Question

An acetal polymer block is fixed to the rigid plates at its top and bottom surfaces. If the top plate displaces 2 mm horizontally when it is subjected to a horizontal force P = 2 kN ,determine the shear modulus of the polymer. The width of the block is 100 mm. Assume that the polymer is linearly elastic and use small angle analysi

Answer 1

Answer:

The shear modulus of the polymer is 5 MPa

Solution:

As per the question:

displacement of the top plate, d = 2 mm = 0.002 m

Horizontal Force, P = 2 kN = 2000 N

Width of the block, w = 100 mm = 0.1 m

By small angle analysis:

Angle, $\gamma = \frac{2}{200} = 0.01 rad$

Now,

Stress, $\tau$ = $\frac{P}{Area} = \frac{2000}{0.4\times 0.1} = 50000 Pa$

$G = \frac{\tau}{\gamma} = \frac{50000}{0.01} = 5 MPa$