Question

A small block starts sliding down an inclined plane forming an angle $\alpha$ with the horizontal. The coefficient of friction between the block and the plane depends on the distance covered from rest along the plane as $\mu =ax$ where $a=$constant. Find the distance covered by the block down the plane, till it stops sliding, and its maximum velocity during this journey.

Answer 1

The equation of motion down the inclined plane given by

$a=g(\sin \alpha -ax\cos \alpha )$ where $a$ is accleration and equation of motion of maximum velocity

$v^2=2g(\sin \alpha -ax\cos \alpha )x$

$v=\sqrt{2gx(\sin \alpha -ax\cos \alpha )}$

when the velocity is zero the distance covered by

$x=\frac{tana}{a}$