A pendulum consists of a small object hanging from the ceiling at the end of a s

Question

A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.73 m. With the string hanging vertically, the object is given an initial velocity of 2.9 m/s parallel to the ground and swings upward in a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle ? with its initial vertical orientation and then swings back downward. Find the angle ?.

Explanation / Answer

height reached = L(1- cos?). from conservation of energy, mgh = 0.5mv^2, so h = v^2/2g --> 0.73(1- cos?) = 2.9 x 2.9 /9.8 x 2 --> (1- cos?) = 0.5877, so ? = 65.655 degrees Ans

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