Saturday, March 18, 2006

Dimensional Analysis of a Pendulum Period

If a pendulum is taken to Mars, how would its period change?



Related Resources
Dimensional Analysis
Measurements, Dimensions and Units
The Conical Pendulum

What is the Acceleration of a Fastball?

Elsewhere on the Web
Simple Pendulum
Mars

Q) If a pendulum has a period of 4s on the earth, what would its period be if it were placed on Mars? (Use gM/gE~ 1/3.) Use only dimensional analysis.

A) First, we must determine the relationship between the pendulum's period and gravity.

The period (P) of a pendulum of length l is a time, so

    =T

    if P α lagb

    T=[l]a[g]b

    T=La(L/T2)b

    Thus, a=1/2 and b=-1/2

    P α √(l/g)

Now, if we move to Mars, we don't change the length of the pendulum - Thus:

    TM/TE=√(gE/gM)

    TM=TE√(gE/gM)

    TM=(4s)√3

    TM~7s

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