- #1

fluidistic

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## Homework Statement

I'm stuck on a relatively simple problem. I can't use Lagrangian mechanics, only Newtonian one.

A mass m slides without friction over a sphere of radius r and mass M. Find its period and the allowed values of its speed.

## Homework Equations

The sphere isn't in an external gravitational field. So there's the gravitational force between the mass m and the sphere.

## The Attempt at a Solution

I found out the period of the mass to be [itex]T=\frac{2\pi R}{v}[/itex] where v is the speed of the mass.

And now this is where I'm stuck. I know that the modulus of the gravitational force between the mass and the sphere is [itex]F_g=\frac{GMm}{R^2}[/itex]. I also know that for a critical value of v, the mass will start to be in orbit over the sphere. This happens when the normal force is worth 0N. So I think I must express the modulus of the normal force acting on the mass in function of the speed of the mass. But I don't know how to "include v" in the expression for the normal force. Hmm.

Is that a reasonable way to approach the problem? Could you give me any tip? Thanks in advance.