# Work Done by a Force

## Work Done by a Force Revision

**Work Done by a Force**

**Work done** is the **energy** used by a** force** to move an object a certain **distance**.

**What is Work Done?**

When an object is moved by a **force through a distance**, energy is transferred and there is **work done** on the object. This is because to move an object with mass, there must be a force. Whatever is applying this force (e.g a hand) requires **energy** to move the object. Therefore **energy** is transferred and the** force does work** on the object.

The **energy** is transferred to the **kinetic energy** store of the object, but if there is friction on the object then work is done against the frictional forces. This means there is a transfer to thermal **energy** and hence there is a temperature rise in the object.

An example where we can see this in action is a man pushing a heavy box on floor with lots of friction:

- Because the man is using force to push the box, he is
**doing work**on the box, against the**friction**of the floor. **Energy**is being transferred to the kinetic energy store of the box.- There is also some wasted energy transferred to thermal energy due to the friction between the box and the floor.

**Calculating Work Done**

The amount of **work done** on an object due to a force can be calculated using the following equation:

\textcolor{f21cc2}{W = Fs}

- \textcolor{f21cc2}{W} is
**work done**in Joules \left(\text{J}\right) - \textcolor{f21cc2}{F} is
**force**in Newtons, \left(\text{N}\right) - \textcolor{f21cc2}{s} is
**distance**in metres \left(\text{m}\right).

1 \: \text{J} of **work is done** when a force of 1 \: \text{N} moves an object through a distance of 1 \: \text{m}.

Therefore \bold{\textcolor{f21cc2}{1}}** Joule = **\bold{\textcolor{f21cc2}{1}}** Newton-meter**.

**Example: Calculating Work Done**

A man pushes a box through a distance of \textcolor{f21cc2}{12 \: \text{m}}, and he exerts \textcolor{aa57ff}{14 \: \text{N}} of force on the box. Calculate the **work done** by the man. Ignore the frictional force.

**[2 marks]**

Using the **work done** equation:

W = Fs

Substitute in the values:

W = \textcolor{aa57ff}{14} \times \textcolor{f21cc2}{12}

Calculate the answer:

W = 168 \: \text{J or Nm}

## Work Done by a Force Example Questions

**Question 1**: State what is meant by the term “work done”.

**[2 marks]**

Work done is the amount of **energy transferred** to an object when a** force** moves the object through a** distance**.

**Question 2**: A car drives 200 \: \text{m} and the engine effectively applies 150 \: \text{N} of force. Calculate the work done by the car’s engine and give the appropriate units.

**[3 marks]**

Using the work done equation:

\begin{aligned} \boldsymbol{W} &\boldsymbol{= Fs} \\ \boldsymbol{W} &\boldsymbol{= 150 }\: \textbf{N} \boldsymbol{\times \: 200 }\: \textbf{m} \\ \boldsymbol{W} &\boldsymbol{= 3000} \: \textbf{J} \: \text{or} \: \textbf{Nm} \end{aligned}

**Question 3**: A man pushes a box 4 \: \text{m}, and 100 \: \text{J} of energy is transferred to the kinetic energy store of the box. Calculate the force exerted by the man on the box.

**[3 marks]**

Using the work done equation:

W = Fs

Rearrange to get the force:

F = \dfrac{W}{s}

F = \dfrac{100 \: \text{J}}{4 \: \text{m}}

\bold{F = 25} \: \textbf{N}