Question

Comic-book superheroes are sometimes able to punch holes through steel walls. (a) If the ultimate shear strength of steel is taken to be 2.60 x 109 Pa, what force is required to punch through a steel plate 1.90 cm thick? Assume the superhero's fist has cross-sectional area of 1.02 × 102 cm2 and is approximately circular.

Answer 1

Shear strength = 2.6*10^9 Pa

thickness = t = 1.9 cm

Area = A = 102 cm^2

shear stress is the measure of the material's resistance to cause "sliding" motion of its layers.
Since the hero has to take a cylindrical piece of metal out, the area which will cause this force is 2*pi*r*t

r = sqrt(A/pi) = 5.7 cm = 0.057 m

Then so the force required is shear strength into this area = 2.6*10^9*2pi*0.057*0.019 = 17.7*10^6 N