Question

Two parallel and opposite forces, each of magnitude $4000N$, are applied tangentially to the upper and lower faces of a cubical metal block $25cm$ on a side. Find the displacement of the upper surface relative to the lower surface (in $\times 10^{-5}cm$ ). The shear modulus for the metal is $80Gpa$.

Answer 1

Answer: 2

We use the approximate from $S=F/(A\varphi )$.
Putting $S=8\times 10^{10}N/m^2,F=4000N$ and $A=(0.25m{)}^2$
$=6.25\times 10^{-2}{m}^2$ in the above equation and solving for $\varphi$, we get
$\varphi =\frac{(4000N)}{\left(6.25\times 10^{-2}{m}^2\right)\left(8\times 10^{10}N/m^2\right)}=8.0\times 10^{-7}rad$
The displacement of the upper surface is given by $d=L\varphi$, where $L$ is an edge of the cube.
$\therefore d=\left(8.0\times 10^{-7}\right)(25cm)$
$=2.0\times 10^{-5}cm$