Question

Two parallel and opposite forces, each of magnitude `4000 N`, are applied tangentially to the upper and lower faces of a cubical metal blcok `25 cm` on a side. Find the angle of shear and the displacement of the upper surface relative to the lower surface. The shear mdulus for the metal is `80 GPa`.

Answer 1

We use approxmate from `S=F//(Aphi)`
Puttin `S=8xx10^(10)N//m^(2), F=4000N` and `A+(0.25m)^(2)=6.25xx10^(-2)m^(2)` in the above equation and solving for `phi`, we get
`phi=((4000N))/((6.25xx10^(-2)m^(2))(8xx10^(10)N//m^(2)))=8.0xx10^(-7)rad`
The displaced of the upper surface is given by `d=Lphi` where `L` is an edge of the cube.
`:.d=(8.0xx10^(-7))925cm=2.0xx10^(-5)cm`