Question

Calculate the youngs modulus for the material of the wire

Answer 1

First, plot the data shown as points.

The points are (0,0), (1.4, 10), (2.8, 20), (4.2, 30), (4.9, 35), (5.8, 40), and (8, 45).

The graph shows a proportional part (a straight line) and a curvy part. So, the limit of proportionality is shown at the end of the straight line segment. The image below shows this limit.

The gradient of the straight-line portion refers to the slope. Let's use the points (1.4, 10) and (2.8, 20).

`m=(y_2-y_1)/(x_2-x_1)=(20-10)/(2.8-1.4)=(10)/(1.4)\approx7.14`

Therefore, the gradient is 7.14.

The Young modulus formula is

`E=((F)/(A))/((\Delta l)/(l))`

Let's use the greater force and the greater extension.

`E=((45N)/(7*10^(-8)m^2))/((8*10^(-3)m)/(2m))=1.6*10^(11)`

Therefore, Young Modulus is 1.6x10^11.