Consider a pendulum bob on a string attached to the ceiling. THe length of the p

Question

Consider a pendulum bob on a string attached to the ceiling. THe length of the pendulum is 1.00m. The bob is pulled off to the left, to a small angle with the vertical, and let go. The string is cut instantly by a razor blade at opposite end of the swing. The floor is 0.750m below the bob when the string is cut.

a) What is the bob's velocity when the string is cut. Explain.

b) determine the total amount of time from when the bob is first released, to when the bob hits the floor. (think of it in two parts: Before it is cut, it is simple pendulum. After it is cut, the bob is in freefall)

Thanks for your help, it is greatly appreciated!

Explanation / Answer

Given The length of the pendulum is, l = 1.00m The bob is at a height , h = 0.75 m a) By law of conservation of energy        1/2 m v^2 = m gh                  v = 2 gh = 2*9.8 m/s^2*0.75 m                  v = 3.83 m/s is the velocity of the bob b) Time period of the bob , when it is simple pendulum,                             T1 = 2 l/ g                                   = 2* 3.14 *1.0 m /9.8 m/s^2                             T1 = 2.0 s When the bob freely falls at a height 0.75 m, the time taken to reach ground is                       h = 1/2 g t^2                     0.75 m = 0.5 *9.8 m/s^2 * t^2                           t = 0.39 s Total time , T = T1 + t = 2.0 s +0.39 s                    T = 2.39 s ˜ 2.4 s

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