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Chapter 1: Q10DQ (page 459)

If a pendulum has a period of 2.5 s on earth, what would be its period in a space station orbiting the earth? If a mass hung from a vertical spring has a period of 5.0 s on earth, what would its period be in the space station? Justify your answers.

Short Answer

Expert verified

The pendulum would not swing back and forth in space.

The same period as in Earth, 5.0 s .

Step by step solution

01

Determine the formula for SHM

The period of simple pendulum having small amplitude is given by

T=2蟿蟿Lg

Where L is pendulum length and g is acceleration due to gravity.

02

Determine the period in the space and space station

The earth's orbit, there is no gravity i.e. g=0. Hence the period of simple pendulum is infinite in the earth's orbit. This means there is no restoring force to swing the pendulum back and forth.

Hence from equation the period of simple pendulum in the earth's orbit

T=2蟿蟿L0=鈭�

The period of spring-mass system is given by

T=2蟿蟿mk

The period of a vertical spring-mass system is independent of the gravity. Hence the period of the vertical spring-mass remains same in the space station i.e.

Tspace=5s

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