# An inclined plane is sliding,

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

To solve the problem you must make the free body diagram of theblock, i’m using a convenient reference system since the majorityof forces are acting on that sense. The acceleration has nowcomponents on the new reference system. Then we state the x and yaxis equations.

We put the friction force as a function of the normal force andfriction coefficient.

We solve for the acceleration using both equations and obtain anacceleration of 1.53 m/s2 to the left, since the sign ischanged meaning that we assumed an opposite direction

That’s for the maximum acceleration, the minimum acceleration iszero, since if the system is not in motion or it’s not acceleratedthe block will remain on the plane as a consecuence of the staticfriction

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