A 120.0 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 1.000 $\times$ 10⁶ N/m².The smallest diameter the nail can be is A) 10.46 mm. B) 12.36 mm. C) 14.84 mm. D) 16.67 mm. E) 18.35 mm.

Question

Quizplus · Accepted Answer

The maximum shear stress that the nail can sustain is given by:
τmax = F/A

Where,
F = 120.0 N (the weight of the picture)
A = πd^2/4 (the cross-sectional area of the nail)
τmax = 1.000×10^10 N/m^2 = 10^7 Pa

Substituting the values, we get:
10^7 Pa = 120.0 N / (πd^2/4)
d^2 = 4 × 120.0 N / (π × 10^7 Pa)
d^2 = 0.01528
d = 0.1236 m = 12.36 mm

Therefore, the smallest diameter the nail can be is 12.36 mm, which corresponds to choice B).

A 1200 N Picture Hangs from a Nail in the Wall