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 0.645. The slope of the incline plane is 34.8 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

(A) Sine 34.8 = .570, friction = .645;

consider the component of force acting downward , which means there will a component og mgsin(theta) against the frictional force.

now, since

Sine 34.8 = .570, friction = .645;

so, the block will not slide even if the incline ins not accelerating.

no acceleration required.

(B)

consider the component of force acting downward , which means there will a component , mgsin(theta) against the frictional force.and due to acceleration there will be pseudo force acting on the block on the opposite direction.

Cosine 34.8 = .8211,

friction = .645

max acceleration to avoid sliding will be gcos(theta) - mu*g= 0.1761g acceleration.

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