A 24.0 N picture hangs from a nail in the wall.The diameter of the nail is 2.00 mm.The shear stress on the nail is A) 7.64 $\times$ 10⁶ N/m². B) 6.24 $\times$ 10⁶ N/m². C) 5.65 $\times$ 10⁶ N/m². D) 4.37 $\times$ 10⁶ N/m². E) 4.02 $\times$ 10⁶ N/m².

Question

Quizplus · Accepted Answer

The shear stress on the nail can be found by dividing the force (weight of the picture) by the cross-sectional area of the nail.

First, we need to find the area of the nail in square meters:
diameter = 2 mm = 0.002 m (convert mm to m)
radius = 0.001 m (half of diameter)
area = πr^2 = π(0.001 m)^2 = 7.85×10^-7 m^2

Next, we divide the force by the area to get the shear stress:
shear stress = force/area
shear stress = 24.0 N / 7.85×10^-7 m^2
shear stress = 7.64×10^10 N/m^2

Therefore, the answer is choice A, 7.64×10^10 N/m^2.

A 240 N Picture Hangs from a Nail in the Wall