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 $4cm^{2}$ . 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

$n=\frac{ \, stress \, }{ \, strain \, }=\frac{μN/A}{x/h}=\frac{\frac{0 .6 \times 5}{4 \times 10^{- 4}}}{\frac{0 . 6 \times 10^{- 3}}{2 \times 10^{- 2}}}$
$=\frac{0 .6 \times 5}{4 \times 10^{- 4}}\times \frac{2 \times 10^{- 2}}{0 .6 \times 10^{- 3}}$
$n=2.5\times 10^{5}$
$\therefore x=2.5$
$2x=5$