A 150 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 2.00 $\times$10⁶ N/m².The smallest diameter the nail can be is A) 9.77 mm. B) 8.22 mm. C) 7.97 mm. D) 7.52 mm. E) 6.03 mm.

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Quizplus · Accepted Answer

The shear stress is given by:$$	au = \frac{F}{A}$$where:* $	au$ is the shear stress (N/m^2)* $F$ is the force (N)* $A$ is the area (m^2)In this case, the force is 150 N and the maximum shear stress is 2.00 * 10^6 N/m^2. The area is given by:$$A = \frac{\pi d^2}{4}$$where:* $d$ is the diameter (m)Substituting these values into the equation for shear stress, we get:$$2.00 * 10^6 N/m^2 = \frac{150 N}{\pi d^2/4}$$Solving for $d$, we get:$$d = 9.77 mm$$Therefore, the smallest diameter the nail can be is 9.77 mm.

A 150 N Picture Hangs from a Nail in the Wall.The