Calculating work done and power

In a nutshell

Work done is the energy transferred by a force. Power is the rate of energy transfer.

Equations

Word Equation	Symbol Equation
$work\: done = force\times distance$	$W = F\times s$
$power = \frac{energy\:transferred}{time}$	$P = \frac{E}{t}$

Variable definitions

Quantity name	symbol	unit name	unit
$work\;done$	$W$	$joule$	$J$
$force$	$F$	$newton$	$N$
$distance$	$s$	$metre$	$m$
$power$	$P$	$watt$	$W$
$energy \:tranferred$	$E$	$joule$	$J$
$time$	$t$	$second$	$s$

Work done

Definition

Work done is the energy transferred by a force. It is measured in joules ( $J$ ).

The amount of work done depends on the size of the force and the distance moved in the direction of the force.

$work\:done = force \times distance\text{ (moved in the direction of the force)} \\ \ \\ W=F\times s$

Note: In this equation, $s$ is used for distance instead of $d$ . Different exam boards use different symbols, so make sure to check the formula book!

Example

A box is pushed along the corridor of a house. The corridor is $10\,m$ long and a force of $15 \,N$ is exerted on the box. What is the work done on the box when it reaches the end of the corridor?

Physics; Forces and energy; KS4 Year 10; Calculating work done and power

1.	Initial position of box
2.	Final position of box

First, write out the quantities given and check they are in the correct form:

$F = 15\,N\\ \ \\ s = 10 \,m$

Next, write out the equation needed:

$W = F \times s$ 

Then, substitute the values into the equation:

$W = 15 \times 10 = 150$

Make sure to include units:

$\text{work done, }W = 150\, J$ 

Therefore, the work done on the trolley is $\underline{150\,J}$ .

Power

Definition

Power is the rate of energy transfer or work done. This means the amount of energy transferred per second of time.

Power is measured in watts ( $W$ ) which is equivalent to $J/s$ .

$power = \frac{energy\:transferred}{time}\\ \ \\P = \frac{E}{t}$

Work done is another way of saying energy transferred so the equation can also be written using work done.

$power = \frac{work\:done}{time} \\ \ \\ P = \frac{W}{t}$

Note: Although work done and energy transferred are the same, they have different symbols. Don't get confused between work done $W$ and the units for power $W$ !

Example

What is the power of a kettle which transfers $120\,000\,J$ of energy in $0.60\,mins$ ?

First, write out the quantities given and check they are in the correct form:

$E = 120\,000\,J\\ \ \\ t = 0.6 \,mins = 0.6 \times 60 = 36 \,s$

Next, write out the equation you need to use:

$P = \frac{E}{T}$ 

Then, substitute the values into the equation:

$P = \frac{120\,000}{36} = 3333.\dot{3}$

Make sure to include units and round to two significant figures:

$\text{Power, } P = 3300\,W$ 

Therefore, work done on the trolley is $\underline{3300\,W}$ .

Tip: These types of questions come up very frequently. Without looking at the summary, try to recall the step-by-step solution on a piece of paper for extra practice!

Rearranging the power equation

The power equation can be rearranged to make energy transferred the subject.

$energy \ transferred = power\times time$

$E = P\times t$

$work\ done = power \times time$

$W = P\times t$