Motion on the inclined plane when the surface is rough:

The figure given above shows a body having weight W, sliding down on rough inclined plane. Assume,

θ= Angle which is made by inclined plane with horizontal

a = Acceleration of the body

m = Mass of the body = W/g

µ = Co-efficient of friction

Fr = Force of friction when body tends to move down:

R = w.cosθ

Fr = µ.R = µ.W.cosθ

Net force acting on body F = W.sinθ   - µ.W.cosθ

That is,         m.a = W.sin θ  - µ.W.cosθ

Put m = W/g we get

a =  g.[sin θ - µ.cosθ] (when the body tends to move down)

a = -g.[sinθ  - µ.cosθ ] (when the body tends to move up)