Question

A block slides down an inclined surface of inclination ${30}^o$ with the horizontal starting from rest. If it covers $8m$ in the first two seconds, find the coefficient of kinetic friction between the block and the surface.

Answer 1

frictional force is;

$f=\mu mg\cos \theta$

acceleration of block $m$ is;

$a=\frac{mg\sin \theta -f}{m}$$=\frac{mg\sin \theta -\mu mg\cos \theta }{m}$$=g\sin \theta -\mu g\cos \theta$$=10\sin {30}^{\circ }-\mu \times 10\cos {30}^{\circ }=5-5\sqrt{3}\mu$ ...............(1)

If block covers $8m$ in $2s$ starting from rest;

then,

$s=ut+\frac{1}{2}a{t}^2$

$8=\frac{1}{2}a(2{)}^2$

$a=\frac{16}{4}=4m/s^2$

Putting it in eq. (1);

$4=5-5\sqrt{3}\mu$

$\mu =\frac{1}{5\sqrt{3}}$