Work done by a force, mechanical power as work done per second, and the relationships work equals force times distance and power equals work over time.

What this key area is asking

The SQA wants you to calculate the work done by a force using $E_w = F \times d$, understand that work transfers energy, and calculate mechanical power as work done per second.

Work done

If a force does not move (no movement, or the force is at right angles to the motion), then no work is done by that force. Lifting a crate a height $h$ does work $F \times h$ against gravity, where $F$ is the weight being lifted.

Energy transfer

Because work done equals energy transferred, the joule is the unit of both. When a forklift lifts a load it does work against gravity, transferring energy to the load as gravitational potential energy. When a motor drives a mechanism, it does work that becomes the useful output plus the wasted heat. This links straight back to the conservation of energy: the energy put in equals the useful work out plus the energy wasted.

This connection also lets you find efficiency from work and power. Since efficiency is the useful output energy divided by the total input energy (times 100%), and work done is the energy transferred, you can compare the useful work a machine delivers with the total work put into it. A hoist that takes in 8000 J of input work but delivers only 6000 J of useful lifting work is 75% efficient, with the missing 2000 J wasted as heat through friction - the same idea as comparing mechanical advantage with velocity ratio.

Power

Putting work and power together

Many questions give a force, a distance and a time, and ask for the power. The method is always: first find the work done with $E_w = F \times d$, then divide by the time with $P = E_w / t$.

Why this matters

Work and power tie the whole mechanical area together. A mechanism's efficiency compares the useful work out with the energy in; a motor's power rating tells you how quickly it can do work; and lifting, pushing and driving are all work calculations. These are among the most frequently examined relationships in the course.

Try this

Q1. A force of $80 \text{ N}$ moves a box $3.0 \text{ m}$ in the direction of the force. Calculate the work done. [2 marks]

• Cue. $E_w = F \times d = 80 \times 3.0 = 240 \text{ J}$.

Q2. State the unit of power and what it is equivalent to. [1 mark]

• Cue. The watt (W), equal to one joule per second.

Q3. A machine does $9000 \text{ J}$ of work in $45 \text{ s}$. Calculate its power. [2 marks]

• Cue. $P = E_w/t = 9000/45 = 200 \text{ W}$.