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Chapter 4 · Class 9 · Physics · CBSE/NCERT

Work and Energy

From hydroelectric dams like Tehri to the electricity bill at home, energy is the backbone of everything we do. This chapter covers the scientific meaning of work, kinetic and potential energy, conservation of mechanical energy, power, and the commercial unit kWh.

WorkKinetic EnergyPotential EnergyConservationPowerkWh
Complete Chapter Roadmap — 12 Topics
01Scientific Meaning of Work02Positive, Negative, and Zero Work03Work Done Against Gravity04Kinetic Energy05Work-Energy Theorem06Potential Energy07Gravitational PE08Conservation of Mechanical Energy09Power10Commercial Unit of Energy — kWh11Energy Transformation12Chapter Summary
1

Scientific Meaning of Work

Force must cause displacement in its direction

Formula
W=F⋅s⋅cos⁡θW = F \cdot s \cdot \cos\theta

FF = force applied, ss = displacement, θ\theta = angle between force and displacement direction.
In everyday life, any effort feels like work. In science, work has a precise meaning: work is done on an object only when a force is applied and the object moves in the direction of the force, or has a component of displacement along the direction of the force.
If no displacement takes place, or if the displacement is perpendicular to the applied force, the work done is zero according to physics.
A student pushing a heavy almirah that does not move has done no work in the physics sense, even though the student feels exhausted. Similarly, a coolie at a railway station who carries luggage on his head and walks horizontally exerts force upward but moves horizontally — since force and displacement are perpendicular, the work done by the coolie's upward force on the luggage is zero.
2

Positive, Negative, and Zero Work

Direction of displacement relative to force decides the sign

Three Cases
θ = 0°: W is maximum positive.
θ = 90°: W = 0 (force and displacement perpendicular).
θ = 180°: W is negative (opposing forces like friction).
Work is positive when the force and displacement are in the same direction (θ = 0°). When you push a cart on a road in the same direction it moves, the work done by you is positive.
Work is negative when the force acts opposite to the displacement (θ = 180°). The work done by friction on a sliding box is negative because friction acts backward while the box moves forward.
Work is zero when force is perpendicular to displacement (θ = 90°). The tension in a string of a stone revolving in a horizontal circle does zero work because the tension is directed toward the centre while the motion is along the circle.
Quick Check
Is the work done by gravity positive or negative when a ball is thrown upward?

Answer: Negative. The ball moves upward but gravity acts downward, so θ = 180° and work done by gravity is negative.
3

Work Done Against Gravity

Lifting an object stores energy in it

Formula
Wagainst gravity=mghW_{against\,gravity} = mgh
When you lift an object of mass m through a vertical height h, you do work against gravity. The force needed is at least equal to the weight mg, and the displacement is h upward.
The work done against gravity becomes stored as gravitational potential energy in the object. When the object is released, this stored energy can be converted back to kinetic energy.
Labourers in Indian construction sites who carry bricks or cement bags up several floors of a building are doing work against gravity with every step. The amount of work done depends on the mass of the load and the height gained.
Solved Example

Lifting a bag up a staircase

A 10 kg school bag is carried up a staircase of height 3 m. Find work done against gravity (g = 10 m/s²).

W=mgh=10×10×3=300 JW = mgh = 10 \times 10 \times 3 = 300\ \text{J}
4

Kinetic Energy

Energy possessed by a body because of its motion

Formula
KE=12mv2KE = \frac{1}{2}mv^2

mm = mass in kg, vv = speed in m/s, KE in joules (J).
A moving body has the capacity to do work because of its motion. This energy of motion is called kinetic energy.
Kinetic energy depends on both the mass and the speed of the body. If speed doubles, kinetic energy becomes four times larger. This is why accidents on national highways are far more dangerous at high speed than at low speed.
A cricket ball bowled by a fast bowler carries much more kinetic energy than a gentle slow ball because of the higher speed, even though the mass is the same. A loaded goods truck moving slowly can have more kinetic energy than a small car at the same speed because of its much greater mass.
Solved Example

KE of a moving scooter

Find the kinetic energy of a 150 kg scooter moving at 20 m/s.

KE=12×150×202=12×150×400=30,000 J=30 kJKE = \frac{1}{2} \times 150 \times 20^2 = \frac{1}{2} \times 150 \times 400 = 30{,}000\ \text{J} = 30\ \text{kJ}
5

Work-Energy Theorem

Net work done equals change in kinetic energy

Theorem
Wnet=ΔKE=12mv2−12mu2W_{net} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2
The work-energy theorem states that the net work done on a body equals the change in its kinetic energy.
If the net force does positive work on a body, its kinetic energy increases and it speeds up. If the net force does negative work (like friction or brakes on a vehicle), kinetic energy decreases and the body slows down.
This theorem explains why a car needs much more braking force to stop from a high speed than from a low speed — the higher KE requires more work (larger force × larger distance) to reduce it to zero.
Show a braking distance problem using work-energy theorem

A car of mass 1000 kg moving at 20 m/s is stopped by brakes. Find the work done by brakes.

W=ΔKE=0−12×1000×400=−200,000W = \Delta KE = 0 - \tfrac{1}{2} \times 1000 \times 400 = -200{,}000 J = −200-200 kJ.

The negative sign means the braking force acts opposite to the direction of motion.

Quick Practice
A body of mass 5 kg increases from rest to 10 m/s. Find the work done on it.

Answer: W=12×5×100−0=250W = \tfrac{1}{2} \times 5 \times 100 - 0 = 250 J.
6

Potential Energy

Energy stored by virtue of position or configuration

Two Types You Must Know
Gravitational PE: stored due to height above a reference level.
PE=mghPE = mgh

Elastic PE: stored in a deformed elastic body (spring, rubber band).
Potential energy is the energy possessed by a body because of its position or configuration. A body can store energy even when it is not moving.
A drawn bowstring, a compressed spring in a watch, a stretched rubber band, and a raised water tank on the rooftop of a building in Mumbai all have potential energy stored in them.
When the constraint is released — the bowstring is let go, the spring is released, the rubber band snaps — the stored potential energy converts into kinetic energy or other forms of energy.
7

Gravitational Potential Energy

Energy stored by height above the reference level

Formula
PE=mghPE = mgh

mm = mass (kg), gg ≈ 9.8 m/s², hh = height above reference (m).
Gravitational potential energy is the energy stored in a body when it is raised to a height above a reference level. The formula is PE = mgh.
Hydroelectric power plants like the Bhakra Nangal Dam in Punjab and the Tehri Dam in Uttarakhand use this principle on a massive scale. Water stored at a great height in a reservoir has huge gravitational potential energy. When released, this water falls and the potential energy converts to kinetic energy of the water, which then drives turbines to generate electrical energy.
The reference level for measuring height is chosen by the solver and is usually taken as the ground or the lowest point in the problem.
Solved Example

Water in an overhead tank

A 500 kg water tank is at a height of 10 m above the ground. Find its gravitational PE (g = 10 m/s²).

PE=500×10×10=50,000 J=50 kJPE = 500 \times 10 \times 10 = 50{,}000\ \text{J} = 50\ \text{kJ}
8

Conservation of Mechanical Energy

Total KE + PE stays constant in absence of friction

Conservation Law
KE+PE=constantKE + PE = \text{constant}

When KE increases, PE decreases by the same amount, and vice versa (in absence of friction).
The law of conservation of energy states that energy can neither be created nor destroyed — it can only be converted from one form to another.
In a system where only gravity acts (no friction or air resistance), the sum of kinetic energy and potential energy remains constant. This sum is called mechanical energy.
A child on a garden swing in a park experiences this continuously. At the highest point, the swing moves slowly or stops — KE is minimum, PE is maximum. At the lowest point the swing moves fastest — KE is maximum, PE is minimum. The total mechanical energy stays the same throughout the motion.
Think About It
A 2 kg ball falls from a height of 5 m. Find its speed just before hitting the ground (g = 10 m/s²).

Answer: PEtop=mgh=2×10×5=100PE_{top} = mgh = 2 \times 10 \times 5 = 100 J = KEbottom=12mv2KE_{bottom} = \tfrac{1}{2}mv^2.
So v2=100v^2 = 100 and v=10v = 10 m/s.
9

Power

How quickly work is done

Formula
P=WtP = \frac{W}{t}

Also:
P=FvP = Fv
(when a constant force moves at constant velocity).
Power is the rate at which work is done or energy is transferred. A powerful machine completes the same task faster than a less powerful one.
Two construction workers at a building site may lift the same total load to the same height, but the one who does it in less time has greater power.
The SI unit of power is the watt (W). One watt equals one joule of work done per second. Power is also sometimes expressed in horsepower (hp) in the context of engines and motor vehicles. 1 hp = 746 W.
Solved Example

Power of a water pump

A pump lifts 300 kg of water to a height of 10 m in 5 minutes. Find the power (g = 10 m/s²).

Work done = mgh=300×10×10=30,000mgh = 300 \times 10 \times 10 = 30{,}000 J.
Time = 5×60=3005 \times 60 = 300 s.
P=30,000300=100 WP = \frac{30{,}000}{300} = 100\ \text{W}
10

Commercial Unit of Energy — kWh

The unit on your electricity bill

Conversion
1 kWh=3.6×106 J1\ \text{kWh} = 3.6 \times 10^6\ \text{J}

Energy (kWh) = Power (kW) × Time (h).
In everyday commercial use, energy is measured in kilowatt-hours (kWh) rather than joules, because joule is too small a unit for household quantities.
One kilowatt-hour is the energy consumed by a device of 1000 W power running for 1 hour. On your electricity bill in India, each unit is 1 kWh. If electricity costs ₹5 per unit, a 1000 W geyser running for 2 hours uses 2 units and costs ₹10.
Converting kWh to joules: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. This large number explains why joule is not practical for billing purposes.
Quick Practice
A 100 W bulb runs for 10 hours. How many units of electricity does it consume?

Answer: Energy = 0.1 kW × 10 h = 1 kWh = 1 unit.
11

Energy Transformation

Energy changes form but the total is always conserved

Energy exists in many forms: kinetic, potential, heat, light, sound, electrical, chemical, and nuclear. These forms can convert from one to another, but the total amount is always conserved.
When wood or dung cake (commonly used in rural India) burns in a hearth, chemical energy converts to heat and light. In a transistor radio or a mobile phone, electrical energy converts to sound energy. In a solar panel installed on Indian rooftops, light energy converts to electrical energy.
When we say energy is "wasted," we mean it has converted to a less useful form — usually heat that dissipates into surroundings. Energy is not lost; it simply becomes unavailable for further useful work. Improving efficiency means reducing the amount that converts to waste heat.
Energy Chain

From dam to light bulb

In a hydroelectric plant like Tehri Dam:
Gravitational PE of stored water → Kinetic energy of falling water → Kinetic energy of turbine → Electrical energy in generator → Light and heat energy in bulb.

At each step, total energy is conserved, but some converts to heat due to friction in the machinery.
12

Complete Chapter Summary

Key formulas and ideas to revise before exams

Work:
W=Fscos⁡θW = Fs\cos\theta
. Work is zero when force ⊥ displacement.
Kinetic energy:
KE=12mv2KE = \tfrac{1}{2}mv^2
. Potential energy:
PE=mghPE = mgh
.
Work-energy theorem:
Wnet=ΔKEW_{net} = \Delta KE
.
Conservation:
KE+PE=constantKE + PE = \text{constant}
in absence of friction.
Power:
P=W/tP = W/t
. SI unit: watt (W).
Commercial energy unit: 1 kWh = 3.6 × 10⁶ J.

Work and Energy: revision sheet

Close the notes and explain each idea in your own words. Then check the formulas and attempt the examples before opening their solutions.

Recall checklist
  • What Work Means in Physics
  • Kinetic Energy and Potential Energy
  • Power and Commercial Unit of Energy
  • Conservation and Transformation of Energy

For each topic: state the rule, explain when it applies, give an example and identify one mistake to avoid. Return to any topic you cannot explain without looking.

Formula recap (6)

What Work Means in Physics

W=FsW = Fs
When force and displacement are in the same direction.

What Work Means in Physics

W=Fscos⁡θW = Fs\cos\theta
When force and displacement make angle θ.

Kinetic Energy and Potential Energy

KE=12mv2KE = \frac{1}{2}mv^2

Kinetic Energy and Potential Energy

PE=mghPE = mgh

Power and Commercial Unit of Energy

Power=Work doneTime takenPower = \frac{\text{Work done}}{\text{Time taken}}

Power and Commercial Unit of Energy

1 kWh=3.6×106 J1\ \text{kWh} = 3.6 \times 10^6\ \text{J}

Explain your method

Write the given information, choose a method, show the steps, then check units and whether the answer makes sense.

A force of 20 N moves a box through 5 m in the same direction. Find the work done.
Check worked solution 1
W = Fs = 20 x 5 = 100 J.
Why is no work done when a person pushes a wall that does not move?
Check worked solution 2
Because displacement is zero.

Apply the concept, avoid the trap

Common mistake: Assuming that doubling speed only doubles kinetic energy.

Use this reasoning: Kinetic energy is proportional to v² for fixed mass. Distinguish the energy at a speed from the change in energy between two speeds.

Worked application

A 2 kg trolley speeds up from 3 m/s to 6 m/s. Find the change in kinetic energy and the net work done on it.

Reveal the method and checks
  1. Initial kinetic energy = (1/2) × 2 × 3² = 9 J. Final kinetic energy = (1/2) × 2 × 6² = 36 J.
  2. The increase is 36 − 9 = 27 J. Net work equals this change in kinetic energy, so the net work is 27 J.
  3. The final energy is four times the initial energy; the increase is three times the initial energy. These are different comparisons.

Check your understanding

What is the net work if the trolley instead slows from 6 m/s to 3 m/s?

Check your reasoning

−27 J. Negative net work means kinetic energy decreases; it does not mean the final kinetic energy itself is negative.

Turn mistakes into revision

Record the question, the step that went wrong and the corrected reason. Try it again tomorrow without the solution, then revisit it after a week. A correct guess still needs an explanation.

Practise this chapter