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