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

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Physics

Kadyn Bowen

14 March, 20:57

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

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Kalan · Answer 1

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