Work, Energy and Simple Machines

Lesson

Part 1: when a force does work, how much energy a moving body has, and how work changes energy.

In this lesson you will

Calculate work done and identify positive, negative and zero work
Read work from a force–displacement graph
Derive kinetic energy ½mv² and potential energy mgh
State the work–energy theorem and use it

Table of four everyday situations and whether work is done in the science sense
Situation	Work in the science sense?
A farmer drags a sack along a lane	yes, the force moves the sack
A student holds a bucket still at the well	no, nothing moves
A porter walks on a level platform carrying a trunk on his head	no, the lift is at right angles to the motion
A girl climbs a flight of steps	yes, she works against gravity

Concept

Work done by a force

When a force $F$ moves a body through a displacement $s$ in the direction of the force, the work done is $W = F \times s$ The SI unit of work is the joule (J): $1\ \text{J} = 1\ \text{N m}$ , the work done when a force of 1 N moves a body by 1 m along the force. Work has only a size, no direction, so it is a scalar. No displacement means no work, however large the force.

Table of work done for different forces and displacements
Force	Displacement	Work done
25 N	0 m (wall does not move)	0 J
25 N	2.0 m along the force	50 J
100 N	0.50 m along the force	50 J
100 N	0 m	0 J

Diagram

Positive, negative and zero work

Work can be positive, zero or negative.

If the force makes an angle $\theta$ with the displacement, the work is $W = F s \cos\theta$ . We use only three angles. At $\theta = 0^\circ$ , $\cos\theta = 1$ and the work is positive: the force helps the motion. At $90^\circ$ , $\cos\theta = 0$ and the work is zero: the force is at right angles to the motion. At $180^\circ$ , $\cos\theta = -1$ and the work is negative: the force opposes the motion, as friction does.

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