Work, Energy and Power is one of the highest-scoring chapters in NDA Physics because the formulas are short and the logic is clean. Once you nail the idea that work transfers energy and energy is never destroyed, you can solve almost any numerical in under a minute. Let us build that intuition step by step.
Why this chapter is a scoring goldmine
In everyday speech, “work” means any effort — reading, thinking, pushing a wall. In physics, the meaning is far stricter, and that strictness is exactly what makes NDA questions predictable.
Every year the NDA General Ability Test (GAT) carries a handful of direct questions from this chapter: a numerical on work done, a conceptual question on energy conversion, or a one-liner on the unit of power. Because the formulas are few and reusable, this is a topic you should aim to never lose marks on.
The good news for a busy Class 11-12 student is that you do not need heavy calculus here. Almost everything reduces to three short formulas — one for work, one for kinetic energy and one for power — plus a single big idea, the conservation of energy. Master those and you have covered the bulk of the questions ever asked.
Throughout this lesson we will keep the language plain and lean on real-life examples — a falling stone, a water pump, a moving car — so the physics sticks even if you are revising at the last minute.
This chapter sits at the heart of mechanics. The same energy idea reappears in heat, sound, electricity and even atomic physics — so learning it well pays off across the whole syllabus.
What ‘work’ really means in physics
Work is done only when a force produces displacement in the direction of the force. If either the force is zero, or the displacement is zero, or the displacement is perpendicular to the force, the work done is zero.
Work done, W = F × s × cosθ
where F is the force, s is the displacement, and θ is the angle between the force and the displacement.
SI unit of work: joule (J); 1 J = 1 N × 1 m.
The factor cosθ tells you how much of the force actually acts along the motion:
- If θ = 0° (force along motion), cos0° = 1, so W = F × s — maximum positive work.
- If θ = 90° (force perpendicular), cos90° = 0, so W = 0 — no work at all.
- If θ = 180° (force opposes motion), cos180° = −1, so W is negative.
Carrying a heavy bag while walking on level ground does zero work against gravity, because gravity acts downward while your displacement is horizontal (θ = 90°). Many students wrongly assume tiredness equals physics work.
Positive, negative and zero work
The sign of work tells you whether energy is being given to a body or taken away.
Positive work
When the force has a component along the displacement, energy is transferred to the body and it speeds up. Example: gravity pulling a freely falling stone downward.
Negative work
When the force opposes the motion, energy is removed and the body slows down. Example: friction acting on a sliding box, or gravity on a ball thrown upward.
Zero work
Either no displacement, no force, or the two are perpendicular. Example: the centripetal force on a satellite does zero work because it is always perpendicular to the circular path, which is why a satellite keeps the same speed.
Whenever a body moves in a circle at constant speed, the work done by the central (centripetal) force is always zero. This is a favourite one-mark trick question.
Kinetic energy — energy of motion
Energy is the capacity to do work, and it shares the same unit as work: the joule. A moving body possesses kinetic energy because of its motion.
Kinetic energy, KE = ½ m v2
where m is the mass (kg) and v is the speed (m/s).
Notice that kinetic energy depends on the square of the speed. So if a car doubles its speed, its kinetic energy becomes four times larger — which is exactly why high-speed crashes are so much more dangerous and braking distances grow rapidly.
Kinetic energy is always a positive quantity, because both mass and the square of speed are positive. A body at rest has zero kinetic energy, and the moment it starts moving it gains some. This is the energy that does work when one body collides with another: a moving hammer drives a nail precisely because it carries kinetic energy that gets transferred on impact.
Double the mass → double the KE. Double the speed → four times the KE. Speed matters far more than mass.
Potential energy — stored energy of position
Potential energy is the energy a body has because of its position or configuration. The most common type in NDA is gravitational potential energy, the energy stored when an object is raised against gravity.
Gravitational PE, PE = m g h
where m is mass (kg), g is acceleration due to gravity (≈ 9.8 m/s2), and h is the height above the reference level.
Other forms include elastic potential energy in a stretched or compressed spring, and chemical potential energy stored in fuels and food. Whenever you do work against a force without changing speed, that work is usually stored as potential energy.
Potential energy is always measured relative to a chosen reference level, usually the ground. An object on a tabletop has positive PE with respect to the floor but zero PE with respect to the tabletop itself. In NDA problems the ground is almost always taken as the zero level, so just use the height above the ground for h.
A simple way to picture it: lifting a brick to the roof “charges” it with potential energy. Drop it, and that stored energy is released as motion. The higher you lift it or the heavier the brick, the more energy it stores.
For a stretched spring, elastic PE = ½ k x2, where k is the spring constant and x is the extension. Like KE, it depends on the square of the displacement.
The work-energy theorem
This single idea links work and kinetic energy and unlocks most numericals.
The work-energy theorem states that the net work done on a body equals its change in kinetic energy:
Wnet = KEfinal − KEinitial = ½ m v2 − ½ m u2
In words: if positive work is done, the body speeds up; if negative work (like friction) is done, it slows down. You do not need to know the time taken or the path — only the start and end speeds.
This theorem is powerful because it sidesteps messy force-and-acceleration calculations. Many NDA stopping-distance and braking problems are solved fastest using it.
Here is a practical use. When a car brakes, friction does negative work that exactly removes the car’s kinetic energy and brings it to rest. Because KE depends on speed squared, a car moving at twice the speed has four times the kinetic energy and therefore needs roughly four times the braking distance to stop. That single insight, drawn straight from the work-energy theorem, explains many road-safety facts and is a frequent exam theme.
Law of conservation of energy
This is the most important law in the whole chapter and a guaranteed exam favourite.
Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system stays constant.
For a body falling freely (ignoring air resistance), the total mechanical energy — the sum of KE and PE — remains the same at every point:
KE + PE = constant
Energy transformations to remember
- Falling object: PE → KE
- Stretched bow / spring: elastic PE → KE of arrow
- Electric bulb: electrical energy → light + heat
- Hydroelectric dam: PE of water → KE → electrical energy
- Burning fuel: chemical energy → heat + light
Friction does not “destroy” energy — it converts mechanical energy into heat and sound. The total energy is still conserved; it has just changed form.
Power — how fast work is done
Power is the rate of doing work, or equivalently the rate of transferring energy. Two engines may do the same work, but the one that finishes faster is more powerful.
Power = Work done ÷ Time taken = W / t
Also, Power = Force × velocity (P = F × v) when force acts along the motion.
SI unit: watt (W); 1 W = 1 J/s.
Handy unit conversions
- 1 kilowatt (kW) = 1000 W
- 1 megawatt (MW) = 106 W
- 1 horsepower (hp) ≈ 746 W
- 1 kilowatt-hour (kWh) = 3.6 × 106 J — this is the ‘unit’ on your electricity bill, a unit of energy, not power.
The kilowatt-hour (kWh) measures energy, while the kilowatt (kW) measures power. Confusing the two is a classic NDA trap.
Worked example
A 2 kg ball is dropped from a height of 5 m. Find (a) its potential energy at the top, and (b) its speed just before hitting the ground. Take g = 10 m/s2.
So the ball reaches the ground with a speed of 10 m/s, carrying 100 J that has fully converted from potential to kinetic energy.
A quick power calculation
A pump lifts 600 kg of water through a height of 10 m in 20 seconds. Find the power of the pump. Take g = 10 m/s2.
The pump delivers a power of 3 kW. Notice we first found the work (energy) and only then divided by time.
For lifting problems, always compute work as m g h first, then divide by time for power. Keep units in kg, m and s to land in joules and watts directly.
Previous-year style question
Q. When a body moves in a horizontal circle at constant speed, the work done by the centripetal force is:
Answer: Zero. The centripetal force always points toward the centre, perpendicular to the body’s velocity (θ = 90°, cos90° = 0), so W = F × s × cos90° = 0. That is why the speed stays constant in uniform circular motion.
Perpendicular force → zero work → no change in speed. This logic also explains why magnetic force does no work on a moving charge.
Quick revision
- Work W = F × s × cosθ; unit = joule (J).
- Work is zero when force and displacement are perpendicular.
- Kinetic energy KE = ½ m v2; depends on speed squared.
- Potential energy PE = m g h.
- Work-energy theorem: net work = change in KE.
- Energy is conserved — only transformed, never destroyed.
- Power P = W / t = F × v; unit = watt (W); 1 hp ≈ 746 W.
- kWh is a unit of energy, not power.
Revise these eight lines the night before your exam and you can answer almost any Work, Energy and Power question with confidence.
Frequently asked questions
What is the SI unit of work and energy?
Both work and energy share the same SI unit, the joule (J). One joule is the work done when a force of one newton moves a body through one metre in the direction of the force.
Why is no work done when you carry a bag while walking on level ground?
Gravity acts vertically downward, but your displacement is horizontal, so the angle between them is 90°. Since cos90° = 0, the work done against gravity is zero even though you feel tired.
What is the difference between energy and power?
Energy is the total capacity to do work, measured in joules. Power is how fast that work is done, measured in watts (joules per second). A more powerful machine does the same work in less time.
State the law of conservation of energy.
Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system always stays constant.
How much is one horsepower in watts?
One horsepower (hp) is approximately equal to 746 watts. It is a commonly used unit for the power of engines and motors in NDA questions.
Why does kinetic energy increase four times when speed doubles?
Kinetic energy is given by ½ m v², which depends on the square of the speed. So doubling the speed multiplies the kinetic energy by 2² = 4, while the mass stays unchanged.
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