The figure below shows a massless wheel of radius R, mounted on a frictionless h

Question

The figure below shows a massless wheel of radius R, mounted on a frictionless horizontal axle. A point mass M is glued to the edge of the wheel and a mass m hangs from a string wrapped around the perimeter of the wheel. When 0 0 both M and m stay at the same level 1. B Potential energy-zero a) If you were given with the same set up what would be the motion that you would expect? b) Write down the potential energy of M in terms R and . c) Write down the Potential energy of m in terms R and e d) Then what is the total potential energy of the system e) Use this potential energy to find the values of m and M for which there are any positions of equilibrium. (consider m>M and m

Explanation / Answer

b) Potential energy U1 of mass M = MgR(1- cos theta)

c) Potential energy U2 of mass m = - mg*R*theta

d) Total Potential energy, U = U1 + U2 = MgR(1- cos theta) - mg*R*theta

e) it will be in equilibrium if potential energy will be minimum.

dU/dtheta = 0

MgR*( sin theta) - mgR = 0

M sin theta - m =0

sin theta = m/M

M> or = m

f) Equilibrium position will be at theta = sin-1(m/M)

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