Calcualate the force F needed to punch a 1.46 cm diameter hole in a steel plate 1.27 cm thick. The ultimate shear strenght of steel is 345 `MN//m^(2)`.

Explanation

In punching shear elasticity is involved, the hole will be punched if
`[(F_(||))/(A)]gt` Ultimate shear stres.
i.e., `F_(||) gt ("Shear stress") xx ("Area")`
So, `(F_(||))_(min) = (3.45 xx 10^(8)) (2pi rL) " " ["as here" A = 2pi r L]`
i.e., `(F_(||))_(min)=(3.45xx10^(8))(2xx3.14)xx(0.73xx10^(-2))(1.27xx10^(-2))=200kN`