4.2.4

# Young Modulus

Test yourself

## The Young Modulus

Stress and strain can be combined to give a property of a material. This property of the material is called the Young modulus and it is the same for any sample of the material; it does not depend on the size or shape of the sample.

### Young modulus

• Young modulus gets it name from the scientist Thomas Young.
• It is defined as the ratio of stress to strain.
• The Young modulus can be written as:
• Young modulus $= \frac{stress}{strain}$
• $E = \frac{\sigma}{\epsilon}$

### Stiffness of a material

• The Young modulus represents the stiffness of a material.
• Stiff materials have a small strain for large stresses.

• The gradient of the linear section of a stress-strain graph is the Young modulus.

## Determining the Young Modulus

The Young modulus can be determined simply. The simple method involves stretching a long thin wire and recording the stress and strain.

### Equipment

• Set up your equipment as shown.

### Method

• Determine the cross-sectional area of the wire by assuming a circular cross section.
• A micrometer screw gauge would be the best piece of equipment to use here.
• Determine the un-stretched length of the wire.
• Add masses and record the extension of the wire. You can work out the applied force from the masses added.
• For each set of masses added, you can obtain pairs of stress-strain values.

### Result

• The gradient of the linear section of a stress-strain graph is the Young modulus.