A simple pendulum is made up of a 2.0 kg masssuspended on a thin aluminum wire.

Question

    A simple pendulum is made up of a 2.0 kg masssuspended on a thin aluminum wire. This pendulum has a periodof exactly 4.0 s when operated near the equator at a temperature of122oF. The pendulum is then moved to an Antarcticweather station where the temperature is –49oF. The linear coefficient of thermal expansionfor aluminum is 24 x 10-6/oC.

a.       (10 points) What isthe length of the pendulum wire at the equator?

b.     (10 points) What is the period of the pendulum at theAntarctic weather station?

Please show all Formulas and Work Used to get the answerthank you

Explanation / Answer

    A simple pendulum is made up of a 2.0 kg masssuspended on a thin aluminum wire. This pendulum has a periodof exactly 4.0 s when operated near the equator at a temperature of122oF. The pendulum is then moved to an Antarcticweather station where the temperature is –49oF. The linear coefficient of thermal expansionfor aluminum is 24 x 10-6/oC

a.       What is the length of thependulum wire at the equator?

         T=2l/g

        length=g*T2/4* = 9.8*16/4*3.14*3.14=3.975m

4

T

b.    What is theperiod of the pendulum at the Antarctic weather station?

l2=3.975- 24 x 10-6*230C

since 73degree F=23degree C

new length=3.974448m

so time period=2*3.143.97448/9.8=3.999sec

pl note that the value of acceleration due to gravity is takenas constant at these two places.

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