A worker is pushing a box of mass M up a rough incline by applying a horizontal pushing force of constant magnitude P. The incline makes an angle θ with respect to the vertical, and the coefficient of kinetic friction between the slope and the box is μ. Derive an expression for the acceleration of the box

Explanation:

The incline makes an angle θ with respect to the vertical ,

component of weight along the inclined plane,downwards = mgcosθ

component of weight perpendicular to inclined surface,downwards = mg sinθ

Component of force P along the surface,upwards = Psinθ

component of force P perpendicular to surface = Pcosθ

Reaction force of surface

R = Pcosθ + mgsinθ

Force of friction

=  μ.(  Pcosθ + mgsinθ ) acting downwards

Net force in upward direction

=  P sinθ -mgcosθ - μ.(  Pcosθ + mgsinθ )

acceleration

a = [P sinθ -mgcosθ - μ.(  Pcosθ + mgsinθ ) ] / m

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