A nail with a diameter of 1.00 mm projects 25.0 mm horizontally outward from a wall. A 40.0 N picture is hung from the end of the nail. If the shear modulus is 3.40 × 10¹⁰ N/m², then how much does the nail deflect downward? A) 3.74 × 10^-5 m B) 4.45 × 10^-5 m C) 4.78 × 10^-5 m D) 5.65 × 10^-5 m E) 7.85 × 10^-5 m

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Quizplus · Accepted Answer

The deflection of the nail can be calculated using the formula for shear deformation: $\delta = \frac{FL}{AG}$, where $F$ is the force applied (40.0 N), $L$ is the length of the nail (25.0 mm or 0.025 m), $A$ is the cross-sectional area of the nail ($\pi r^2$, with $r = 0.5 \times 10^{-3} m$), and $G$ is the shear modulus (3.40 × $10^{10}$ N/m$^2$). Calculating $A$ gives $A = \pi (0.5 \times 10^{-3})^2 = 7.85 \times 10^{-7} m^2$. Substituting these values into the formula gives a deflection $\delta = 3.74 \times 10^{-5} m$.

A Nail with a Diameter of 1