Comic-book superheroes are sometimes able to punch holes through steel walls.

Question

(a) If the ultimate shear strength of steel is taken to be 3.00 x 10^9 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 8.00 x 10^1 cm2 and is approximately circular.

Answer 1

To calculate the force required to punch through the steel plate, we can use the formula:

Force = (shear strength) x (area) x (thickness)

First, we need to calculate the area where the force will be applied, which is the overlapping area between the superhero's fist and the steel plate. Since the fist has a cross-sectional area of 8.00 x 10^1 cm^2 and is approximately circular, this means that the overlapping area is also approximately circular with the same area:

Area = 8.00 x 10^1 cm^2

Now we can plug this into the formula:

Force = (3.00 x 10^9 Pa) x (8.00 x 10^1 cm^2) x (1.90 cm)

But before we continue, we need to convert all measurements to the same unit. Here, we need to convert the area and thickness from cm to m:

Area = (8.00 x 10^1 cm^2) x (1 m/100 cm)^2 = 8.00 x 10^(-3) m^2
Thickness = (1.90 cm) x (1 m/100 cm) = 0.019 m

Now we plug these values back into the formula:

Force = (3.00 x 10^9 Pa) x (8.00 x 10^(-3) m^2) x (0.019 m)

Force = 456000000 N

The force required to punch through a steel plate 1.90 cm thick is approximately 456 million newtons.