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Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

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Student-friendly explanation

When net work is done on a body, its speed changes. If net work is positive, kinetic energy increases. If net work is negative, kinetic energy decreases. This theorem links force-displacement calculations with motion and energy.

How to write this in exams

  1. 1

    Start with the exact idea

    The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

  2. 2

    Then show how to use it

    Write initial and final speeds, calculate initial and final kinetic energy, subtract initial from final, and match it with net work.

  3. 3

    Add one concrete example

    If the net work done on a cart is 80 J, its kinetic energy increases by 80 J.

  4. 4

    Avoid this incomplete answer

    Using only final kinetic energy as net work is wrong when the object already had initial speed.

Definition

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

Example

If the net work done on a cart is 80 J, its kinetic energy increases by 80 J.

Rule to remember

W_net = ΔKE = KE_final - KE_initial = 1/2 mv² - 1/2 mu².

Memory hook

Net work changes motion energy.

Examples and method

Worked example

A 2 kg object speeds up from 3 m/s to 5 m/s. Change in KE = 1/2 × 2 × (25 - 9) = 16 J, so net work done is 16 J.

Method to apply

Write initial and final speeds, calculate initial and final kinetic energy, subtract initial from final, and match it with net work.

Diagram support

A before-after speed diagram can show a body speeding up or slowing down due to net work.

How CBSE asks it

Questions may ask for net work from change in speed, or ask students to predict whether kinetic energy increases or decreases.

Avoid common mistakes

Common confusion

Students sometimes use total work by one force instead of net work by all forces acting on the object.

Common wrong answer

Using only final kinetic energy as net work is wrong when the object already had initial speed.

Exam tip

Look for the word net. The theorem is about total effective work after considering all forces, not only the applied force.

Quick check

If net work done on a body is negative, what happens to its kinetic energy?

Its kinetic energy decreases because negative net work reduces the body's speed or opposes its motion.

Answer writing and exam use

1-mark answer

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

2-mark answer

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. W_net = ΔKE = KE_final - KE_initial = 1/2 mv² - 1/2 mu². If the net work done on a cart is 80 J, its kinetic energy increases by 80 J.

3-mark answer

When net work is done on a body, its speed changes. If net work is positive, kinetic energy increases. If net work is negative, kinetic energy decreases. This theorem links force-displacement calculations with motion and energy. W_net = ΔKE = KE_final - KE_initial = 1/2 mv² - 1/2 mu². A 2 kg object speeds up from 3 m/s to 5 m/s. Change in KE = 1/2 × 2 × (25 - 9) = 16 J, so net work done is 16 J. Questions may ask for net work from change in speed, or ask students to predict whether kinetic energy increases or decreases. Using only final kinetic energy as net work is wrong when the object already had initial speed.
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