Assume that if the shear stress in steel exceeds about 4.00 108 N/m2, the steel ruptures.
(a) Determine the shearing force necessary to shear a steel bolt 1.40 cm in diameter.
(b) Determine the shearing force necessary to punch a 1.75-cm-diameter hole in a steel plate 0.690 cm thick.
N
Got A just don't understand B
To determine the shearing force necessary to punch a hole in a steel plate, we can use the equation for shear stress:
Shear stress = Shearing force / Area
(a) First, let's solve part (a):
Given that the steel bolt's diameter is 1.40 cm, we can find its radius:
Radius = diameter / 2 = 1.40 cm / 2 = 0.70 cm = 0.007 m
Now we can calculate the area of the bolt:
Area = π * radius^2 = π * (0.007 m)^2
Next, we can rearrange the equation for shear stress to solve for the shearing force:
Shearing force = Shear stress * Area
Since the shear stress is given as 4.00 * 10^8 N/m^2, we can substitute the values and calculate the shearing force.
(b) Now let's move on to part (b):
Given that the steel plate has a thickness of 0.690 cm, we can find its height:
Height = 0.690 cm = 0.0069 m
Given that the diameter of the hole to be punched in the plate is 1.75 cm, we can find its radius:
Radius = diameter / 2 = 1.75 cm / 2 = 0.875 cm = 0.00875 m
To calculate the area of the hole, we subtract the area of the inner circle from the area of the plate:
Area = π * (radius_outer^2 - radius_inner^2)
Since the radius_inner is zero (as it is the center of the hole), the equation simplifies to:
Area = π * radius_outer^2
Now, we can substitute the values into the equation for shear stress and solve for the shearing force, just like in part (a):
Shearing force = Shear stress * Area
By following these steps, you should be able to calculate the shearing force necessary to punch a 1.75 cm diameter hole in a steel plate 0.690 cm thick.