of the examples are: wind energy, solar power, hydroelectricity, geothermal.	Some of the examples are: petrol, coal, natural gas, nuclear energy. Fossil fuels.
Can be replaced by a natural process in a short period of time or can be recycled.	These are natural resources that either cannot be replaced or may take millions of years to replace by natural processes for example coal and oil.
No harm done to the environment because of its	Huge harm done to the environment because of the harmful emissions.

 Types of energy

The types of energy are:

(a) Thermal or heat energy

Temperature is a measure of how much thermal energy a material like steel metal or wood has. The higher the temperature, the faster the molecules are moving around and / or vibrating, that is, the more kinetic and potential energy the molecules have.

Thermal energy (heat and light energy) is the total potential and kinetic energy associated with the particles in a material

 (b) Mechanical energy

• The energy acquired by the objects upon which work is done is known as mechanical energy.
• Thus, mechanical energy is the energy that is possessed by an object due to its motion or due to its position. M
• Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).
• In other words, it describes the energy of an object because of its motion or position, or both.
• Objects have mechanical energy if they are in motion and / or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position). A moving car possesses mechanical energy due to its motion (kinetic energy). A moving baseball possesses mechanical energy due to its high speed (kinetic energy).

 (c) Electrical energy

• Electrical energy is the energy generated by the movement of electrons from one point to another. The movement of charged particles along / through a medium (say wire) constitutes current or electricity. The following are some examples of electrical energy:
• In a car battery, a chemical reaction results in the formation of an electron that possesses the energy to move in an electric. These moving charges provide electrical energy to the circuits in the car
• Lighting during thunderstorm, is an example of electrical energy. What we see as lighting is nothing but electricity discharging in the atmosphere
• Electric eels (snake like fish) generate electrical energy and use against predators for defense
• Metals are good examples of materials where electric energy is highly experienced because their electrons are loosely ached to their atoms and can conduct electric charges

(d) Light energy

• This is the energy that enables us to see
• This is the energy transmitted to the earth from the sun by light (or produced by any glowing object like fireflies)
• It is also produced by glowing objects like the sun, the stars, glowworms, and burning objects

 (e) Sound energy

• This is energy that enables us to hear
• Sound energy is the energy produced by vibrating objects.
• Sound energy depends on the ear getting the vibrations, so the farther the audience is from the source of the sound, the less the vibrations they will hear
• Sound energy travels fastest in solids, followed by in liquids and then finally in air. Sound cannot travel in a vacuum or a free space (without air

(f) Nuclear energy

• Nuclear energy is the energy discharged by nuclear reactions in the process of either fission or fusion,
• In nuclear fusion, smaller nuclei combine to form a larger nucleus
• In nuclear fission, the division of larger nucleus takes place to form smaller nuclei by releasing energy

Research 1.1

Energy sources and their applications

What you need

• Internet, other textbooks.

In groups, discuss practical examples of each of the above types of energy and where they are applied

(g) Solar energy

• As discussed in Activity 1.3, the sun provides us with energy. This energy is called solar energy. Every hour, enough solar energy reaches the earth to meet the world’s energy demand

 Ways of exploiting solar energy

Solar energy is most commonly exploited in three ways. These are explained below:

Photovoltaic systems – for electricity generation: A photovoltaic (PV) system generates electricity directly from solar energy radiation.

The sun creates two main types of energy light and heat – that we can harness for many activities, ranging from photosynthesis in plants to creating electricity with photovoltaic (PV) cells to heating water and food.

We normally exploit solar energy by using solar panels to generate electricity using solar energy. Solar panels are illustrated in Figure 1.5.

Figure 1.5: Solar panels

Solar energy is classified into two types:

(i) Photovoltaic solar technology – to obtain electricity. This system directly converts sunlight into electricity using panels (as illustrated in Figure 1.5). The solar panels are made of semi – conductor cells

 (ii) Solar thermal technology – to obtain heat. This system captures the sun’s heat and converts it into mechanical energy and then electricity. It can be used directly as the sun’s heat or used after being converted into mechanical energy.

 Environmental impact of solar energy

We need energy to do different activities in our society. Man has, therefore, tried to discover different sources of energy and has opted to use solar energy because it seems to be friendly to our environment.

Activity 1.6 discussing the impact of solar energy

 Key Question: Discuss the positive and negative impacts of solar energy.

What you need

• Internet, textbooks.

 What to do

(a) In groups, carry out comprehensive research about the positive and negative effects of solar energy.

(B)Write a comprehensive report about your findings.

(C)Report / discuss / make a presentation about your findings to the whole class. You may use a PowerPoint presentation.

DID YOU KNOW that the earth receives 1.6 x 10 watts of energy from the sun annually, which is 20,000 times the energy requirement of humanity?

Exercise 1.2

 Figure 1.5 shows how energy from the sun is absorbed and reflected by different objects in the solar system. Study it carefully and answer the questions that follow.

Figure 1.5 Energy received from the sun

(a) Does the whole amount of energy from the sun reach the earth’s surface? If no, where does the rest go?

(c) Estimate, in percentage, the amount of solar radiation that is reflected before reaching the earth.

d)  Imagine there was nothing in space / the atmosphere to reflect or absorb solar radiation, would the earth be habitable? Explain.

 Assessment 1.2

(a) What are some of the ways in which humans used renewable resources for energy centuries or even millennia ago?

b) Research on what kind (s) of renewable energy your country Uganda produces.

c) Choose one renewable energy resource. Brainstorm three to five types of jobs in that field.

Mechanical Energy

Scientists classify forms of mechanical energy into two major categories: potential energy and kinetic energy. In other words, mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object. That is E = K.e + Pe

Where E is mechanical energy, Pe is potential energy and K.e is kinetic energy

Potential energy

Potential energy is the energy possessed by an object because of its position in reference to the ground.

A bicycle on top of a hill, a book held over your head, and a stretched spring all have potential energy

Types of potential energy

There are three main types of potential energy and they are:

• Chemical potential energy.
• Elastic potential energy
• Gravitational potential energy.

a) Chemical potential energy

 Consider the ability of your body to do work. The glucose (blood sugar) in your body is said to have “chemical energy” because the glucose releases energy when chemically reacted (combusted) with oxygen. Your muscles use this energy to generate the mechanical force used to do work and also produce heat.

b) Elastic potential energy

The elastic potential energy of the system can be thought of as the energy stored in the deformed spring (one that is either compressed or stretched from its equilibrium position) or a stretched rubber band.

 You may notice that when you stretch a rubber band, it becomes longer. However, when the stretching force is removed, the rubber returns to its original length / size. Thus, the energy stored in this stretched rubber band is elastic potential energy

 c) Gravitational potential energy (potential energy of position)

An object raised to a height has energy due to the position it is in from the ground. An object raised to a higher level has more gravitational potential energy.

The gravitational potential energy, U, of a mass, m, at a height, h is calculated from U = mgh, where g is acceleration due to gravity and its value is 10ms^-2.

Example 1.2

A ball of mass 2kg is kept on a hill of height 3km. Calculate the potential energy possessed by it .

Kinetic energy

Kinetic energy is the energy a body has because of its motion. The kinetic energy equation is given as follows:

Where, E is the kinetic energy, m is the mass of the 2 body and v is the velocity of the body

 Example 1.3

A 145g spear is thrown at a speed of 25m / s to kill a wild animal

1. What is its kinetic energy?
2. How much work was done on the spear to make it reach this speed, if it started from rest?

 (b) Since the initial kinetic energy was zero, the net work done is just equal to the final kinetic energy, 45.3J

Exercise 1.3

Aim: To calculate kinetic energy and velocity of a falling object.

Attempt these questions in pairs.

(a) If you drop a 3kg ball from a height h of 10m, ignoring frictional forces, what is?

The velocity when the ball hits the ground?

The kinetic energy of the body as it hits the ground? Use acceleration due to gravity g = 10m / s²

 (b) Comment on how kinetic energy varies as the body falls under the action of gravity.

 Energy transformation

Have you ever wondered what happens in the following?

• Dropping a stone from a certain height.
• Kicking a ball and it moves from one point to another.
• Switching on lights and torches.
• A solar panel generating electricity.

All the above involve energy transformation. Therefore, energy can be changed from one form to another. The following are some examples of energy transformation in real life.

The sun transforms nuclear energy into heat and light energy.

Our bodies convert chemical energy in our food into mechanical energy for us to move and perform other tasks.

1. An electric fan transforms electrical energy into kinetic energy.

• The chart in Figure 1.6 summarizes some of the energy transformations as indicated by the arrows.

Figure 1.7: Energy transformations

Exercise 1.4 1.

1. Discuss the energy transformations shown in Figure 1.6.
2. Brainstorm, in groups, other energy transformation processes that take place in your daily lives.

Activity 1.7 explaining the energy transformations

What you need

• Internet, textbooks.

What to do

 (a) In groups, explain the energy transformations that take place:

1. At waterfalls.
2. When a diesel generator is used to provide light and heat.
3. When fruits fall from the tree to the ground.

 (b) Communicate your answers to the whole class.

Assessment 1.3

In groups.

 (a) Discuss energy and energy transformations.

(b) Using posters, explain how potential energy is converted into kinetic energy as an object falls

c) Discuss the energy changes that take place as a pendulum swings.

1.4 Conservation of Energy

We know that some trucks use petrol or diesel. For a truck using diesel, for it to move, some diesel must be burnt. When diesel is burnt in a truck’s engine, some of the chemical energy stored in the diesel is converted into kinetic energy of the truck and some is wasted as thermal energy.

 When the truck stops, its kinetic energy is converted into internal energy in the brakes. This causes the temperature of the brakes to increase, and heat energy is released. The outcome is that chemical energy has been converted into heat energy, which goes to the atmosphere and is of no further use. However, the total energy present in the universe has remained constant.

 Activity 1.8  Discussing the conservation of energy

 The picture below was a painting that was designed by an S.2 Fine Art learner. He was told to convey a message to people using his creative drawing. This is what he came up with.

 Figure 1.8: A painting about saving energy

Interpret Figure 1.7 carefully and answer the following questions:

Discuss in groups:

(a) What message is indicated in the painting?

(b) What do you think triggered the learner to have such a painting?

(c) As a change maker in your community, what have you done to save energy in your community?

(d) Do you think in the ecosystem, energy is totally destroyed? Explain your reasoning.

(e)  Suggest other ways of conserving energy.

As discussed, our society needs to find a sustainable energy solution that:

• Fulfills global energy needs in the long term.
• Does not degrade the environment.

Law of conservation of energy

So far, you have learnt about energy transformation. It means energy changes form, as illustrated in Figure 1.8. However, the overall amount of energy is constant. Hence during transformation, energy is conserved.

 Assessment 1.4

In groups, use the internet or other textbooks to state and explain briefly the law of conservation of energy.

ENERGY CONSERVATION

Never confuse the expressions conservation of energy and “energy conservation.  Conservation of energy is a law of nature. Energy conservation, which refers to the wise use of energy resources, is the act of saving energy by reducing the length of use. In other words, to conserve energy, you need to cut back on your usage.

Activity 1.9 Suggesting ways of conserving energy

In groups, suggest different ways man has innovated to save the amount of energy used.

ENERGY STORAGE

Human beings have been looking for a good way to store energy for a long time. One of the major things that have been holding up the development of electric cars is battery technology to store electric energy. There are other technologies that people commonly used to store energy, such as:

(a) Falling weight: You lift the weight to store the energy in it and then let the weight fall to extract the energy

 (b) Repeatable mechanical deformation: This is the idea behind a spring used in a wind – up clock or a rubber band used in a wind – up airplane. You store the energy by bending (deforming) the material in a spring and the material releases the energy as it returns to its origin shape.

 (c) Nature has been storing energy for a long time, and if you want to think about it in this way, gasoline is really a form of stored energy. Plants absorb sunlight and turn it into carbohydrates. Another technique that nature uses to store energy is the use of fat!

(d) You can take energy and split water into its hydrogen and oxygen atoms using electrolysis. By storing the hydrogen and oxygen in tanks, you can later create energy by burning it, or (more efficiently) by running it through a fuel cell.

 (e) You can store heat directly and later convert it (the heat) to another form of energy, like electricity.

 Activity 1.10 Researching and suggesting ways of conserving energy

In groups, using the internet and other sources:

1. Suggest and explain other ways in which energy can be stored

2. How are the ways suggested above useful to the environment and society?

POWER

The term “power “is one that we normally use in our daily life. You will always need a powerful person to accomplish any task.

We all do work but the rate at which that work is done differs. For example, can a person weighing 30kg lift a 50kg bag of sugar at the same rate as a 100kg person?

This is where power comes into play. The one that is heavier is also powerful; can lift a bag of sugar 50kg easily, while the one that is not heavy is less powerful and cannot lift the bag of sugar 50kg easily.

The rate of doing work is called “power” or the rate at which work is done or energy is transferred is called “power”

The SI unit of power is the watt (W) if work done is in joules and time taken is in seconds.

Therefore, the watt is the power developed when 1j of work is done in 1s.

Example 1.4

Shelby does 150J of work to lift a stone in 30 seconds. How much power did Shelby develop to do this work?

1. 4,500W
2. 450W
3. 50W
4. 5W

Activity 1.11: Estimating the power developed by an individual climbing a flight of stairs

What you need

• Stopwatch, weighing machine, tape measure.

What to do

In pairs,

(a) Find a set of stairs that you can safely walk and run up.

(b) Count the number of stairs, measure the vertical height of each stair and then find the total height of the stairs in meters.

 (c) Let one member weigh him / her on a weighing machine and record the weight down.

 Let him / her walk, and then run up the stairs. Using a stopwatch, record the time taken in seconds to walk and run up the stairs, as shown in Figure 1.9.

(d) Calculate the work done in walking and running up the stairs. Let each group member do the activity. Is the work done by different members in walking and running up the stairs the same? Discuss

(e) Calculate the power developed by each individual in walking and running up the stairs. Which one required more power, walking or running up the flight of stairs? Why?

(f) Suggest other scenarios of estimating the power of an individual. Using the instruments stated above, perform one of the suggested scenarios in pairs / groups.

 MACHINES

 From way back, performing work needed a lot of power / strength which a person could not provide to easily perform and finish the work in time. So, using technology, a person innovated the idea of developing something called a machine to help in making work easier.

To understand the idea of a machine very well, study Activity 1.12:

 Activity 1.12 explaining the significance of using a machine

(a) In both cases (A) and (B) of Figure 1.10, the aim is to construct a road. Basing on your analysis, in which case will the road are accomplished in the shortest period of time.

 (b) Explain your answer in (b) above.

(c) From your explanation above, explain the significance of using machines in day – to – day work.

 (d) As a 5.2 learner, where have you used machines to simplify your work? You can give, say, 3 cases

From this discussion, you realize that there are two kinds of machines, i.e., simple and complex machines. Both work in the same way. However, complex machines like bicycles, tractors and others are made up of many simple machines put together and perform work more easily and quickly than simple machines like hoes.

DID YOU KNOW? A machine is an appliance which eases work by using a small force (effort) applied at one point to overcome a large force (load) at another point?

 Activity 1.13 explaining the principles of moments of a force

 In groups, using prior knowledge and the internet, explain the principles of moments of a force; where possible, use diagrams on a poster. Information on moments of force will help you understand machines very well

Terms used in simple machines

When one wants to understand simple machines easily, the following terms must be understood first:

Fulcrum (F), Effort (E) and Load (L).

• Fulcrum (F) is a point on a lever about which the lever turns.
• Effort (E) refers to the force applied on a machine so that it can perform work.
• Load (L) refers to the force (weight) of an object on which the machine has to overcome as it performs work.

1.5 Mechanical Advantage

Mechanical advantage is the ratio of load to effort.

Mechanical advantage has no units because it is a ratio of identical quantities

Example: 1.5

 Determine the value of mechanical advantage if 300 newtons force is required to overcome a load of 700 newtons.

 Mechanical advantage is a measure of how much the machine eases the work for which it is used. The bigger the mechanical advantage, the easier the machine makes the work.

1.6 Efficiency

Note: No machine can ever be more than 100 % efficient because the energy output of the machine can never be more than energy input. Efficiency is a measure of how well a machine works.

 Example 1.6

 An effort of 250N raises a load of 900N through 5m in a machine. If the effort moves through 25m, find:

(a) The useful work done in raising the load.

b) The work done by the effort

c) The efficiency of the machin

Note: If a machine has very light, freely moving parts, its efficiency may be very close to 100 %.

Velocity ratio (VR)

 Velocity ratio is defined as the ratio of the distance moved by the effort (d_E) to the distance moved by the load (dL.)

Activity 1.14 Relating mechanical advantage, velocity ratio and efficiency

 In groups, derive the relationship, Efficiency = VR for a perfect machine. Present you’re working to the rest of the class.

Note:  Efficiency increases as the load increases and efficiency tends to become almost constant with high loads.

Did you know? Machines are classified as either simple or complex machines. Complex machines, like tractors, generators, are made from simple machines like a soda opener, a mit etc. At this level, we shall understand more the principle of simple machines.

1.7 Types of Simple Machines

 

Activity 1.15 Identifying simple machines

 What to do

 In pairs, analyses the different machines shown in Figure 1.11 and state how they are used.

Figure 1.12: Different simple machines

(a) Name each machine shown in the figure above.

 (b) Explain where and how each of the machines is used.

There are six simple machines: pulley, lever, wedge, wheel and axle, inclined plane and screw. However, the wheel – and axle combination is similar in principle to the lever, while the wedge and screw are similar to the inclined plane. Thus, simple machines are only of three categories: the lever, pulley and the inclined plane

 THE LEVER

A lever is a simple machine that makes work easier by applying the principle of moments; it involves moving a load around a pivot (fulcrum) using an effort.

A lever is a rigid bar that rests on a support called a fulcrum. It is used to lift or move loads. Many of our basic tools use levers, including a pair of scissors, pliers, claw hammer, nut crackers and tongs.

Activity 1.16 Classifying different machines we use at home

 What you need

• Pair of scissors, wheelbarrow, hammer and spanner.

What to do

 (a) Classify each of the machines provided according to how or where: (1) effort is applied. (H) Load is placed.

 (b) What is your general comment about the machine we use?

Activity 1.17 discussing the classes of levers

1. In groups, discuss and write short notes, including their definitions, about the three classes of levers.
2.  In each of the classes defined above, state at least three examples.

(c) Identify the classes of levers shown in Figure 1.12. Examples of levers

First class levers

 In a first class lever, the pivot (fulcrum) is between the effort and the load. In an off – centre first class lever (like a pair of pliers), the load is larger than the effort, but is moved through a smaller distance.

Second class levers

 Examples include nut crackers, a wheelbarrow, a paper cutter and the oar of a boat. In second class levers, the load is between the pivot (fulcrum) and the effort.

Third class levers

 Examples: sugar tongs, the human forearm, the treadle of a sewing machine, a fishing rod, a spade. So, in the third class levers, the effort is between the load and the fulcrum.

 In the case of a simple lever, friction is usually quite small. Hence from the law of conservation of energy, the work done by the force, F. (effort) must be equal to the work done on the weight, W, (load).

 Wheel and axle (winch)

The wheel – and – axle uses the principle of levers and is commonly used in removing soil from latrines during construction or putting bricks on top of tall buildings.

 A wheel with a rod, called an axle, through its centre lifts or moves loads. It consists of a rope wound around an axle which is connected to a larger wheel with another rope attached to its rim. Pulling on the wheel rope (applying an effort) lifts a load attached to the axle rope. The velocity ratio of the machine (distance moved by effort divided by the distance moved by load) is equal to the ratio of the wheel radius to the axle radius

Figure 1.15: Wheel – and – axle

The wheel is fixed on the axis. It is easily seen that in one complete rotation, the force F (effort is applied) will raise a distance equal to the circumference of the wheel, while load L will raise a distance equal to the circumference of the axle.

 If R and r are radii of the wheel and axle respectively, then

Gears

 Gears are modified wheel – and – axle. A gear is a wheel with equally spaced teeth around it along its circumference which can rotate about its center. The small gear wheel (the driving wheel or effort gear with n teeth) turns and makes the bigger wheel (the driven wheel or load wheel) turn.

Figure 1.16: Gears as modified wheel – and – axle

 The teeth are spaced the same on both sprockets and the rear sprocket is firmly attached to the rear wheel of a bicycle.

Activity 1.18 Researching and stating examples of wheel and – axle

In groups, using the internet and other textbooks:

(a) State other examples of wheel – and – axle.

 (b) Explain why it is easier to undo a tight nut using a spanner with a long handle than one with a short handle.

(c) Present your findings before your teacher to the rest of the class.

Wedge

A wedge is an object with at least one slanting side ending in a sharp edge, which cuts material apart

A wedge is simply a triangular tool, often made of metal, wood, stone or plastic. It is thick at one end and tapers to a thin or sharp edge at the other end. Technically, it is an inclined plane (or two inclined planes put together to form a triangle) that moves .A wedge may be attached to a handle to make it easier to use. Good examples of wedges are nails, knives, axes and your teeth!

A wedge can be used in many ways:

• To cut (knife).
• To split (axe).
• To tighten and to hold back (doorstopper).
•  To hold together (nail)
•  To scrape (blades on the snow plough or farm grader).

Wedges work by changing direction and the force applied to it.

Pulley

A pulley is a simple machine that uses grooved wheels and a rope to raise, lower or move a load.

 A pulley is a machine consisting of a fixed grooved wheel, sometimes in a block, around which a rope or chain can be run. A simple pulley serves only to change the direction of the applied force (i.e. applied effort). The use of more than one pulley results in a higher mechanical advantage, so that a given effort can raise a heavier load.

 Types of pulleys

Single fixed

 A fixed or class 1 pulley has a fixed axle, i.e., the axle does not move. It is used to change the direction of the force on a rope (called a belt).

A fixed pulley has a mechanical advantage of f one means that the effort applied to the pulley is equal to the load being overcome by the pulley

 L = E

Figure 1.18: A fixed pulley

Single movable pulley

A single movable pulley has one pulley freely moving over the supporting rope:

E = L/2

A movable pulley is used to multiply forces.

A movable pulley is used to multiply forces and it has a mechanical advantage of 2. That is, if one end of the rope is fixed, pulling on the other end of the rope will apply a doubled force to the object attached to the pulley.

Compound pulley systems

 A compound pulley is a combination of fixed and movable pulley

A simple compound pulley system consists of one movable pulley and one fixed pulley and are used for lifting a weight W as shown in Figure 1.19, the tension in each line of the strings is yielding a mechanical advantage of 3. An additional pulley redirects the lifting force downward.

 Assessment 1.5

Discuss how the M.A and V.R of a compound pulley system can be obtained.

Screw jack

A screw is an inclined plane wrapped around a pole which holds things together or lifts materials. 2xr P Figure 1.20: Simple pulley

Figure 1.21: Screw

A screw jack is simply a ramp wrapped around an axle, with the axle rotated by a handle used as a lever. If the circular motion of the handle is 30cm per revolution, for example, and one turn of the screw lifts a weight by 1cm, then the mechanical advantage is 30 to 1.

 When a screw is rotated through one complete turn, it moves through a distance equal to its pitch. A pitch is the distance between one thread and the next measured along the axis of the screw.

The efficiency of a screw jack is always less than 50 %.

 Bolts screw and wedges are based on the principle of the inclined plane.

A screw is simply an inclined plane around a cylinder. To describe this better, you can view it as a cylinder with a head (solid top) at one end and a pointed tip (like a nail) at the other end. More importantly, it has ridges winding around it. The correct term for the ridges (or grooves) around the shaft or cylinder is the thread.

The distance between threads are the same for each screw but are different on other screws. The distance between the threads is called pitch.

 Screws are very useful for holding things together. They can pull or push an object together. They can be used to lift very heavy objects and tighten things too.

Assessment 1.6

1. In groups, using the internet or other textbooks, explain and present how to calculate the velocity ratio in screws.

The inclined plane

Study Figure 1.11.

Where in a real – life situation is the use of the shown technique applied? Do you think lifting the load vertically to the desired height is better than using the method used in the figure above?

Activity 1.19 demonstrating the importance of inclined planes

What you need

• Pieces of wood and timber (smooth), trolley, or you can use a bottle top, and thread.

 What to do

 (a) Arrange the materials as indicated in Figure 1.22.

(b) Displace the trolley or bottle top on your incline.

 Figure 1.23: An inclined plane

i) Basing on your observations, discuss the need to have inclined planes in solving problems.

 (ii) Where in real life are inclined planes applied?

An inclined plane is a slanting surface connecting a lower level to a higher level. Common experience shows that when a heavy body is to be raised, it is easier to push it or roll it up a sloping surface than to lift it directly. Workmen loading heavy boxes onto a lorry usually roll them up a sloping plank.

 If a force , F , is applied parallel to the length , I , of the plane , the work done by F is equal to W.d = Fx I , while the barrel of weight , W , is raised through a distance , h , and the work done on the barrel is W.d=wxh .

Chapter Summary

In this chapter, you have learnt that:

• Work is the product of force and distance moved in the direction of the force.
• Energy is the capacity to do work.
• Energy can neither be created nor destroyed, but it can be transformed from one form to another.
• Power is the rate of doing work.
• A machine is any device that is used to simplify man’s work.
• Simple machines make work easier.
• Simple machines are classified into levers, wheel – and – axle, wedges, pulleys, screw jack and inclined planes.