A block is placed on an inclined plane with a slope angle $ heta$. If the block is pushed down with

Question

A block is placed on an inclined plane with a slope angle $	heta$. If the block is pushed down with an initial velocity and it slides down the plane with a constant acceleration $a$,  the coefficient of kinetic friction $\mu_k$ is equal to

Professor PC Thomas Classes · Answer

Equation of motion down the incline: $mg \sin 	heta - \mu_k mg \cos 	heta = ma$. Dividing by $mg \cos 	heta$: $	an 	heta - \mu_k = \frac{a}{g \cos 	heta}$. Therefore, $\mu_k = 	an 	heta - \frac{a}{g \cos 	heta}$.