A simple pendulum is made up of a 2.0 kg mass suspended on a thinaluminum wire.

Question

A simple pendulum is made up of a 2.0 kg mass suspended on a thinaluminum wire. The pendulum has a period of exactly. 4.0 secondswhen operated near the equator at a temperature of 122 degrees F.The pendulum is then moved to an antarctic weather station wherethe temperature is -49 degrees F. The linear coefficient of thermalexpansion for aluminum is 24 x 10-6/degrees C

1. What is the length of the pendulum wire at the equator?

2. What is the period of the pendulum at the antarctic weatherstation?

Please show all work and formulas

Explanation / Answer

For a pendulum,    period = 2g/L .           4.0 = 2 9.80/L . Solve for L...    L = 24.1806 meters . Now... the length contracts when it goes to antarctica. First convert temperatures... .       L = -49 - 122 = -171 F =   -171* 5/9 =    -95 C .         L = L T = 24.18 * 24 x10-6 * -95   = 0.055130  meters . So the new length is   24.1806 - 0.055130 =   24.1255 meters . And now    period = 2g/L = 2 9.80/24.1255 =   4.0046 seconds

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