The figure shows a thin rod, of length L = 1.9 m and negligible mass, that can p

Question

The figure shows a thin rod, of length L = 1.9 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 10 kg is attached to the other end. The rod is pulled aside to angle 0 = 13° and released with initial velocity v Overscript right-arrow EndScripts Subscript 0 = 0. As the ball descends to its lowest point, (a) how much work does the gravitational force do on it and (b) what is the change in the gravitational potential energy of the ball-Earth system? (c) If the gravitational potential energy is taken to be zero at the lowest point, what is its value just as the ball is released?

Explanation / Answer

The vertical component of the displacement vector is downward with magnitude h

W = F*d = mgh

h = L - Lcostheta

W = mgL(1-costheta)

W = 10 * 9.8 * 1.9 ( 1- cos13)

W = 4.77 J

part b )

dU = -W = -4.77 J

part c )

y = h

U = mgL(1-costheta) = 4.77 J

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