Particle Energy on a Smooth Sphere: Finding the Point of Departure

[bernvall]

Homework Statement

A Particle is place on a smooth sphere of radius b at a distance b/2 above the central plane. As the particle slides down the side of the sphere at what point will it leave?

Homework Equations

potential and kinetic energies

The Attempt at a Solution

no idea

 

[Acut]

The particle leaves the sphere when the normal force is zero. So the only force acting on it will be the gravitational force.

Find the centripetal component of the gravitational force as a function of the angle theta. Then write the expressions for the conservation of mechanical energy, and use the fact that F = (mv^2)/b. A few mathematical manipulations later, you will find an expression of the type sin θ = constant, or cos θ = constant. Use the arc sine or arc cosine functions accordingly to find θ. That will be your answer. You may transform to rectangular coordinates if the problem asks for it.

I know it sounds like a lot of work, but it actually isn't.

 

[bernvall]

Thanks, i actually managed it, it came b/3 :)

Thanks for the help.