Like the title says, I have a homework problem that asks for the maximum diameter of a hole that can be punched into a sheet of polystryrene 6 mm thick, knowing that the force exerted by the punch is 45 kN and that a 55 MPa average shearing stress is required to cause the material to fail.
τ = P/A
τ = ((1/2)F)/A
The Attempt at a Solution
I simply made the cross sectional area A = (0.006 m)(D) then plugged that in and solved for D.
55 x 10^6 Pa = 45000 N/(0.006 m)(D)
and I keep getting D = 68.3 mm. BUT the back of the book claims it to be 43.4 mm. What am I doing wrong??