Engineering
Physics
Static and Kinetic Friction
Motion of Block on Inclined Surface
Free Body Diagram
Question

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is µ and tan θ > µ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg (sin θ – µ cos θ) to P2 = mg(sin θ + µ cos θ), the frictional force f versus P graph will look like

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Solution
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Tanθµ

 

force for which f = 0   P0 = mg sin θ

 Case I  P = mg (sin θ – µ cos θ) P < P0

 

    P + f = mg sin θ

 mg (sinq – µcosθ) + f = mg sinθ

  f = µ mgcosθ

 Case II P = mg (sinθ + µ cosθ) > P0                                         

 

  P = f + mg sinq

  mg (sinq + µ cosθ) = f + mg sinθ

  f = µ mg cosθ]