A pendulum bob with mass of 0.13 kg is attached to a strong with alenth of 0.95

Question

A pendulum bob with mass of 0.13 kg is attached to a strong with alenth of 0.95
m. We choose the potential energy to be zero when the string makesan anlge of
90 degrees with the vertical. a) find the potential energy of thissystem when
the string makes an angle of 45 degrees with the vertical. b) isthe magnitude
of the cfhange in potential energy from an angle of 90 to 45degrees greater
than, less than, or the same as the magnitude of the change from 45to 0
degrees? Calculate the potential energy of the system when thestring is
vertical.

Any ideas? :)

Explanation / Answer

given mass of pendulum = m = 0.13kg    length of pendulum = l = 0.95m when it is vertical potential energy is 0    U90 = 0 1) potential energy pendulam at 450 U45 = U90 +U = 0+mgy= (0.13)(9.81) (-0.95 cos45) = -0.86J 2) it is greater because the change in the heightis greater for the first 45 degree decreases than for seconed450 decreases. 3) U0 = U90 +U = 0+mgy= (0.13 ) (9.81) (-0.95) = -1.2J U45 = U90 +U = 0+mgy= (0.13)(9.81) (-0.95 cos45) = -0.86J 2) it is greater because the change in the heightis greater for the first 45 degree decreases than for seconed450 decreases. 3) U0 = U90 +U = 0+mgy= (0.13 ) (9.81) (-0.95) = -1.2J

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