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April 16, 2014

April 16, 2014

Posted by **Anonymous** on Friday, March 25, 2011 at 6:43pm.

h =

- physics -
**Damon**, Friday, March 25, 2011 at 7:06pmAc at top of loop = g = v^2/R

so

v^2 at top of loop must be g R

Height difference = (h-2R)

so total Ke at top of loop = m g (h-2R)

but

total Ke = (1/2)m v^2 + (1/2)I w^2

but v = w r so w = v/r

total Ke = (1/2) [m + I/r^2]v^2

but

v^2 must be gR

so

total Ke = (1/2)[m + I/r^2]gR

but we know total Ke is loss of Pe = m g (h-2R)

so

(h-2R) = (1/2)[ 1 + I/mr^2] R

h = 2R + (1/2)[ 1 + I/mr^2] R

I is (2/5) m r^2

so

h = 2R + (1/2) [ 7/5 ]R

h = 2.7 R

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