Calculate the force F needed to punch at `1.46` cm diameter hole in a steel plate `1.27 cm` thick fig. The ultimates shear stress of steel is `3.45 xx 10^(8)Nm^(-2)`.

Explanation

In punching, shear elasticity
The hole will be punced if , `F/A ge` ultimate shear stress
or `F ge (shear stress) xx A`
where `A = 2 pi r d`
`:. F = (3.45 xx 10^(8)) xx 2 pi r d`
`=(3.45 xx 10^(8)) xx 2 xx (22//7) xx (0.73 xx 10^(-2)) xx (1.27 xx 10^(-2))`
`=2 xx 10^(5)N`.