C
CraftExam
medium difficulty6 min

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.

In one line: Work needs force plus displacement.

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Understand it

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.

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).

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1A force of 15 N moves a trolley through 4 m in the direction of force.
  2. 2Work done = F × s = 15 × 4 = 60 J.

Method you can reuse

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.

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
The work done on the wall is zero because there is force but no displacement of the wall.

Common wrong answer

Writing 15 + 4 = 19 J.

Why it loses marks: Work depends on multiplication of force and displacement, not addition.

Don't mix this up

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

Exam tip

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

Work Done by a Force diagram

Open full screen to read every label clearly.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

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.
  1. 1

    Enough for 1 mark

    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

    Add for 2 marks

    In school-level problems, work is calculated as force multiplied by displacement in the direction of force.

  3. 3

    Add for 3 marks

    If a force is applied but the object does not move, work done is zero.

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