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Work Done by a Force

Work is done by a force when the force causes displacement of an object in the direction of the force or with a component along the displacement.

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Student-friendly explanation

In school-level problems, work is calculated as force multiplied by displacement in the direction of force. If a force is applied but the object does not move, work done is zero. If the force and displacement are at an angle, only the component of force along displacement contributes to work.

How to write this in exams

  1. 1

    Start with the exact idea

    Work is done by a force when the force causes displacement of an object in the direction of the force or with a component along the displacement.

  2. 2

    Then show how to use it

    Identify the force, identify displacement, check the angle between them, use W = F × s for same direction, and write the answer with joule as unit.

  3. 3

    Add one concrete example

    If a student pushes a box with a force of 20 N and the box moves 3 m in the same direction, work done is 20 × 3 = 60 J.

  4. 4

    Avoid this incomplete answer

    Writing 15 + 4 = 19 J is wrong because work depends on multiplication of force and displacement, not addition.

Definition

Work is done by a force when the force causes displacement of an object in the direction of the force or with a component along the displacement.

Example

If a student pushes a box with a force of 20 N and the box moves 3 m in the same direction, work done is 20 × 3 = 60 J.

Rule to remember

W = F × s when force and displacement are in the same direction. More generally, W = F·s·cosθ, where θ is the angle between force and displacement. SI unit of work is joule (J).

Memory hook

Work needs force plus displacement.

Examples and method

Worked example

A force of 15 N moves a trolley through 4 m in the direction of force. Work done = F × s = 15 × 4 = 60 J.

Method to apply

Identify the force, identify displacement, check the angle between them, use W = F × s for same direction, and write the answer with joule as unit.

Diagram support

A simple arrow diagram may show force and displacement in the same direction, opposite direction, or perpendicular directions.

How CBSE asks it

Questions usually ask students to decide whether work is done, calculate work from force and displacement, or explain zero work in daily-life situations.

Avoid common mistakes

Common confusion

Students often write work as force × time or calculate work even when the object has not moved.

Common wrong answer

Writing 15 + 4 = 19 J is wrong because work depends on multiplication of force and displacement, not addition.

Exam tip

Always check two things before calculating work: force must act, and displacement must occur along the force or its component.

Quick check

A boy pushes a wall for two minutes, but the wall does not move. How much work is done on the wall?

The work done on the wall is zero because there is force but no displacement of the wall.

Study the work done by a force diagram carefully

Use the labelled diagram to keep work done by a force clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of work done by a force in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on work done by a force.

Revision cue

Revise work done by a force through the labels before writing the answer.

Answer writing and exam use

1-mark answer

Work is done by a force when the force causes displacement of an object in the direction of the force or with a component along the displacement.

2-mark answer

Work is done by a force when the force causes displacement of an object in the direction of the force or with a component along the displacement. W = F × s when force and displacement are in the same direction. More generally, W = F·s·cosθ, where θ is the angle between force and displacement. SI unit of work is joule (J). If a student pushes a box with a force of 20 N and the box moves 3 m in the same direction, work done is 20 × 3 = 60 J.

3-mark answer

In school-level problems, work is calculated as force multiplied by displacement in the direction of force. If a force is applied but the object does not move, work done is zero. If the force and displacement are at an angle, only the component of force along displacement contributes to work. W = F × s when force and displacement are in the same direction. More generally, W = F·s·cosθ, where θ is the angle between force and displacement. SI unit of work is joule (J). A force of 15 N moves a trolley through 4 m in the direction of force. Work done = F × s = 15 × 4 = 60 J. Questions usually ask students to decide whether work is done, calculate work from force and displacement, or explain zero work in daily-life situations. Writing 15 + 4 = 19 J is wrong because work depends on multiplication of force and displacement, not addition.
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