Tue September 01, 2009 By: Sukhmaneet Kaur

Please solve the numerical

Expert Reply
Tue September 01, 2009

" the radius of the depth well in a circus is 25m"

We take this to mean the radius of the vertical loop and solve.

Let the minimum speed be vmin, then the kinetic energy is, mvmin2/2.

If we consider the bottom point as reference for potential energy zero, then potential energy at highest point is,

mg(2R) = 2mgR

At the highest point the centripetal force is provided by weight of the performer and bike,

mv2/R = mg

v2 = Rg

Hence KE at the highest point is mRg/2 and potential energy 2mgR

So total energy =  mRg/2 + 2mgR = 5mgR/2,

This must be equal to the total energy at bottom, KE + PE = mvmin2/2 + 0

mvmin2/2 = 5mgR/2

vmin = (5gR)





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