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

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

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

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

|F = |Wperpl |F;l "p/ W. par perp Weight