A 120 N picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is 1.00 × 10⁶ N/m². The smallest diameter the nail can be is A) 10.5 mm. B) 12.4 mm. C) 13.7 mm. D) 14.4 mm. E) 15.9 mm.

Question

Quizplus · Accepted Answer

The maximum shear stress ($\tau_{max}$) formula is given by $\tau_{max} = \frac{F}{A}$, where $F$ is the force applied, and $A$ is the cross-sectional area of the nail. The force applied by the picture is 120 N, and the maximum shear stress the nail can sustain is $1.00 \times 10^6 \, \text{N/m}^2$. The cross-sectional area of a circular nail is given by $A = \frac{\pi d^2}{4}$, where $d$ is the diameter of the nail. Substituting the given values and solving for $d$, we get:$$1.00 \times 10^6 = \frac{120}{\frac{\pi d^2}{4}}$$Solving for $d$ gives a diameter of approximately 12.4 mm, making option B the correct choice.

A 120 N Picture Hangs from a Nail in the Wall