# Forces and elasticity: Hooke's Law

## In a nutshell

Applying a force can not only push or pull an object, it can also change the shape or size of the object as well. Deformation is what happens when the shape of an object is changed due to an applied force. Every material behaves differently when a force is applied and, in some cases. the shape of the object is permanently changed after the force is applied.

**Equations**

#### word equation | #### SYMBOL EQUATION |

$force = spring \space constant \times extension$ | $F = k \times e$ |

**Variable definitions**

#### QUANTITY NAME | #### symbol | #### UNIT NAME | #### UNIT |

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

$spring \space constant$ | $k$ | $newton \space per \space metre$ | $N/m$ |

$extension$ | $e$ | $metre$ | $m$ |

## Deformation

When an object is deformed due to an applied force, it can either be stretched or compressed. A stretched object increases in length, this is usually the result of a pulling force on the surface of the object. A compressed, or squashed, object decreases in length. The greater the force applied, the more deformed the object becomes.

Only elastic materials return to their original shape after the force is removed, this means that the deformation of these materials is not permanent. For inelastic materials, the deformation is permanent and if the force is strong enough, the material may break as well.

**Type of material** | **Shape afterwards** | **Deformation** |

**Elastic** | Object returns to original shape. | Not permanent |

**Inelastic** | Object does not return to original shape. | Permanent |

## Hooke's law

The amount that an object is extended by is proportional to the force that was applied to it.

| 1. | Original length of the spring | 2. | Extended length of the spring | 3. | Extension of the spring | |

The constant of proportionality is known as the Spring constant, with units of newtons per metre, and the amount that the object is extended by is called the extension. The extension is the increase in length, so it is measured in metres.

$force = spring \space constant \times extension$

$F = k \times e$

This rule holds for certain elastic materials. Even though a *rubber band* is very elastic, there will be a point where the force is so great that the rubber band stops returning to its original size.

At this point, the force and extension will no longer be proportional in the way they are in Hooke's law. This means that even elastic objects stop obeying Hooke's law when enough force is applied.

**Note: **Hooke's law only works up to a certain point for all materials.