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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)
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