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 0.785. The slope of the incline plane is 42.1 degrees with respect to the horizontal.

I have found that the minimum acceleration of the inclined plane for the square block not to slide is 0.6805 m/s^2.

But, what is maximum acceleration of the inclined plane for the square block not to slide?

Explanation / Answer

for maximum accleration use

a cos theta = g sin theta + ug cos theta

a cos 42.1 = (9.8 sin 42.1) + ( 0.785 * 9.8* cos 42.1)

a = 12.27/ cos 42.1

a = 16.54 m/s ^2

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