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Although the magnitude of a friction force varies with the magnitude of the normal force, assume that for the below situation it remains constant at 100 pounds. At what angle, theta, will the box begin to slide?

The box will slide off when the force of gravity along the tilting surface is > 100lbs. Since the acceleration of gravity is directed downwards, the component of this vector along the surface needs to be calculated. Let x be the angle of the surface with respect to horizontal, i.e., x = 0 when the surface is horizontal and 90 degrees (pi/2 radians) when the surface is vertical. If the mass of the box is M then its weight is Mg. The component of force (weight) of the box along the surface is Mgsinx so the box will slide when x is given by Mgsinx = 100 lbs.

BTW, this looks like a homework problem, which I could have rejected immediately. In the future, please try to work the problem and show your work or at least ask a question related to the problem with which you are having trouble. Our website is not meant to be a homework service.

Also, BTW, you didn't include the "below situation" or the mass of the box.

Randy

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