(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a small solid sphere of mass m and radius r starts from rest and rolls down a hill without slipping. the sphere encounters a loop of radius R where R >> r.

Given R determine the min height h such that the ball remains on the track throughout the loop

2. Relevant equations

I = 2/5 mR^2

ω = v/r

3. The attempt at a solution

highest point requiring most energy is at top of loop:

mgh = mg2R + 1/2 Iω^2

mgh = mg2R + 1/2 * 2/5 m r^2 *v^2/r^2

gh = 2Rg + 1/5*v^2

at top of loop, normal force is 0,

Fy = N + mg

ma = mg

m*v^2/R = mg

v^2 = gR

...

gh = 2Rg + 1/5 Rg

h = 11/5 R

this is correct?

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# Homework Help: Simple energy question with rotation

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