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A simple pendulum is made up of a 2.0kg mass suspended on athin aluminum wire. T

ID: 1727545 • 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 4swhen operated near the equator at a temperature of 122F. Thependulum is then moved to an Antartic weather station where thetemperature is -44F. The linear coefficient of thermalexpansion for aluminum is 24x10-6/C. a. What is the lenght of the pendulum wire at theequator? b. What is the period of the pendulum at the Antarcticweather station? A simple pendulum is made up of a 2.0kg mass suspended on athin aluminum wire. This pendulum has a period of exactly 4swhen operated near the equator at a temperature of 122F. Thependulum is then moved to an Antartic weather station where thetemperature is -44F. The linear coefficient of thermalexpansion for aluminum is 24x10-6/C. a. What is the lenght of the pendulum wire at theequator? b. What is the period of the pendulum at the Antarcticweather station?

Explanation / Answer

    Mass of the pendulum bob, M = 2 kg     Initial time period, T = 4 s     Fall in temperature , t = 122 - ( - 44)                                         = 166 oF                                         = 166 * ( 5/9 )          = 92.22 oC     Coefficient of thermal expansion, = 24 X10 -6 / oC     a)        Time-period, T = 2 (L / g )        Length of the pendulum, L = ( g T2 ) / ( 4 2 )                                                = ( 9.8 * 16 ) / ( 4 * 3.14 2 )                                                = 3.976 m     b)          New length, L ' = L [ 1 - t ]                                 = 3.976 [ 1 - ( 24 X 10 -6 ) ( 92.22 ) ]                                 = 3.9672 m        Time period is directlyproportional to the square root of length                                       T      L                                      ( T ' / T ) = ( L ' / L )                                                    = 0.9989     New time-period , T ' = 0.9989 * 4                                      = 3.99 s

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