Box on a sphere is nudged- when does it fall off?

[Aesops]

Box on a sphere is nudged-- when does it fall off?

Homework Statement

A box of mass "m" is placed on a sphere of radius "r". The box is given an extremely small nudge to get it moving.

(a) What is the maximum speed the ball may have without leaving the sphere?
(b) At what angle from the vertical does the ball last touch the sphere?

Homework Equations

I think this is a question requiring energy, so

U_gpe = mgh
KE = mv²/2

But knowing there is a circle involved,

F_c = mv²/r

The Attempt at a Solution

I'm not sure how to attack the problem... I do know that our physics class has not yet gone over anything beyond Newton's three laws and the concepts of gravitational potential and kinetic energy.

 

[kushan]

ball on sphere?
you asked box on sphere
please rephrase question correctly

 

[Doc Al]

I'm not sure how to attack the problem... I do know that our physics class has not yet gone over anything beyond Newton's three laws and the concepts of gravitational potential and kinetic energy.

That's all you need. Hint: In addition to energy conservation, make use of Newton's 2nd law. What forces act on the box as it slides down?