Work, Energy and Power: Concepts, Formulas and Numerical Practice

Energy keeps a fan spinning, lifts an elevator, and powers your laptop battery. But in physics, words like work, energy and power carry very specific meanings that often differ from everyday usage. Understanding these definitions is essential for scoring high in board exams and competitive tests across India, Pakistan, and other STEM curricula worldwide.

This guide explains the meaning of work, the different forms of energy, the concept of power, and the all-important law of conservation of energy — supported by solved problems and exam-focused FAQs.

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What Is Work in Physics?

Work is said to be done when a force applied on an object causes it to be displaced in the direction of the force. If you push a wall and it does not move, no work has been done — no matter how tired you feel.

Formula: W = F × s × cos θ

where F is the applied force, s is the displacement, and θ is the angle between force and displacement.

SI unit: joule (J). One joule = one newton × one metre.

Types of Work

Positive work: Force and displacement are in the same direction (e.g., a falling apple).
Negative work: Force and displacement are in opposite directions (e.g., friction acting on a sliding box).
Zero work: Force is perpendicular to displacement (e.g., a coolie carrying a load horizontally).

What Is Energy?

Energy is the capacity to do work. It cannot be seen directly but can be measured through the work it produces. Energy exists in many forms — mechanical, thermal, chemical, electrical, nuclear, and radiant — but at school level we focus mainly on mechanical energy.

Kinetic Energy

The energy possessed by a body due to its motion.

Formula: KE = ½ m v²

Potential Energy

The energy possessed by a body due to its position or configuration.

Gravitational PE: PE = m g h

Solved Numerical 1

Question: Find the kinetic energy of a 2 kg ball moving at 10 m/s.

Solution:
KE = ½ × 2 × (10)² = 100 J

Solved Numerical 2

Question: A 5 kg object is lifted to a height of 4 m. Calculate its potential energy. (g = 10 m/s²)

Solution:
PE = m g h = 5 × 10 × 4 = 200 J

The Work–Energy Theorem

The work done by the net force acting on a body equals the change in its kinetic energy.

W_net = ΔKE = ½ m v² − ½ m u²

This theorem is one of the most powerful tools for solving motion problems where forces and distances are known, but time is not.

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 remains constant.

For example, when a stone falls from a height, its potential energy gradually changes into kinetic energy. Just before hitting the ground, almost all the energy has become kinetic.

Power — The Rate of Doing Work

Power tells us how fast work is being done. Two people may lift the same load to the same height, but the one who does it faster has more power.

Formula: P = W / t

SI unit: watt (W). 1 watt = 1 joule per second.

Commercial unit of energy is the kilowatt-hour (kWh), where 1 kWh = 3.6 × 10⁶ J.

Solved Numerical 3

Question: An electric motor lifts a 100 kg load to a height of 10 m in 20 seconds. Calculate the power output. (g = 10 m/s²)

Solution:
Work done = mgh = 100 × 10 × 10 = 10,000 J
Power = W / t = 10,000 / 20 = 500 W

Conservative vs Non-Conservative Forces

A conservative force (like gravity) does work that depends only on initial and final positions, not on the path taken. A non-conservative force (like friction) depends on the path — the longer the path, the more energy is dissipated as heat.

Common Mistakes Students Make

Forgetting the cosine factor when force and displacement are not aligned.
Confusing watts with joules — power is not the same as energy.
Treating friction work as positive; it is almost always negative.

Frequently Asked Questions

Q1. Is work a scalar or vector quantity?
Work is a scalar quantity, although it is derived from two vectors (force and displacement).

Q2. Why is no work done when you hold a heavy bag stationary?
Because there is no displacement. Although you feel tired due to muscle effort, in physics, displacement is required for work to be done.

Q3. Can kinetic energy be negative?
No. Since mass is positive and velocity is squared, kinetic energy is always zero or positive.

Q4. What is the difference between energy and power?
Energy is the total work done or capacity to do work. Power is the rate at which energy is used or transferred.

Q5. Is 1 horsepower equal to 1 kilowatt?
No. 1 horsepower ≈ 746 watts, which is less than 1 kilowatt (1000 W).

Key Takeaways

Work, energy, and power form the backbone of mechanics. Work depends on force and displacement; energy is the capacity to do work and exists in many interconvertible forms; and power measures how quickly energy is used. The conservation of energy principle is one of the most universal laws in physics, applying everywhere from a falling apple to nuclear reactors.