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

Variable definitions

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!

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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?

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:

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​$$W = 15 \times 10 = 150$$​

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 $$W$$​!

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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:

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

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Next, write out the equation you need to use:

$$P = \frac{E}{T}$$​​

Then, substitute the values into the equation:

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

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.

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$$energy \ transferred = power\times time$$

​$$E = P\times t$$​​

​​$$work\ done = power \times time$$​​

​$$W = P\times t$$