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21 February, 00:18

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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  1. 21 February, 02:01
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    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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