- #1

fluidistic

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## Homework Statement

A friend of mine is stuck on a problem (that I saw about 2 years ago on the internet) so I thought about how to solve it but was totally unable.

Here it comes : Consider a particle on the top of a sphere of radius r. If there's no friction between the particle and the particle is falling, at what point will it leave out the sphere?

## Homework Equations

## The Attempt at a Solution

I was tempted to use the formula [tex]\sum \vec{F}=m\vec{a}[/tex] until I realized that there was some complications. For example I got that the acceleration in the x-axis is worth [tex]g\sin \left( \theta(t) \right)[/tex] and I have no clue about how to express [tex]\theta[/tex] in function of the time. It's not like the particle is following a circular path. More precisely, there's no centripetal force... the only force that influences the movement is the weight of the particle (assume it has a mass m).

I've also thought about conservation of energy... but since I don't know at what height it will leave the sphere, I can't get the velocity which could have helped me maybe.

Can you help me a very bit? Thanks in advance.