An inclined plane is sliding, and accelerating, on a horizontal frictionless sur

Question

An inclined plane is sliding, and accelerating, on a horizontal frictionless surface. There is a block at rest on the sloping surface, held in place by static friction through the horizontal acceleration of the system. The coefficient of static friction between the block and the inclined plane is 0.615. The slope of the incline plane is 40.5 degrees with respect to the horizontal.
What is minimum acceleration of the inclined plane for the square block not to slide? What is maximum acceleration of the inclined plane for the square block not to slide?

Explanation / Answer

the minium acceleration of the inclined plane for the square block not to slide is

f_s = u_s N = u_s mg costhea

ma = u_s mg costhea

a = u_s g costhea= (0.615 ) ( 9.8 ) cos 40.5 = 4.58 m/s^2

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