Question

A block of mass $m$ is kept on a rough inclined plane of inclination $\theta$. Coefficient of friction between the block and the plane is $\mu$. What force $F$ parallel to the inclined plane should be applied on the block so that is just begins to slide up the plane? Given, $\mu <\cot \theta$.

Answer 1

$N=mg\cos \theta$

frictional force, $f$ is

$f=\mu mg\cos \theta$

Therefore for move up then

$F=mg\sin \theta +f=mg\sin \theta +\mu mg\cos \theta$

$F=mg(\sin \theta +\mu \cos \theta )$