- #1

- 94

- 6

## Homework Statement

A particle is placed on top of a smooth (frictionless) sphere of radius R. If the particle is slightly

disturbed, at what point will it leave the sphere?

## Homework Equations

Same as first question, just

F = ma = ΣF_i

## The Attempt at a Solution

Similarly, we want to know when the normal force of the sphere on the particle is overcome:

F_norm = F_cent

mg CosΘ = (mv2/r)

CosΘ = y/R (where

**y**is the height above the center of the sphere)

So:

y = v2/g

Finding v2:

Using conservation of energy, PE_initial = PE_final + KE_final

mgR = mgy + mv2/2

Solving for v2

v2 = 2g(R-y)

Placing into equation for y:

y = 2g(R-y)/g = 2(R-y)

Solving for y:

y = (2/3) R

Correct? Or am I making a horrible mistake?