A metal cube, 5 cm on edge, undergoes a shearing force of 14,000 N (on opposing ends). If the shear modulus is $9 \times 10 ^ { 10 }$ Pa, the distance that the cube is sheared is
A) $7.5 \mu$ m.
B) $4.4 \mu$ m.
C) $3.1 \mu$ m.
D) $5.6 \mu$ m.

Question

Quizplus · Accepted Answer

The shear strain is given by $\frac{F}{A \cdot G}$, where $F$ is the force, $A$ is the area, and $G$ is the shear modulus. The area $A = 5 \times 5 = 25 \, \text{cm}^2 = 0.0025 \, \text{m}^2$. Thus, the shear strain is $\frac{14000}{0.0025 \times 9 \times 10^{10}}$, which gives a displacement of approximately $3.1 \, \mu\text{m}$.

A Metal Cube, 5 Cm on Edge, Undergoes a Shearing 9×10109 \times 10 ^ { 10 }9×1010

A Metal Cube, 5 Cm on Edge, Undergoes a Shearing $9 \times 10 ^ { 10 }$