Question

A) You want to use a pendulum to create a clock with a period of exactly one second in Boone, NC. How long will the pendulum be? Show all your work. (We can predict the period of your simple pendulum using your measurements and Boone’s local gravity g = 9.79 ± 0.01 m/s^2).

B) You move your (C1) pendulum to a planet which has a local acceleration due to gravity of 1/9th that of 9.8 m/s^2. How would the period change? Show all work.

Answer 1

T = time period

L = length of the pendulum

g = the gravity

using equation T = 2 $\pi$ $\sqrt{}$ L / g

given T = 1 second

g = 9.8 m / sec²

then L = ?

1 = 2 X 3.14 X $\sqrt{}$ L / 9.8

1 / 6.28 = $\sqrt{}$ L / 9.8

0.159 = $\sqrt{}$ L / 9.8

0.0252 = L / 9.8

L = 0.0252 X 9.8

L= 0.246 m

the pendulum should have the length is L = 0.246 m