A clock pendulum is made from a small weight attached to the end of a light stri

Question

A clock pendulum is made from a small weight attached to the end of a light string or rod that that is suspended from a pivot. If properly designed, the pendulum can be made to swing back and forth once per second.

Design a pendulum that will work on the surface of the earth.

Design a pendulum that would work on the surface of the moon.

Explain how you would use a pendulum to measure the acceleration due to gravity at the surface of a new planet that you are exploring.

If you take your pendulum from sea level to the top of a tall mountain, will its period change? Explain your reasoning.

Explanation / Answer

let length of the pendulum is l.
then the time period is given by

T=2*pi*sqrt(l/g)

where g=acceleration due to gravity

on earth g=9.8 m/s^2

Time period=1 second

==> length=l=(T/(2*pi))^2*g=0.2482 m

part 2:

on surface of moon, acceleration due to gravity is 1.6 m/s^2

then length required=(T/(2*pi))^2*g=0.0405 m

part 3:

measure the length of the planet

caclulate the time period of the pendulum

then use the formula T=2*pi*sqrt(l/g)

to calculate g.

part 4.

from sea level to top of a tall mountain, value of g decreases

hence time period will increase (as it varies inversely with square root of g)

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