### Stretching Materials

- When forces are applied to materials, the size and shape of the material can change
- The method below describes a typical procedure for carrying out an investigation into the properties of a material

*An experiment to measure the extension of a spring** *

- Set up the apparatus as shown in the diagram
- A single mass (0.1 kg, 100g) is attached to the spring, with a pointer attached to the bottom, and the position of the spring is measured against the ruler
- The mass (in kg) and position (in cm) are recorded in a table
- A further mass is added and the new position measured
- The above process continues until a total of 7 masses have been added
- The masses are then removed and the entire process repeated again, until it has been carried out a total of three times, and averages can then be taken

- Once measurements have been taken:
- The force on the spring can be found by multiplying the mass on the spring (in kg) by 10 N/kg (the gravitational field strength)
- The extension of the spring can be found by subtracting the original position of the spring from each of the subsequent positions

- Finally, a graph of extension (on the y-axis) against force (on the x-axis) should be plotted

*A graph of force against extension for a metal spring*

### Hooke's Law

- Hooke’s law states that:
**The extension of a spring is proportional to the applied force**

(where k is the spring constant, which represents how stiff a spring is)

** **

- Many other materials (such as metal wires) also obey Hooke’s law
- Hooke’s law is associated with the initial linear (straight) part of a force-extension graph
- Objects that obey Hooke’s law will return to their original length after being stretched
- If an object continues to be stretched it can be taken past the
**limit of proportionality**(sometimes called the elastic limit). At this point the object will no longer obey Hooke’s law and will not return to its original length

*The spring on the right has been stretched beyond the limit of proportionality*

#### Exam Tip

A relationship is said to be **proportional** if the graph is a **straight line going through the origin.**

If a graph is a straight line but **does not go through the origin** the relationship is said to be **linear.**