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Block sliding on a sphere

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A small block slides from rest from the top of a frictionless sphere of radius R. How far below the top of the sphere does the block lose contact with the sphere? The sphere does not move. Gravity is acting on the block.

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Solution Summary

The solution calculates how far below the top of the sphere does the block lose contact with the sphere in the case of a small block sliding from rest from the top of a frictionless sphere.

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Weight of the small block= mg
At the position shown in the diagram
Centripetal force= mg Sin phi - N where N is the normal reaction from the sphere
At the point where the sphere loses contact with the block N is equal to ...

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