How much force is required to punch a hole 3cm in diameter from an 8cm thick steel plate with a shear stress of 670 GPa?

To determine the force required to punch a hole from a steel plate, the relevant calculation involves the area of the hole and the shear stress of the material.

First, calculate the area of the hole. The diameter of the hole is given as 3 cm, which means the radius is 1.5 cm or 0.015 m. The area (A) of the hole can be calculated using the formula for the area of a circle, A = πr².

Substituting the radius into the formula:

[ A = \pi (0.015 , \text{m})^2 ]

[ A = \pi (0.000225) ]

[ A \approx 7.06858 \times 10^{-4} , \text{m}^2 ]

Next, using the shear stress, which is given as 670 GPa (or 670 x 10^9 Pa), the force (F) required to punch the hole can be found using the formula:

[ F = \text{Shear Stress} \times \text{Area} ]

Converting the shear stress to proper units:

[ F = 670 \times 10^9 \