Question

The shear modulus for a metal is 50000 MPa. Suppose that a shear force of 200 N is applied to the upper surface of a cube of this metal that is 3.0 cm on each edge. How far will the top surface be displaced?

• A. $\Delta$L =$0.133\mu m$
• B. $\Delta$L =$0.3\mu m$
• C. $\Delta$L =$0.4\mu m$
• D. $\Delta$L =$0.5\mu m$

Answer 1

Answer: (A)

$\Delta$L =$0.133\mu m$

Shearing strain$=\frac{△L}{L}=\frac{\left(\frac{F}{A}\right)}{s}$

$\eta =\frac{F}{l^2}\times \frac{l}{△l}$

$△l=\frac{F}{\eta l}=\frac{200}{3\times {10}^{-2}\times 50000\times {10}^6}=\frac{2}{15}\times {10}^{-6}$

$△l=0.133\mu m$