Work, Energy and Power — Part 1: Work, units and power: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Hard work or no work?

Part 1 — in physics, work is done only when a force moves its point of application. Holding a heavy bag still may tire you, but it does no work on the bag.

In this lesson you will

Calculate work done using W = F s cos θ
Explain when no work is done
Convert between joule, erg, calorie, kilowatt hour and electron volt
Calculate power and convert between watt and horsepower

Table of four everyday situations and whether work is done
Situation	Work done on the object?
Lifting a bucket from a well	Yes
Holding a bag still at shoulder height	No (no displacement)
Carrying a bag along a level corridor	No (force ⟂ displacement)
Pushing a stalled car that moves 5 m	Yes

Diagram

Work done by a force

Work is done when a force displaces a body: $W = F\,s\cos\theta$ , where $\theta$ is the angle between the force and the displacement. Only the component $F\cos\theta$ along the displacement does work. Special cases: $\theta = 0^\circ$ : $W = Fs$ (maximum); $\theta = 90^\circ$ : $W = 0$ (a coolie carrying a load on his head across a level platform does no work against gravity); $\theta = 180^\circ$ : $W = -Fs$ (friction does negative work). Work against gravity: lifting a mass $m$ through height $h$ : $W = mgh$ . Work is a scalar.

Worked example

Worked example: pulling at an angle

Problem. A child pulls a toy cart 8 m along the floor with a force of 15 N along a string at $60^\circ$ to the floor. Find the work done. How much work would the same force do if the string were horizontal?

At $60^\circ$ : $W = F s \cos\theta = 15 \times 8 \times \cos 60^\circ = 15 \times 8 \times 0.5 = 60\ \text{J}$ .

Horizontal: $W = 15 \times 8 = 120\ \text{J}$ — the pull at an angle wastes part of the force lifting rather than moving the cart.

Table of work done by a 15 newton force over 8 metres at three angles
Angle of string	cos θ	Work (J)
0°	1	120
60°	0.5	60
90°	0	0

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