Question

A cylindrical eraser of negligible mass is dragged across a paper at a constant velocity to the right by its pencil. The coefficient of kinetic friction between eraser and paper is $0.6$ . The pencil pushes down with $5N$ . The height of the eraser is $2cm$ and its circular area is $4c{m}^2$ . Its top surface is displaced horizontally $0.6mm$ relative to the bottom. If the shear modulus of the eraser material is $x\times 10^{5}Pa$ . Find value of $2x$

Answer 1

Answer: 5

$n=\frac{stress}{strain}=\frac{\mu N/A}{x/h}=\frac{\frac{0.6\times 5}{4\times 10^{-4}}}{\frac{0.6\times 10^{-3}}{2\times 10^{-2}}}$
$=\frac{0.6\times 5}{4\times 10^{-4}}\times \frac{2\times 10^{-2}}{0.6\times 10^{-3}}$
$n=2.5\times 10^5$
$\therefore x=2.5$
$2x=5$