

Upward motion of a body on a rough inclined plane-
Free body diagram

When a body of mass m,moves as the direction in the figure,these forces will act on it.
1. The weight force mg, downwards.
2. The normal force N, perpendicular to the inclined plane.
3. and as the body moves upwards along the plane, the frictional force f ,downwards along the plane.
So, the minimum force required to move the body up = mg sinθ+ f
= mg sinθ + µ.N
Fmin = mg sinθ +µ mg.cosθ
(F= ma)
So, ma = mg sinθ +µ mg.cosθ
and acceleration, a= g(sinθ +µ cosθ)
Therefore, the required acceleration in upward direction along the plane to move the body = a= g(sinθ +µ cosθ)
