1. Dec 28, 2004

### Elphaba

A particle of mass m slides down a fixed, frictionless shpere of radius R, starting from rest at the top.

(a) in terms of m, g, R, and (theta), determine each of the following for the particle while it is sliding on the sphere.

i. the Kinetic energy of the particle
ii. the centipetal acceleration of the mass (would you still use Ac=v^2/r?)
iii. The tangential acceleration of the mass (What's this?)

(b) determine the value of (Theta) at which the particle leaves the sphere.

2. Dec 28, 2004

### dextercioby

HINTS:

1.Make a drawing.
2.Mark all forces that are present between the three bodies from the system
3.Make the symplifying assmption that the sphere's mass is infinite,so the sphere will not move,slide,roll...
4.Write down Newton's second law of dynamics in vector form for the sliding body down the sphere.
5.Chose a system of axis whiwh will enable u to project the eq.written at 4. in a symple form.
6.Write down the condition for the sliding body to lose contat with the sphere.
7.After finding the angle at 6. all kinetic variables (quantities) will be known:liner and angular acceleration;linear and angular velocity and you'll easily find the kinetic energy of the particle up until the moment of "breakin' loose'.

Daniel.