If W is weight of a body, α is angle of an inclined plane and ϕ is angle of friction, then the force required to drag the body when it is just impending to move the plane, is_____

Explanation

Explanation : The screw is considered as an inclined plane with inclination α. When a load is being raised, the following force acts on it at a point on the inclined plane. Load (W) : It always acts in a vertically downward direction, Normal Reaction (N) : It acts perpendicular to the inclined plane. Frictional force (μN) : Frictional force acts opposite to the motion. Since the load is moving up the inclined plane, the frictional force acts along the inclined plane in the downward direction. Effort (P) : Effort P acts perpendicular to the load W. It acts towards right for lifting the load and towards left for lowering the load. From FBD of the figure. ΣF x= 0 P × sin α + W × cos α = N. ΣF y= 0 W × sin α + μN = P × cos α W × sin α + μ(P × sin α + W × cos α) = P × cos α W × sin α + μW × cos α = P × cos α - μP × sin α ∴ P = W × tan (α + ϕ) .