# Mechanical energy and work done

## In a nutshell

When energy is transferred using a force this is called work done. Mechanical work can be calculated by multiplying force and distance.

**Equations**

#### Word Equation | #### Symbol Equation |

$work \space done = force \times distance$ | $W = F \times s$ |

**Variable definitions**

#### Quantity Name | #### Symbol | #### Unit Name | #### Unit |

$force$ | $F$ | $newton$ | $N$ |

$distance$ | $s$ | $metre$ | $m$ |

$work \space done$ | $W$ | $joule$ | $J$ |

## Work done

### Definition

Work done is the energy transferred from or to an object using a force. Work can be done either mechanically or electrically. This allows energy to transfer from one store to another.

#### Work done | #### Examples |

**Mechanically** | *Pushing a table, skydiving, running * |

**Electrically** | *Light bulb turning on, signals being sent from your brain to your body* |

## Mechanical work

Mechanical work is done when a force is applied to an object.

##### Example

*Describe the energy transfers for a skydiver using an energy transfer diagram.*

$\boxed{gravitational \space potential \space energy} \xrightarrow [mechanically]{energy \space transferred} \boxed {kinetic \space energy}$

You can calculate work done by using the following equation.

$work \space done = force \times distance \\ \ \\ W = F \times s$

##### Example

*The force needed to push a bike for $5 \, m$ is $50 \, N$. How much work is done?*

*First select the correct equation:*

$W = F \times s$

*Then, substitute in the values:*

$W = 50 \times 5$

*Don't forget to include your units in your final answer:*

$250 \space J$

*$\underline{250\,J}$ of mechanical work was done to push the bike.*

## Electrical work

Electrical work is done when an electric charge flows. For example, the device you are on now is doing electrical work in order for you to use it. A force is needed in order to do this, but you don't need the equation for this just yet.

##### Example

*Describe the energy transfer between a battery and a light bulb using an energy transfer diagram.*

*$\boxed{chemical \space energy \space in \space battery} \xrightarrow[electrically] {energy \space transferred} \boxed {thermal \space energy \space and \space radiation}$*