A pendulum consists of a large weight suspended by a steel wire that is 0.9500 m

Question

A pendulum consists of a large weight suspended by a steel wire that is 0.9500 m long. (a) If the temperature increases, does the period of the pendulum increase, decrease, or stay the same? Explain. (b) Calculate the change in length of the pendulum if the temperature increase is 150 degrees celsius. (c) Calculate the period of the pendulum before and after the temperature increase. (Assume the coefficient of linear expansion for the wire is 12.00 x 10^-6 K^-1, and that g=9.810 m/s^2 at the location of the pendulum.)

Explanation / Answer

Length of the pendulum l = 0.95 m (a) If the temperature increases then length of the pendulum is also increase. We know that Time period of the pendulum (T) is directly proportional to squareroot of the length(l) of the pendulum. So as temperature increses timepr=eriod also increses. (b) Coefficient of linear expansion for the wire = 12.00 x 10^-6 K^-1 change in length = l*coefficient of linear expansion of steel*change in temperature                          = 0.95*12*10^-6*150                          = 0.0171 m (c) Final length l' = 0.9671 m Initial Time period T1 = 2*Pi*sqrt(l/g)                                 = 2*3.14*sqrt(0.95/9.810)                                 = 1.954 s Final Time period  T2 = 2*Pi*sqrt(l'/g)                                       = 2*3.14*sqrt(0.9671/9.810)                                 = 1.971 s

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