# HW help! Finding the diameter of a hole punched in a wall.

1. Nov 20, 2011

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

τ = P/A
τ = ((1/2)F)/A

3. 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??

2. Nov 20, 2011

### cepheid

Staff Emeritus
It seems like the area that is relevant for shear stress is the area of the "inner lining" of the hole. If you imagine "unwrapping" this circular strip, you end up with a rectangle whose width is the hole thickness, and whose length is the circumference of the hole. But the circumference of the hole is πD, not just D.

3. Nov 20, 2011

### SteamKing

Staff Emeritus
The shearing stress is developed around the circumference of the hole. Try using the circumference of the hole and the thickness of the styrene to calculate shear area.

4. Nov 20, 2011