Superhero punching through a wall, breaking point of steel

[sbennett3348]

Homework Statement

Comic-book superheroes are sometimes able to punch holes through steel walls.
(a) If the ultimate shear strength of steel is taken to be 2.60X10^9 Pa, what force is required to punch through a steel plate 1.60 cm thick? Assume the superhero's fist has cross-sectional area of 104 cm2 and is approximately circular.

Homework Equations

P=F/A
Possibly F/A=Y*DeltaL/Linitial

The Attempt at a Solution

My attempt was P=F/A 2.6x10^9*(pi.104^2)=88346611.86

My teacher began doing the problem but got lost and was unsure how to proceed...she said she would have to look into it She gave us the answer which was 10500000N. I got lost with what she was doing and tried my own attempt. Meanwhile, our homework with an identical problem with different numbers is due before our next class. I am completely lost on how to do this problem. I would greatly appreciate help.

 

[anathema]

Dear fellow scientist,

Thank you for bringing this forum post to my attention. I understand your confusion and I am happy to assist you in solving this problem.

To start, let's review the given information. We know that the ultimate shear strength of steel is 2.60x10^9 Pa and the thickness of the steel plate is 1.60 cm. We also know the cross-sectional area of the superhero's fist is 104 cm^2 and it is approximately circular.

To solve this problem, we need to use the equation P=F/A, where P is the pressure, F is the force, and A is the cross-sectional area. We can also use the equation F/A=Y*DeltaL/Linitial, where Y is the shear modulus of the material, DeltaL is the change in length, and Linitial is the initial length.

First, let's calculate the pressure needed to punch through the steel plate. We can do this by substituting the given values into the equation P=F/A. Therefore, P=(2.60x10^9 Pa)(pi)(104 cm^2)=88346611.86 Pa. This is the pressure needed to punch through the steel plate.

Next, we can use the equation F/A=Y*DeltaL/Linitial to calculate the force needed. We know the pressure (P) and the shear modulus (Y), so we need to find DeltaL and Linitial. We can do this by using the thickness of the steel plate (1.60 cm) and the cross-sectional area of the superhero's fist (104 cm^2).

First, we need to find the radius of the superhero's fist. We can do this by using the formula A=pi*r^2, where A is the cross-sectional area and r is the radius. Therefore, r=sqrt(104 cm^2/pi)=5.75 cm.

Now we can calculate DeltaL by using the formula DeltaL=2r, which is the diameter of the superhero's fist. Therefore, DeltaL=2(5.75 cm)=11.5 cm.

Next, we need to find Linitial. We can do this by adding the thickness of the steel plate (1.60 cm) to the diameter of the superhero's fist (11.5 cm). Therefore, Linitial=1.60 cm + 11.5 cm=13.1 cm.

Now we