Question

A $50kg$ motor rests on four cylindrical rubber blocks. Each block has a height of $4cm$ and a cross-sectional area of $16c{m}^2$. The shear modulus of rubber is $2\times {10}^{6}N/m^2$. A sideways force of $500N$ is applied to the motor. The distance that the motor moves sideways (in $cm$) is:

Answer 1

Given

height of each block $=4cm$
Area of cross section $A=16\times {10}^{-4}{m}^2$
Shear Modulus $G=2\times {10}^{6}N/m^2$
Force on each block $F=\frac{500}{4}N$

Shear strain
$\theta =\frac{x}{L}$
Strain stress relation $\sigma =G\theta$

$\theta =\frac{F}{AG}$

$\Rightarrow x=\frac{FL}{AG}$

$\Rightarrow x=\frac{500\times 4\times {10}^{-2}}{4\times 16\times {10}^{-4}\times 2\times {10}^6}=0.156cm$