A pendulum is swinging back and forth with a period of 2.0 seconds here on Earth. This pendulum is then brought to the Moon, where the acceleration due to gravity is much smaller. What will happen to the period of the pendulum, assuming everything else about it (mass, length, initial swing height, etc) remains exactly the same

Question

Physics

Brennen Grimes

28 April, 09:49

A pendulum is swinging back and forth with a period of 2.0 seconds here on Earth. This pendulum is then brought to the Moon, where the acceleration due to gravity is much smaller. What will happen to the period of the pendulum, assuming everything else about it (mass, length, initial swing height, etc) remains exactly the same

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Answers (1)

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Jovanny Reed · Answer 1

Answer: The period will be larger, with T = 4.92 seconds

Explanation:

The period of a pendulum can be obtained by the equation

T = 2*pi*√ (L/g)

Where pi = 3.14, L = lenght of the pendulum and g = gravity acceleration.

You can see that the gravitational acceleration is on the denominator, this means that if we decrease the value of g, then the value of T will increase.

In Earth we have that:

2s = 2*3.14*√ (L/9.8m/s^2)

L = (1/3.14) ^2*9.8 m = 1m

In the moon we have g = 1.62 m/s^2

then the period in the moon is:

T = 2*3.14√ (1/1.62) = 4.92s