A pendulum made of a string of length 10.7m and a spherical bob of mass 1.2 kg a

Question

A pendulum made of a string of length 10.7m and a spherical bob of mass 1.2 kg and negligible raius swings in a vertical plane. The pendulum is released from an angular position 41 degrees from vertical. The string hits a peg located a distance of 7m below the point of suspension and swings about the peg up to an angle alpha on the other side of the peg. Then, the bob proceeds to oscillate back and forth between these two angular positions. The acceleration of gravity is 9.8 m/s^2. What is the maximum angle alpha which the pendulum will swing to the right after hitting the peg shown as above. Answer in units of degrees. (Note: the pendulum bob is released at a height below the height of the peg)

Explanation / Answer

applying conservation of energy from one extreme to other

that is first when it is making 41 degrees angle with a string of length 10.7 m to that making an angle alpha with a string of lenth 10.7-7 = 3.7m

so we get

mg*10.7(1-cos41) = mg*3.7*(1-cos)

solving for we get

= 73.1 degrees

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