[Physics] Ratio of the magnitude of the normal force to the magnitude of the gravitational force?

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I'm working through some practice problems in preparation for my physics final and ran into one that I'm not sure how to do.


A mass is released from rest from the edge of a large hemispherical, frictionless bowl. When the mass slides through the bottom of the bowl, what is the ratio of the magnitude of the normal force to the magnitude of the gravitational force acting on the mass?


I know the answer is 3, but I'm not sure how they arrived at it. Any suggestions on how to start?

Best Answer

You need mgR equal kinetic energy as the first equation. Now your net force in the upward direction is the normal force N-mg and this equals centripetal force. Using the two equations one for energy conservation the other for the forces mentioned above should help you.

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