The pendulum in your grandfather\'s clock comprises a thin bar of length l and a

Question

The pendulum in your grandfather's clock comprises a thin bar of length l and a heavy mass m. The vertical bar can pivot about it's upper end and the mass is attached to the lower end. You exert a small force on the mass in order to start the pendulum swinging. When the mass is at its highest point, the bar makes an angle theta with the vertical. Ignoring the mass of the bar, show that during the time the mass descends from its highest point to its lowest point, the work done by gravity is given by

Explanation / Answer

Given,

the clock comprises a thin bar of length l and heavy mass m.

if the mass is at its highest point, the bar makes an angle teta.

cos theta = (l-y1)/l

l* cos theta = l-H

y1 = l*(1-cos theta)

at its lowest point

y2 =0

the work done by gravity is

Wg=mgl(1-cos teta)

work done = m*g*(y1-y2) = m*g*l*(1-cos theta)

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