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![[Post New]](/templates/default/images/icon_minipost_new.gif) 10 Jan 2008 00:15:43 IST
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Problem 78
good one......
initial velocity is v1
let the final velocity be v2
condition that the ball completes the circle is N>= 0
so N + mg = m (v2)^2/ (R-r)
so m (v2)^2 - mg >= 0
so (v2)^2 >= g(R-r).........................1
from conservation of energy......
7/10 m(v1)^2 = 7/10m(v2)^2 + 2mg(R-r)
so , (v2)^2 = (v1)^2 - 20/7 g(R-r).................................2
from 1,
(v1)^2 - 20/7 g(R-r) >= g(R-r)
so v min = ( 27/7 g {R-r} ) ^ 1/2
Please nudge me if you dont understand
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From J.R.R. Tolkien's 'The Lord of the Rings':
All that is gold does not glitter
Not all who wander are lost
The old that is strong does not wither,
Deep roots are not reached by frost.
From ashes a fire shall be woken
From shadows a light shall spring
Renewed shall be blade that's broken
The crown less again shall be king. |
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