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**1. A uniform solid sphere of radius r starts from rest at a height h and rolls without slipping along the loop-the-loop track of radius R as shown.**

a) What is the smallest value of h for which the sphere will not leave the track at the top of the loop?

a) What is the smallest value of h for which the sphere will not leave the track at the top of the loop?

Attempt:

## Homework Equations

[tex]\Delta[/tex]P

_{E}= mgh - 2mgR

[tex]\Delta[/tex]K

_{E}= 1/2 mv

^{2}+ 1/2 Iw

^{2}

a

_{c}= v

^{2}/R

v = rw

## The Attempt at a Solution

mgh = 2mgR + 1/2 Iw

^{2}+ 1/2 mv

^{2}

I = 2/5 mr

^{2}

mgh = 2mgR + 1/5 mr

^{2}w

^{2}+ 1/2 mv

^{2}

N = mg - ma

_{c}= mg - mv

^{2}/R = 0

v

^{2}= gR

mgh = 2mgR + 1/2 mv

^{2}+ 1/5 mv

^{2}+2mgR = 2.7mgR

h = 2.7R

however, this answer is wrong, and the correct one is h = 2.7R - 1.7r. can anybody correct me on this?