An object on an inclined plane does not slide provided the component of the objects weight parallel

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An object on an inclined plane does not slide provided the component of the object’s weight parallel to the plane |Wpar| is less than or equal to the magnitude of the opposing frictional force |Ff|. The magnitude of the frictional force, in turn, is proportional to the component of the object’s weight perpendicular to the plane |Wperp| (see figure). The constant of proportionality is the coefficient of static friction µ > 0.

|F = µ|Wperpl |F;l

a. Suppose a 100-lb block rests on a plane that is tilted at an angle of θ = 20° to the horizontal. Find |Wpar| and |Wperp|.

b. The condition for the block not sliding is |Wpar| ≤  μ|Wperp|. If μ = 0.65, does the block slide?

c. What is the critical angle above which the block slides with μ = 0.65?

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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