A simple pendulum is made up of a 2.0kg mass suspended on athin aluminum wire. T
ID: 1728172 • Letter: A
Question
A simple pendulum is made up of a 2.0kg mass suspended on athin aluminum wire. This pendulum has a period of exactly 4.0s whenoperated near the equator at a temperature of 122F. The pendulum isthen moved to an Anarctic weather station where the temperature is-49F. The linear coefficient of thermal expansion for aluminum is24X10^-6C. A. What is the length of the pendulum wire at theequator? B. What is the period of the pendulum at the Anarctic weatherstation? A simple pendulum is made up of a 2.0kg mass suspended on athin aluminum wire. This pendulum has a period of exactly 4.0s whenoperated near the equator at a temperature of 122F. The pendulum isthen moved to an Anarctic weather station where the temperature is-49F. The linear coefficient of thermal expansion for aluminum is24X10^-6C. A. What is the length of the pendulum wire at theequator? B. What is the period of the pendulum at the Anarctic weatherstation?Explanation / Answer
Mass, M = 2 kg Initial Time-period, T = 4 s Initial temperature, t1 = 122 oF Final temperature, t2 = - 49 oF Coefficient of expansion, = 24 X 10-6 / oC Change in temperature, t = t1 - t2 = 171 oF = 171 * ( 5 / 9 ) oC = 95 oC Initial Length of the pendulum, L = ( g T2 / 4 2 ) = ( 9.8 * 16 / 4 2 ) = 4 m Decrease in length, L = Lt = 24 X 10 -6 * 4 * 95 = 9120 X 10 -6 m = 0.00912 m A) Final length, L' = L - L = 4 - 0.00912 = 3.9908 m B) New Time-period, T' = 2 ( L ' / g) = 2 ( 3.9908 / 9.8 ) = 4.0075 s
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