(10 points) Imagine a grandfather clock here on Earth, with a pendulum that swin
ID: 1591390 • Letter: #
Question
(10 points) Imagine a grandfather clock here on Earth, with a pendulum that swings with a period of 1 s.
a. What is the length of the pendulum?
b. The free-fall acceleration (that is, the equivalent of g) on the moon is 1.6 m/s2. How long would the period of the grandfather clock from part a be if the clock were placed on the moon? Would this clock run fast, or slow? Explain.
**************STEPS FOR EACH PROBLEM*************
Draw and label a diagram for each problem
List the known and unknown variables
List the equations you would use
solve your equations with unknown variables
substitute known variables
Explanation / Answer
The acceleration of gravity (g) is 9.81 m/s^2 on Earth and 1.6 m/s^2 on the moon. It is therefore higher on Earth by a factor of 6.13.
KNown -
acceleration of gravity (g) is 9.81 m/s^2 on Earth
acceleration of gravity (g) is 1.6 m/s^2 on the moon
period on earth is 1 s
The period of a pendulum is
P = 2 pi sqrt(L/g)
1 = 2 * pi*sqrt(L/9.81)
L = 0.248 m
Since you are using the same clock in both places, L stays the same and the period will be longer by a factor sqrt6.13 = 2.47 on the moon.
It will run slow.
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