9th Class Physics · Punjab Board · Complete learning guide

Chapter 5Work, Energy and Power

Every topic, every MCQ and every exercise question, explained step by step in simple language. Written for the Punjab Board new-syllabus Physics book, English medium.

Start reading Try the 24 MCQs Take the self-test

What you will find inside

Part 1

Learn the chapter

12 topics with diagrams

Part 2

MCQs fully solved

24 MCQs with reasoning

Part 3

Short questions

10 exam-ready answers

Comprehensive questions

11 detailed long answers

Formulas, key terms, test

On their own page:Chapter 5 MCQs Chapter 5 Short Questions Chapter 5 Long Questions Chapter 5 Numericals

How to use this guide

Read Part 1 slowly. Do the worked examples yourself on paper, then compare.
Try each MCQ before opening its answer, then read why the wrong options are wrong.
Learn the short answers in your own words, then do the numericals without looking.
Finish with the self-test in Part 7. A wrong answer tells you which topic to read again.

Part 1of 7

Learn the Chapter

Read this first. Everything in the exercises comes from these topics.

1Work
2Work done by a force at an angle
3Work from a force-displacement graph
4Energy and its forms
5Kinetic energy
6Potential energy
7Conservation of energy
8Renewable and non-renewable sources of energy
9Generating electricity: fossil fuels, water and nuclear
10Solar, wind, geothermal, tidal and biomass energy
11Efficiency
12Power

Topic 1

Work

Definition

Work

Work is done when a force acts on a body and moves it through a distance in the direction of the force. It is a scalar quantity.

W = F × S

F = force, S = distance moved in the direction of the force

Definition

Joule (J)

One joule of work is done when a force of one newton moves a body through one metre in its own direction. 1 J = 1 N m. Larger units: 1 kJ = 10³ J, 1 MJ = 10⁶ J.

Two conditions for work

A force must act on the body.
The body must move.
The movement must have a part in the direction of the force.

Situation	Work done?	Why
Lifting a school bag onto a table	Yes	Upward force, upward movement
Pushing hard on a wall that does not move	No	No displacement
Holding a heavy box still	No	No displacement
Carrying a bag along a level road	No (on the bag)	The upward force is at right angles to the motion

Worked exampleA person does 200 J of work in pushing a carton through 5 m. How much force is applied? (Solved Example 5.1)

W = F × S, so F = W ÷ S.
F = 200 ÷ 5.

Answer40 N

Topic 2

Work done by a force at an angle

When a force acts at an angle θ to the direction of motion, only its part along the motion, F cos θ, does work.

W = FS cos θ

The handle pulls at 30° to the floor; only F cos 30° pulls the suitcase along.

Angle θ	cos θ	Work
0° (force along the motion)	1	Largest: W = FS (positive)
90° (force at right angles)	0	Zero
180° (force against the motion)	−1	Negative: W = −FS, as for friction or brakes

Worked exampleFind the work done by a 65 N force pulling a suitcase 20 m, with the handle at 30° to the horizontal. (Solved Example 5.2)

W = FS cos θ = 65 × 20 × cos 30°.
= 65 × 20 × 0.866.

Answer1125.8 J

Remember

Work done by friction is negative: friction acts opposite to the motion and takes energy away from the body.

Topic 3

Work from a force-displacement graph

If force is plotted against displacement, the area under the graph equals the work done. For a constant force the area is a rectangle, F × S.

F acts through L, then 2F through 2L: the two rectangles give FL + 4FL = 5FL.

Exam tip

This also works when the force changes: split the area into rectangles and triangles and add them.

Topic 4

Energy and its forms

Definition

Energy

The ability of a body to do work. It is a scalar; its SI unit is the joule, the same as work. When 1 J of work is done, 1 J of energy is used.

Definition

Mechanical energy

The sum of a body's kinetic energy and potential energy.

Form of energy	Where it is found
Kinetic energy	Any moving body: a running boy, moving car, flowing water
Gravitational potential energy	A body raised above the ground, water stored in a dam
Elastic potential energy	A stretched spring or rubber band, a bent bow
Chemical energy	Food, fuels, batteries
Thermal (internal) energy	Hot bodies; released by burning fuels
Nuclear energy	The nucleus of an atom; released in nuclear fission
Electrical, light and sound energy	Current in a wire; light from the Sun or a bulb; a vibrating drum

Topic 5

Kinetic energy

Definition

Kinetic energy

The energy a body has because of its motion.

Ek = ½mv²

Finding the kinetic energy

A body of mass m moving with speed v is brought to rest by an opposing force F over a distance S. The work done by this force equals the kinetic energy: Ek = F × S.
By Newton's second law, F = ma, where a is the deceleration.
With uniform deceleration, average speed = v/2, so S = (v/2) × t.
The speed falls from v to 0 in time t, so a = v/t.
Ek = F × S = m(v/t) × (v/2)t = ½mv².

Change	Effect on Ek
Double the mass	Ek doubles
Double the speed	Ek becomes four times (Ek ∝ v²)
Double the momentum	Ek becomes four times (Ek = p²/2m)

Worked exampleA 3000 kg truck moves at 54 km h⁻¹. Find its kinetic energy. (Solved Example 5.3)

Speed in m s⁻¹: 54 × 1000 ÷ 3600 = 15 m s⁻¹.
Ek = ½mv² = ½ × 3000 × 15².
= 1500 × 225 = 337 500 J.

Answer3.375 × 10⁵ J (337.5 kJ)

Remember

Kinetic energy can never be negative: m is positive and v² is positive (or zero).

Topic 6

Potential energy

Definition

Potential energy

The energy a body has because of its position or its deformation (change of shape).

Definition

Gravitational potential energy

The energy a body has because of its height above a reference level. It equals the work done in lifting it there.

Ep = mgh

To lift a body at constant speed, the upward force equals its weight mg. Lifting it through a height h does work = force × distance = mg × h, which is stored as gravitational potential energy.

Worked exampleA 180 g ball is thrown up to a height of 12 m. Find its gain in potential energy. (Solved Example 5.4)

Mass in kg: 180 g = 0.18 kg.
Ep = mgh = 0.18 × 10 × 12.

Answer21.6 J

Type	Example
Gravitational	Water held behind a dam; a stone on a cliff
Elastic	A compressed spring, a stretched catapult
Chemical	Fuel in a car tank, food, a charged battery

Check your book

"A body has 1 J of potential energy" is incomplete: potential energy is always measured from a chosen reference level, usually the ground.

Topic 7

Conservation of energy

Definition

Law of conservation of energy

Energy can neither be created nor destroyed. It can change from one form to another, but the total amount of energy stays the same.

A body falling from height h

A body falls from A (height h) through B (height x) to the ground C.

Point	Potential energy	Kinetic energy	Total
A (top, at rest)	mgh	0	mgh
B (height x)	mgx	mg(h − x)	mgh
C (just above the ground)	0	mgh	mgh

As the body falls, potential energy turns into kinetic energy, but the total stays mgh at every point (ignoring air resistance).

Without pedalling: Ep changes to Ek going down from A to B, and back to Ep going up to C.

Device or event	Energy change
Electric fan	Electrical → kinetic (and some heat, sound)
Torch	Chemical → electrical → light (and heat)
Car engine	Chemical (fuel) → heat → kinetic
Hydroelectric dam	Gravitational potential → kinetic → electrical
Ball smashing a window	Kinetic → work breaking the glass + sound + heat

Remember

In every real change some energy is "lost" as heat to the surroundings. It is not destroyed; it just spreads out and is no longer useful. This is called wasted energy.

Topic 8

Renewable and non-renewable sources of energy

Definition

Renewable sources

Sources that are replaced naturally after use, so they will not run out: solar, wind, hydroelectric, tidal, wave, geothermal, biomass.

Definition

Non-renewable sources

Sources that are used up and cannot be replaced in a human lifetime: fossil fuels (coal, oil, natural gas) and nuclear fuel.

Renewable	Non-renewable
Replaced naturally, e.g. rain refills dams	Took millions of years to form
Will not run out	Limited, and running out
Mostly little pollution	Fossil fuels pollute the air and add CO₂
Solar, wind, hydroelectric, tidal, geothermal, biomass	Coal, oil, natural gas, uranium

Check your book

Wood (timber) is renewable because trees can be replanted, but only if new trees are grown as fast as old ones are cut. It takes many years for a tree to grow.

Topic 9

Generating electricity: fossil fuels, water and nuclear

Definition

Fossil fuel energy

The energy released by burning coal, oil and natural gas, which formed from the remains of plants and animals buried for millions of years.

Definition

Hydroelectric energy

Electricity generated from the energy of water falling from a height, such as from a dam.

Block diagrams: hydroelectric power (left) and a fossil-fuel power station (right).

Definition

Nuclear energy

The energy released when the nucleus of a heavy atom such as uranium splits (fission). The heat makes steam that drives turbines, as in a fossil-fuel station.

Source	Advantages	Disadvantages
Fossil fuels	Reliable; power stations can run day and night	Non-renewable; smoke, acid rain and CO₂ (global warming)
Hydroelectric	Renewable; no fuel burnt; no air pollution	Dams are costly; flood land; need a river at height
Nuclear	Huge energy from a little fuel; no CO₂	Radioactive waste; risk of accidents; costly

Topic 10

Solar, wind, geothermal, tidal and biomass energy

Definition

Solar energy

Energy from sunlight. Solar (photovoltaic) cells change light directly into electricity; one cell gives a small voltage, so many are joined in series to make a solar panel.

Definition

Wind energy

Electricity made by wind turbines, which use the kinetic energy of moving air.

Definition

Geothermal energy

The heat of hot rocks deep under the Earth's surface, used to make steam for turbines.

Definition

Tidal and wave energy

Electricity from the rise and fall of the tides (caused by the Moon's gravity) and from ocean waves.

Definition

Biomass energy

Energy from plant and animal matter (wood, crop waste, dung), burnt directly or turned into biogas.

Source	Advantage	Disadvantage
Solar	Free fuel, no pollution, good for remote areas	Only by day; panels are costly
Wind	No fuel, no pollution	Only where it is windy; noisy
Geothermal	Works day and night	Only in a few places
Tidal / wave	Predictable and renewable	Only on coasts; costly to build
Biomass	Uses waste; cheap	Smoke when burnt; needs land

Topic 11

Efficiency

Definition

Efficiency

The ratio of the useful output energy of a system to the total input energy.

Efficiency = (useful output energy ÷ total input energy) × 100%

Energy in = useful energy out + wasted energy. The wasted part is mostly heat.

Worked exampleA 120 N block is dragged up a 20 m slope with a force of 100 N, raising it 10 m. Find the efficiency. (Solved Example 5.6)

Input energy = force × distance along the slope = 100 × 20 = 2000 J.
Useful output = gain in potential energy = weight × height = 120 × 10 = 1200 J.
Efficiency = 1200 ÷ 2000 × 100.

Answer60%

No machine can be 100% efficient: in every energy change some energy is wasted as heat (and sound) because of friction. That is also why a perpetual-motion machine is impossible.

Topic 12

Power

Definition

Power

The rate of doing work, or the energy transferred per second.

P = W ÷ t

also P = E ÷ t

Definition

Watt (W)

Power of one joule per second. 1 W = 1 J s⁻¹; 1 kW = 10³ W; 1 MW = 10⁶ W.

Two boys climbing the same stairs do the same work, but the one who climbs faster has more power.

Worked exampleA 1000 kg car accelerates at 4 m s⁻² and covers 50 m in 5 s. Find the power of its engine. (Solved Example 5.5)

Force: F = ma = 1000 × 4 = 4000 N.
Work: W = F × S = 4000 × 50 = 200 000 J.
Power: P = W ÷ t = 200 000 ÷ 5.

Answer40 000 W = 40 kW

Exam tip

For lifting, W = mgh, so P = mgh ÷ t. Remember to change minutes to seconds.

End of Part 1Next: Part 2 · MCQs fully solved ↓

Part 2of 7

MCQs Fully Solved

Try each one first: tap an option to check it, then read the reasoning and why the others are wrong.

Only the mcqs on one page →

A note about the questions

The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.

Answered 0 of 24 · Correct 0

Set A: Textbook exercise 9 MCQs

The multiple-choice questions at the end of Chapter 5 in your book, in the book's option order.

Q5.1Work

Work done is maximum when the angle between the force F and the displacement d is:

Q5.2Work

A joule can also be written as:

Q5.3Power

The SI unit of power is:

Q5.4Power

The power of a water pump is 2 kW. The amount of water it can raise in one minute to a height of 5 m is:

Q5.5Kinetic Energy

A bullet of mass 0.05 kg has a speed of 300 m s⁻¹. Its kinetic energy will be:

Q5.6Kinetic Energy

If a car doubles its speed, its kinetic energy will be:

Q5.7Potential Energy

The energy possessed by a body by virtue of its position is:

Q5.8Kinetic Energy

The magnitude of momentum of an object is doubled. The kinetic energy of the object will:

Q5.9Sources of Energy

Which of the following is not a renewable energy source?

Set B: More MCQs from this chapter 15 MCQs

Extra questions on the same ideas, of the kind set in board papers and class tests.

QB1Work

Work is done when:

QB2Work

No work is done by gravity on a satellite moving in a circular orbit because:

QB3Work

1 kJ is equal to:

QB4Work

A force of 10 N moves a box 4 m in its own direction. The work done is:

QB5Kinetic Energy

The kinetic energy of a 2 kg ball moving at 3 m s⁻¹ is:

QB6Potential Energy

The potential energy of a 2 kg book on a shelf 5 m above the floor is (g = 10 m s⁻²):

QB7Potential Energy

A stretched rubber band has:

QB8Conservation of Energy

A ball is dropped from a height h. Ignoring air resistance, halfway down its energy is:

QB9Conservation of Energy

The energy changes in a battery-powered torch are:

QB10Sources of Energy

Solar cells convert:

QB11Sources of Energy

Geothermal energy comes from:

QB12Efficiency

A machine is given 500 J of energy and does 400 J of useful work. Its efficiency is:

QB13Efficiency

The efficiency of a real machine is always:

QB14Power

1 watt is equal to:

QB15Power

A 600 W motor runs for 10 s. The energy it uses is:

End of Part 2Next: Part 3 · Short questions ↓

Part 3of 7

Short Questions

Exam-ready answers. Learn the meaning, then write them in your own words.

Only the short questions on one page →

Short Q 5.1

What is the work done on an object that remains at rest when a force is applied on it?

Answer

Zero. Work needs a displacement: W = F × S. If the object stays at rest, S = 0, so W = F × 0 = 0. For example, a man pushing hard against a wall does no work on it, however tired he gets.

Short Q 5.2

A slow-moving car may have more kinetic energy than a fast-moving motorcycle. How is this possible?

Answer

Kinetic energy depends on mass as well as speed: Ek = ½mv². A car is many times heavier than a motorcycle, so even at a lower speed its ½mv² can be larger.

Worked exampleExample

Car: 1000 kg at 10 m s⁻¹, Ek = ½ × 1000 × 100 = 50 000 J.
Motorcycle: 150 kg at 20 m s⁻¹, Ek = ½ × 150 × 400 = 30 000 J.

Answerthe slower car has more kinetic energy

Short Q 5.3

A force F₁ does 5 J of work in 10 s. Another force F₂ does 3 J of work in 5 s. Which force delivers greater power?

Answer

P₁ = W₁ ÷ t₁ = 5 ÷ 10 = 0.5 W.
P₂ = W₂ ÷ t₂ = 3 ÷ 5 = 0.6 W.

So F₂ delivers greater power, even though it does less work, because it does its work faster.

Short Q 5.4

A woman runs up a flight of stairs. The gain in her gravitational potential energy is 4500 J. If she runs up the same stairs with twice the speed, what will be her gain in potential energy?

Answer

Still 4500 J. Gravitational potential energy is Ep = mgh: it depends on her mass and the height of the stairs, not on her speed. Running faster only increases her power (she does the same work in less time).

Short Q 5.5

Define work and its SI unit.

Answer

Definition

Work

The product of a force and the distance moved in the direction of the force: W = F × S.

Definition

Joule

One joule of work is done when a force of 1 N moves a body 1 m in its own direction: 1 J = 1 N m.

Short Q 5.6

What is the potential energy of a body of mass m when it is raised through a height h?

Answer

To raise it at constant speed, a force equal to its weight, mg, must act through the height h. Work done = mg × h, and this is stored as gravitational potential energy:

Ep = mgh

Short Q 5.7

Find an expression for the kinetic energy of a moving body.

Answer

A body of mass m and speed v is stopped by an opposing force F over a distance S; Ek = work done = F × S.
F = ma, and S = average speed × time = (v/2) × t.
The body stops in time t, so a = v/t.
Ek = m(v/t) × (v/2)t = ½mv².

Ek = ½mv²

Short Q 5.8

Define efficiency of a working system. Why can a system not have 100% efficiency?

Answer

Definition

Efficiency

The ratio of useful output energy to total input energy, usually given as a percentage: (useful output ÷ total input) × 100%.

A system can never be 100% efficient because in every energy change some energy is wasted, mostly as heat produced by friction (and sometimes as sound). No device turns all its input into useful output.

Short Q 5.9

What is power? Define the unit used for it.

Answer

Definition

Power

The rate of doing work: P = W ÷ t.

Definition

Watt

The power of a system that does one joule of work per second: 1 W = 1 J s⁻¹.

Short Q 5.10

Differentiate between renewable and non-renewable energy sources.

Answer

Renewable	Non-renewable
Replaced naturally after use	Used up; cannot be replaced quickly
Will not run out	Limited stock
Solar, wind, hydroelectric, tidal, geothermal	Coal, oil, natural gas, nuclear fuel

End of Part 3Next: Part 4 · Constructed response ↓

Part 4of 7

Constructed Response Questions

These test whether you really understand. Give a reason every time.

CRQ 5.1

Can the kinetic energy of a body ever be negative?

Answer

No. Ek = ½mv². Mass is always positive and v² is positive whatever the direction of motion (or zero at rest). So kinetic energy is always positive or zero, never negative.

CRQ 5.2

Which one has the greater kinetic energy: an object travelling with velocity v, or an object twice as heavy travelling with velocity ½v?

Answer

Worked exampleComparison

First object: Ek₁ = ½mv².
Second object: Ek₂ = ½(2m)(v/2)² = ½ × 2m × v²/4 = ¼mv².
Ek₁ ÷ Ek₂ = ½ ÷ ¼ = 2.

Answerthe object moving at v has twice the kinetic energy

Remember

Speed counts more than mass, because it is squared.

CRQ 5.3

A car is moving along a curved road at constant speed. Does its kinetic energy change?

Answer

No. Kinetic energy depends only on mass and speed (Ek = ½mv²), not on direction. The car's direction changes but its speed does not, so its kinetic energy stays the same. (Its velocity, a vector, does change.)

CRQ 5.4

Comment on the statement: "An object has one joule of potential energy."

Answer

The statement is incomplete. Gravitational potential energy depends on the height above a chosen reference level. The same object can have 1 J above the floor and much more above the ground outside. We should say, for example, "the object has 1 J of potential energy relative to the floor".

CRQ 5.5

While driving on a motorway, the tyre of a vehicle sometimes bursts. What may be its cause?

Answer

At high speed for a long time, friction between the tyre and the road (and the constant bending of the rubber) changes kinetic energy into heat. The tyre and the air inside it get hot. Hot air has a higher pressure, and if the tyre is old, worn or over-inflated, the extra pressure bursts it.

CRQ 5.6

While playing cricket on a street, the ball smashes a window pane. Describe the energy changes in this event.

Answer

The bowler's chemical energy (from food) gives the ball kinetic energy; the batsman adds more.
The moving ball's kinetic energy does work on the glass, breaking it.
Some energy becomes sound (the crash) and a little becomes heat.
The glass pieces fly off with some kinetic energy.

Remember

The total energy is the same before and after; it has only changed form.

CRQ 5.7

A man rowing a boat upstream is at rest with respect to the shore. Is he doing work?

Answer

On the boat

No work is done on the boat relative to the shore. The boat does not move, so its displacement is zero and W = F × 0 = 0.

On the water

But the man is not idle. His oars push the water backward, and the water moves, so he does work on the water. His chemical energy goes into the moving water (and heat), which exactly balances the current pushing the boat back.

Check your book

One solved copy simply answers "yes, he is doing work". Both points above are what the physics says: zero work on the boat, positive work on the water.

CRQ 5.8

A cyclist goes downhill from the top of a steep hill without pedalling and coasts up to the top of the next hill. (i) Draw a diagram of what happened. (ii) Analyse this event in terms of potential and kinetic energy.

Answer

(i) Diagram

A: top of the first hill, B: bottom, C: top of the next hill.

(ii) Analysis

At A: the cyclist is high and slow, so potential energy is greatest and kinetic energy least.
From A to B: height falls, so potential energy changes into kinetic energy; the cyclist speeds up.
At B: kinetic energy is greatest and potential energy least.
From B to C: the kinetic energy changes back into potential energy as the cyclist climbs and slows down.

Remember

The next hill must be a little lower than the first, because some energy is wasted against friction and air resistance.

CRQ 5.9

Is timber or wood a renewable source of heat energy? Comment.

Answer

Yes, wood is renewable, because trees can be planted again and grow back. But a tree takes many years to grow, so wood is renewable only if we plant at least as many trees as we cut. Cutting forests faster than they regrow (deforestation) uses wood up like a non-renewable source.

End of Part 4Next: Part 5 · Comprehensive questions ↓

Part 5of 7

Comprehensive (Long) Questions

Long answers, explained in full with headings. Learn the structure: definition, explanation, diagram or table, example.

Only the long questions on one page →

Set A: Textbook comprehensive questions 5 questions

The long questions at the end of the chapter in your book.

Long Q 5.1

What is meant by kinetic energy? State its unit. Describe how it is determined.

Answer

Definition

Kinetic energy

The energy a body has because of its motion. SI unit: joule (J).

Principle

A moving body can do work as it is brought to rest. So its kinetic energy equals the work done by the force that stops it.

Derivation

A body of mass m moves with speed v. A steady opposing force F stops it over a distance S, so Ek = F × S ...(i)
By Newton's second law, F = ma, where a is the deceleration.
The speed falls uniformly from v to 0, so the average speed is v/2 and S = (v/2) × t.
Putting these in (i): Ek = ma × (v/2) × t ...(ii)
From the velocity-time graph, a = v/t. Putting this in (ii): Ek = m × (v/t) × (v/2) × t = ½mv².

Ek = ½mv²

Example

Worked exampleA 0.05 kg bullet at 300 m s⁻¹

Ek = ½ × 0.05 × 300².

Answer2250 J

Conclusion

Kinetic energy depends on mass and on the square of the speed.

Long Q 5.2

State the law of conservation of energy. Explain it with the help of a body falling from a certain height, in terms of its potential and kinetic energy.

Answer

Statement

Definition

Law of conservation of energy

Energy can neither be created nor destroyed; it can only change from one form to another, and the total amount stays constant.

Diagram

A body of mass m falls from A at height h, through B at height x, to C on the ground.

At point A (top)

The body is at rest, so Ek = 0 and Ep = mgh. Total = mgh.

At point B (height x)

Ep = mgx. It has fallen h − x, so v² = 2g(h − x) and Ek = ½mv² = mg(h − x). Total = mgx + mg(h − x) = mgh.

At point C (ground)

Ep = 0. It has fallen h, so v² = 2gh and Ek = ½m(2gh) = mgh. Total = mgh.

Point	Ep	Ek	Total
A	mgh	0	mgh
B	mgx	mg(h − x)	mgh
C	0	mgh	mgh

Conclusion

Potential energy changes into kinetic energy, but the total stays mgh. On hitting the ground the kinetic energy becomes heat and sound; in real falls some energy also goes into air resistance.

Long Q 5.3

Differentiate between renewable and non-renewable sources of energy. Give three examples of each.

Answer

Renewable sources

Definition

Sources that are replaced naturally after use and will not run out.

Rain and snow keep refilling the reservoirs of dams, the Sun keeps shining and the wind keeps blowing, so these sources last.

Non-renewable sources

Definition

Sources that are used up and cannot be replaced in a human lifetime.

Coal, oil and gas formed from plants and animals buried for millions of years. The stock is limited; once used, it takes millions of years to form again.

Differences

Renewable	Non-renewable
Replaced naturally	Not replaced in our lifetime
Will not run out	Will run out
Usually clean	Fossil fuels pollute and add CO₂
Solar, wind, hydroelectric (also tidal, geothermal, biomass)	Coal, oil, natural gas (also nuclear fuel)

Conclusion

Pakistan has strong sunshine and wind along the coast, so solar and wind power can reduce our dependence on imported oil.

Long Q 5.4

Explain what is meant by the efficiency of a machine. How is it calculated? Why is there a limit to the efficiency of a machine?

Answer

Definition

Efficiency

The ratio of the useful output energy of a machine to the total energy put into it.

Formula

Efficiency = (useful output energy ÷ total input energy) × 100%

Efficiency = (useful power output ÷ total power input) × 100%

Diagram

Input energy splits into useful output and wasted energy.

Example

Worked exampleA motor uses 1000 J and lifts a load, giving it 700 J of potential energy

Efficiency = 700 ÷ 1000 × 100.

Answer70%; 300 J is wasted

Why there is a limit

In every machine, moving parts rub, and friction turns some energy into heat.
Some energy is lost as sound and vibration.
So the useful output is always less than the input, and efficiency is always below 100%.
For the same reason a perfect (perpetual-motion) machine that runs for ever without input cannot be built.

Conclusion

Efficiency can be raised (by lubrication, for example) but never to 100%.

Long Q 5.5

Describe the process of electricity generation by drawing a block diagram of the process in the following cases: (i) hydroelectric power generation (ii) fossil fuels.

Answer

(i) Hydroelectric power

Water stored behind a dam at a height has gravitational potential energy. It flows down through tunnels (penstocks), gaining kinetic energy, and turns the blades of a turbine. The turbine turns a generator, which produces electrical energy.

(ii) Fossil fuels

Coal, oil or gas is burnt in a furnace. The heat boils water in a boiler to make high-pressure steam. The steam turns a turbine, which turns a generator to produce electricity. The steam is cooled, condensed back to water and used again.

Block diagrams

Left: hydroelectric. Right: fossil-fuel power station.

	Hydroelectric	Fossil fuel
Starting energy	Gravitational potential energy of water	Chemical energy of fuel
What turns the turbine	Falling water	Steam
Renewable?	Yes	No
Pollution	None in use	Smoke and CO₂

Conclusion

In both, a turbine turns a generator; only the way the turbine is driven differs.

Set B: More important long questions 6 questions

Long questions often set in board papers from this chapter, answered in the same full style.

Imp. LQ 1

Define work. Explain W = FS cos θ, and the cases in which work is positive, zero and negative.

Answer

Definition

Work

Work is done when a force moves a body through a distance in the direction of the force. SI unit: joule.

Force at an angle

If the force F acts at an angle θ to the displacement S, resolve F into F cos θ along the motion and F sin θ at right angles to it. Only F cos θ moves the body, so:

W = (F cos θ) × S = FS cos θ

Pulling a suitcase at 30°: only F cos 30° does work.

Positive, zero and negative work

Case	Angle	Example
Positive work	0° ≤ θ < 90°	Pulling a trolley forward
Zero work	θ = 90°	Carrying a bag on a level road; gravity on a satellite
Negative work	90° < θ ≤ 180°	Friction on a sliding box; brakes on a car

Worked exampleA 20 N force at 60° pulls a box 3 m

W = 20 × 3 × cos 60° = 20 × 3 × 0.5.

Answer30 J

Imp. LQ 2

What is power? Write its units and show that power = force × velocity.

Answer

Definition

Power

The rate of doing work: P = W ÷ t.

Units

watt: 1 W = 1 J s⁻¹
kilowatt: 1 kW = 10³ W
megawatt: 1 MW = 10⁶ W

Power in terms of force and velocity

P = W ÷ t, and W = F × S.
So P = F × S ÷ t.
S ÷ t = v, the speed.
Therefore P = Fv.

P = Fv

Example

Worked exampleA 40 kg boy runs up stairs 10 m high in 8 s

Work = mgh = 40 × 10 × 10 = 4000 J.
P = 4000 ÷ 8.

Answer500 W

Conclusion

The same work done in less time means more power.

Imp. LQ 3

What is potential energy? Derive Ep = mgh and describe the types of potential energy.

Answer

Definition

Potential energy

The energy a body has because of its position or deformation.

Derivation of gravitational potential energy

Lift a body of mass m at constant speed from the ground to a height h.
The force needed equals its weight: F = mg.
Work done = F × h = mgh.
This work is stored in the body as gravitational potential energy.

Ep = mgh

Types

Type	Stored by	Example
Gravitational	Height above the reference level	Water in a dam
Elastic	Stretching or compressing	A wound clock spring, a bow
Chemical	Arrangement of atoms in molecules	Food, petrol, batteries

Reference level

Height is measured from a chosen level (usually the ground), so potential energy is always relative to that level.

Worked exampleA 0.18 kg ball raised 12 m

Ep = 0.18 × 10 × 12.

Answer21.6 J

Imp. LQ 4

Explain energy transformations with examples from daily life.

Answer

Meaning

Energy is useful because it can change from one form to another. In every change the total energy stays the same, though some becomes heat that cannot be used again.

Examples

Device or process	Energy change
Photosynthesis	Light → chemical (food)
Our body	Chemical (food) → kinetic + heat
Electric bulb	Electrical → light + heat
Electric motor, fan	Electrical → kinetic
Generator, dynamo	Kinetic → electrical
Loudspeaker	Electrical → sound
Solar cell	Light → electrical
Car engine	Chemical → heat → kinetic
Bow and arrow	Elastic potential → kinetic

A coasting cyclist: potential energy ↔ kinetic energy.

Conclusion

Energy is never lost, but some is always wasted as heat.

Imp. LQ 5

Describe solar energy. How are solar cells and solar panels used? Give the advantages and disadvantages of solar energy.

Answer

Solar energy

Definition

The energy we get from sunlight. The Sun is the biggest source of energy for the Earth.

Uses of solar energy

Solar heaters and cookers: black surfaces absorb sunlight to heat water or cook food.
Solar cells (photovoltaic cells): change light directly into electricity.
Solar panels: one cell gives a very small voltage, so many cells are joined in series to give a useful voltage, for homes, street lights, tube wells and calculators.

Advantages

Free and renewable.
No pollution or noise.
Useful in remote villages far from power lines.

Disadvantages

No output at night and little on cloudy days.
Panels and batteries are costly.
Large areas are needed for large amounts of power.

Conclusion

Pakistan gets strong sunshine most of the year, so solar energy is a good choice here.

Imp. LQ 6

Explain nuclear, geothermal, wind, tidal and biomass energy, with one advantage and one disadvantage of each.

Answer

Nuclear energy

When the nucleus of a heavy atom such as uranium splits (fission), a large amount of heat is released. It boils water into steam to drive turbines.

Geothermal energy

Deep underground the rocks are very hot. Water pumped down turns into steam, which comes up to drive turbines.

Wind energy

Moving air turns the large blades of a wind turbine, which drives a generator.

Tidal and wave energy

The Moon's pull makes the sea rise and fall twice a day. Water flowing in and out through a barrage turns turbines; waves can also drive generators.

Biomass energy

Wood, crop waste and animal dung are burnt for heat, or allowed to rot in a digester to make biogas.

Comparison

Source	Advantage	Disadvantage
Nuclear	Huge energy from little fuel	Dangerous radioactive waste
Geothermal	Works day and night	Found only in a few places
Wind	No fuel, no pollution	Depends on the wind; noisy
Tidal	Predictable	Only on coasts; costly
Biomass	Uses waste	Smoke when burnt

Conclusion

All of these except nuclear are renewable.

End of Part 5Next: Part 6 · Numericals solved ↓

Part 6of 7

Numericals Solved Step by Step

Each numerical in the order you write it in the exam: Given Data, To Find, Formula, Calculation, Result.

Only the numericals on one page →

Numerical 5.1

A force of 20 N acting at an angle of 60° to the horizontal is used to pull a box through a distance of 3 m across a floor. How much work is done?

Given Data

F = 20 N
θ = 60°
S = 3 m

To Find

Work done W

Formula

W = FS cos θ

Calculation

W = FS cos θ = 20 × 3 × cos 60°.
= 20 × 3 × 0.5 = 30 J.

Result

W = 30 J

Numerical 5.2

A body moves a distance of 5 m in a straight line under the action of a force of 8 N. If the work done is 20 J, find the angle which the force makes with the direction of motion.

Given Data

S = 5 m
F = 8 N
W = 20 J

To Find

Angle θ

Formula

W = FS cos θ, so cos θ = W ÷ (FS)

Calculation

cos θ = W ÷ (FS) = 20 ÷ (8 × 5) = 20 ÷ 40 = 0.5.
θ = cos⁻¹(0.5) = 60°.

Result

θ = 60°

Numerical 5.3

An engine raises 100 kg of water through a height of 80 m in 25 s. What is the power of the engine? (g = 10 m s⁻²)

Given Data

m = 100 kg
h = 80 m
t = 25 s
g = 10 m s⁻²

To Find

Power P

Formulas

W = mgh

P = W ÷ t

Calculation

Work done = mgh = 100 × 10 × 80 = 80 000 J.
P = W ÷ t = 80 000 ÷ 25 = 3200 W.

Result

P = 3200 W (3.2 kW)

Numerical 5.4

A body of mass 20 kg is at rest. A 40 N force acts on it for 5 s. What is the kinetic energy of the body at the end of this time?

Given Data

m = 20 kg
vᵢ = 0
F = 40 N
t = 5 s

To Find

Kinetic energy Ek

Formulas

a = F ÷ m

vf = vᵢ + at

Ek = ½mv²

Calculation

a = F ÷ m = 40 ÷ 20 = 2 m s⁻².
vf = 0 + 2 × 5 = 10 m s⁻¹.
Ek = ½ × 20 × 10² = 1000 J.

Result

Ek = 1000 J

Numerical 5.5

A girl is swinging on a swing. At the lowest point she is 1.2 m above the ground, and at the highest point she is 2.0 m above the ground. What is her maximum velocity, and where? (g = 10 m s⁻²)

She rises 0.8 m between the lowest and highest points of the swing.

Given Data

lowest point h₁ = 1.2 m
highest point h₂ = 2.0 m
drop h = 2.0 − 1.2 = 0.8 m
g = 10 m s⁻²

To Find

Maximum velocity v, and where it occurs

Formulas

loss of Ep = gain of Ek: mgh = ½mv²

v = √(2gh)

Calculation

At the highest point she is momentarily at rest; going down 0.8 m, her potential energy changes into kinetic energy.
mgh = ½mv², so v² = 2gh = 2 × 10 × 0.8 = 16.
v = √16 = 4 m s⁻¹.

Result

v = 4 m s⁻¹, at the lowest point of the swing

Note: The mass cancels, so it is not needed.

Numerical 5.6

A person pushes a lawn mower with a force of 50 N making an angle of 45° with the horizontal. If the mower is moved through a distance of 20 m, how much work is done?

Given Data

F = 50 N
θ = 45°
S = 20 m

To Find

Work done W

Formula

W = FS cos θ

Calculation

W = 50 × 20 × cos 45° = 1000 × 0.707.
W = 707 J.

Result

W ≈ 707 J

Numerical 5.7

Calculate the work done in (i) pushing a 5 kg box up a frictionless inclined plane 10 m long that makes an angle of 30° with the horizontal (ii) lifting the box vertically from the ground to the top of the inclined plane. (g = 10 m s⁻²)

The slope is 10 m long at 30°, so its top is 10 sin 30° = 5 m high.

Given Data

m = 5 kg
length of slope S = 10 m
θ = 30°
g = 10 m s⁻²
no friction

To Find

(i) Work done up the slope
(ii) Work done lifting straight up

Formulas

force along the slope = mg sin θ

W = F × S

h = S sin θ

W = mgh

Calculation

(i) Force needed along the slope = mg sin 30° = 5 × 10 × 0.5 = 25 N.
Work = 25 × 10 = 250 J.
(ii) Height of the top: h = 10 × sin 30° = 5 m.
Work = mgh = 5 × 10 × 5 = 250 J.

Result

(i) 250 J (ii) 250 J

Note: The work is the same either way: a frictionless slope needs a smaller force, but over a longer distance.

Numerical 5.8

A box of mass 10 kg is pushed up a ramp 15 m long with a force of 80 N. If the box rises through a height of 5 m, what is the efficiency of the system? (g = 10 m s⁻²)

An 80 N push along a 15 m ramp raises the box 5 m.

Given Data

m = 10 kg
S = 15 m
F = 80 N
h = 5 m
g = 10 m s⁻²

To Find

Efficiency

Formulas

input = F × S

useful output = mgh

efficiency = output ÷ input × 100%

Calculation

Input energy = F × S = 80 × 15 = 1200 J.
Useful output = mgh = 10 × 10 × 5 = 500 J.
Efficiency = 500 ÷ 1200 × 100 = 41.7%.

Result

Efficiency ≈ 41.7%

Note: The other 700 J is used against friction on the ramp.

Numerical 5.9

A force of 600 N acts on a box to push it 5 m in 15 s. Calculate the power.

Given Data

F = 600 N
S = 5 m
t = 15 s

To Find

Power P

Formulas

W = F × S

P = W ÷ t

Calculation

W = 600 × 5 = 3000 J.
P = 3000 ÷ 15 = 200 W.

Result

P = 200 W

Numerical 5.10

A 40 kg boy runs up stairs 10 m high in 8 s. What power does he develop? (g = 10 m s⁻²)

Given Data

m = 40 kg
h = 10 m
t = 8 s
g = 10 m s⁻²

To Find

Power P

Formula

P = mgh ÷ t

Calculation

Work = mgh = 40 × 10 × 10 = 4000 J.
P = 4000 ÷ 8 = 500 W.

Result

P = 500 W

Numerical 5.11

A force F acts through a distance L on a body. The force is then increased to 2F, which acts through a further distance 2L. Sketch a force-displacement graph and calculate the total work done.

The area under the graph is the work: FL for the first part, 2F × 2L for the second.

Given Data

force F through distance L
then force 2F through a further 2L

To Find

Total work done

Formula

work = area under the force-displacement graph

Calculation

First rectangle: F × L = FL.
Second rectangle: 2F × 2L = 4FL.
Total = FL + 4FL = 5FL.

Result

Total work = 5FL

End of Part 6Next: Part 7 · Revision & self-test ↓

Part 7of 7

Revision, Practice and Self-Test

Use this the night before the test.

One-page formula sheet

Work

W = F × S

Work at an angle

W = FS cos θ

Kinetic energy

Ek = ½mv²

Kinetic energy and momentum

Ek = p² ÷ 2m

Gravitational potential energy

Ep = mgh

Conservation (falling body)

mgh = ½mv², so v = √(2gh)

Efficiency

(useful output ÷ total input) × 100%

Power

P = W ÷ t

Power for lifting

P = mgh ÷ t

Power and velocity

P = Fv

Units

1 J = 1 N m = 1 kg m² s⁻²; 1 W = 1 J s⁻¹

Prefixes

1 kJ = 10³ J, 1 MJ = 10⁶ J, 1 kW = 10³ W

Key definitions 21 terms

Work

Work is done when a force acts on a body and moves it through a distance in the direction of the force. It is a scalar quantity.

Joule (J)

One joule of work is done when a force of one newton moves a body through one metre in its own direction. 1 J = 1 N m. Larger units: 1 kJ = 10³ J, 1 MJ = 10⁶ J.

Energy

The ability of a body to do work. It is a scalar; its SI unit is the joule, the same as work. When 1 J of work is done, 1 J of energy is used.

Mechanical energy

The sum of a body's kinetic energy and potential energy.

Kinetic energy

The energy a body has because of its motion.

Potential energy

The energy a body has because of its position or its deformation (change of shape).

Gravitational potential energy

The energy a body has because of its height above a reference level. It equals the work done in lifting it there.

Law of conservation of energy

Energy can neither be created nor destroyed. It can change from one form to another, but the total amount of energy stays the same.

Renewable sources

Sources that are replaced naturally after use, so they will not run out: solar, wind, hydroelectric, tidal, wave, geothermal, biomass.

Non-renewable sources

Sources that are used up and cannot be replaced in a human lifetime: fossil fuels (coal, oil, natural gas) and nuclear fuel.

Fossil fuel energy

The energy released by burning coal, oil and natural gas, which formed from the remains of plants and animals buried for millions of years.

Hydroelectric energy

Electricity generated from the energy of water falling from a height, such as from a dam.

Nuclear energy

The energy released when the nucleus of a heavy atom such as uranium splits (fission). The heat makes steam that drives turbines, as in a fossil-fuel station.

Solar energy

Energy from sunlight. Solar (photovoltaic) cells change light directly into electricity; one cell gives a small voltage, so many are joined in series to make a solar panel.

Wind energy

Electricity made by wind turbines, which use the kinetic energy of moving air.

Geothermal energy

The heat of hot rocks deep under the Earth's surface, used to make steam for turbines.

Tidal and wave energy

Electricity from the rise and fall of the tides (caused by the Moon's gravity) and from ocean waves.

Biomass energy

Energy from plant and animal matter (wood, crop waste, dung), burnt directly or turned into biogas.

Efficiency

The ratio of the useful output energy of a system to the total input energy.

Power

The rate of doing work, or the energy transferred per second.

Watt (W)

Power of one joule per second. 1 W = 1 J s⁻¹; 1 kW = 10³ W; 1 MW = 10⁶ W.

Common mistakes to avoid

Saying work is done when a force acts but nothing moves: W = 0 if S = 0.
Forgetting cos θ when the force is at an angle to the motion.
Forgetting to square the speed in ½mv², or forgetting the ½.
Not converting km h⁻¹ to m s⁻¹ (divide by 3.6) or grams to kilograms.
Thinking potential energy depends on speed: it depends only on m, g and h.
Writing an efficiency above 100%: output can never exceed input.
Mixing up energy (J) and power (W = J s⁻¹).
Calling wood always renewable: only if trees are replanted as fast as they are cut.

Extra practice tap a question to see its answer

A 15 N force moves a box 6 m in its direction. Find the work.Show answer
15 × 6 = 90 J
A 40 N force at 60° to the ground pulls a sledge 10 m. Find the work.Show answer
40 × 10 × 0.5 = 200 J
Find the kinetic energy of a 4 kg ball moving at 5 m s⁻¹.Show answer
½ × 4 × 25 = 50 J
A 1200 kg car moves at 72 km h⁻¹. Find its kinetic energy.Show answer
v = 20 m s⁻¹; ½ × 1200 × 400 = 2.4 × 10⁵ J
Find the potential energy of a 50 kg boy on a roof 8 m high.Show answer
50 × 10 × 8 = 4000 J
A stone falls from 20 m. Find its speed just before it hits the ground.Show answer
√(2 × 10 × 20) = 20 m s⁻¹
A ball has 60 J of potential energy at the top. What is its kinetic energy halfway down?Show answer
30 J (ignoring air resistance)
A machine is given 800 J and does 600 J of useful work. Find its efficiency.Show answer
600 ÷ 800 × 100 = 75%
A pump of efficiency 50% does 2000 J of useful work. How much energy was supplied?Show answer
2000 ÷ 0.5 = 4000 J
A crane lifts 500 kg through 12 m in 20 s. Find its power.Show answer
500 × 10 × 12 ÷ 20 = 3000 W
A 100 W bulb is on for 1 minute. How much energy does it use?Show answer
100 × 60 = 6000 J
A car engine gives a 2000 N force at 25 m s⁻¹. Find its power.Show answer
P = Fv = 2000 × 25 = 50 kW
Name the energy change in a hydroelectric power station.Show answer
Gravitational potential → kinetic → electrical
Give two renewable sources available in Pakistan.Show answer
Solar and wind (also hydroelectric)

Final self-test

Final self-test: all 24 MCQs, no answers

Give yourself 25 minutes. Pick one option for each question, then submit to see your score and which questions to revise. Any question you get wrong tells you which topic to read again.

End of Part 7Back to Part 1 ↑