Young Modulus Experiment

Young Modulus Experiment

The Young's modulus is a number that tells us how elastic or how hard a material is. It allows us to predict how much the material can be stretched or compressed under a load.

The Young modulus is Y = stress / strain = FL/Ae, where L is the length of a material, A the cross=sectional area, F the load and e the extension.

This suggests that we can find the Young modulus of any material by measuring these quantities. In practice, if the material is very hard, like metal, the extension is likely to be very small and difficult to measure or even see.

In the case of metal, we can overcome this problem by using a long, thin wire. To see how this helps, recall that for a given material, the same stress would always produce the same strain, regardless of the size and shape.

If we use a wire that is thin, A is small and stress F/A is large. This gives a large strain e/L. To make the extension e even larger and easier to measure, make L large. So the wire must be long and thin wire.

With this understanding, we can set up a experiment using a long thin wire. Fix one end to a support. Place a metre rule next to it and measure its length L. Then fix a weight F to the other end, and measure the extension e. Use a micrometer screw gauge to measure its diameter and calculate the cross-sectional area A. Use Y = FL/Ae to find the Young modulus.

Problem. A thin wire of length 1 m and cross-sectional area 1 mm², hangs from a support. A weight of 1 N is attached to the lower end, causing an extension of 1 cm. Find the Young modulus. Answer. Y = FL/Ae = 1 N x 1 m / (10^-6 m² x 0.01 m) = 10⁸ N m².

The Physics Notes