Question

A stone is projected vertically upward with a viscosity of 100ms^-1  at an angle of 30⁰ to the radius 1mm is extended by 25mm on the application of a force of 10⁴N. Calculate (i) Young modulus (ii) strain energy per unit volume.

Answer 1

i)

$$Y=\frac{\sigma}{\epsilon}\\Y=\frac{Fl}{\pi r^2\Delta l} \\Y=\frac{10^4(1)}{\pi (0.001)^2(0.025)}=1.3\cdot10^{11}Pa$$

ii)

$$E=\frac{10^4(0.025)}{2\pi (0.001)^2(1)}=4.0\cdot10^7\frac{J}{m^3}$$