Answer to Question #111994 in Physics for Anna

Question

You have a cylindrical sample of the material that has a radius of 0.50 mm, a length of 3.1 mm, and you apply a shear force of 103 N. If the bottom of the sample is fixed in place and the top of the sample deflects 0.16 mm under the shear force then what is the shear modulus of the material the sample is made of? (to 2 s.f in GPa)

Answer 1

$$S=\frac{Fh}{Ax}=\frac{Fh}{\pi r^2x}$$

$$S=\frac{(103)(0.0031)}{\pi (0.0005)^2(0.00016)}=2.54\cdot10^9\ Pa=2.5\ GPa$$