# Period of pendulum moved to Jupiter's moon Io

• robax25
In summary: Okay, so you need formulae or equations for g1 and g2 . What formula can you use for this?g=GM/r^2If you divideT1/T2=2*π√l/g1 / 2*π√l/g2. the you get the equation l= radious of the Pendulum and g is the gravitational constant.
robax25

## Homework Statement

you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s

T=2*π√l/g[/B]

## The Attempt at a Solution

T1/T2=√(g2/g1)

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robax25 said:
T1/T2=√(D1/D2)
=√((Gmr^2/9,81)/D1)
What are D1 and D2, and how do you get the second equation from the first?

D means g . If you divideT1/T2=2*π√l1/g / 2*π√l2/g. the you get the equation

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Moderator's note: I've changed the title of this thread to be more specific and descriptive of the actual problem.

robax25 said:
D means g . If you divideT1/T2=2*π√l1/g / 2*π√l2/g. the you get the equation
What is l (lower-case L)? What is g?

NascentOxygen said:
What is l (lower-case L)? What is g?
L is the length of the pendulum and g is the Gravitational costant

It's one pendulum clock that gets transported to Io, so how can there be two different pendulum lengths?

Usually G is the gravitational constant symbol. What numerical value are you using for lower-case g here?

NascentOxygen said:
It's one pendulum clock that gets transported to Io, so how can there be two different pendulum lengths?

Usually G is the gravitational constant symbol. What numerical value are you using for lower-case g here?
yes, G differs from Earth to Jupiter's moon Io. For earth, it is 9.81m/s^2... and Io moon is not mentioned. so we need to use gravitational formula to solve it

robax25 said:

## Homework Statement

you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the Earth's surface this oscillation time was 1s
I have clarified the problem statement here, to present it as I believe would have been intended.

NascentOxygen said:
I have clarified the problem statement here, to present it as I believe would have been intended.
i mean that.

So you have a final equation for TIo that involves the mass of Io?

NascentOxygen said:
So you have a final equation for TIo that involves the mass of Io?
No, I do not have the equation. I am confused.

Where's the confusion?

NascentOxygen said:
Where's the confusion?

## The Attempt at a Solution

T1/T2=√(g2/g1)

You'll need to show the working you followed in deriving that equation, by starting with something that you know to be right.

NascentOxygen said:
You'll need to show the working you followed in deriving that equation, by starting with something that you know to be right.
If you divideT1/T2=2*π√l/g1 / 2*π√l/g2. the you get the equation l= radious of the Pendulum and g is the gravitational constant.

Okay, so you need formulae or equations for g1 and g2 . What formula can you use for this?

g=GM/r^2

Go ahead and see whether you can now finish this.

## 1. What is the period of a pendulum on Jupiter's moon Io?

The period of a pendulum on Jupiter's moon Io would depend on several factors, such as the length of the pendulum, the strength of gravity on Io, and the amplitude of the pendulum's swing. However, assuming a standard pendulum length and amplitude, the period would be approximately 45 minutes.

## 2. How does the period of a pendulum on Io compare to Earth?

The period of a pendulum on Io would be significantly shorter than on Earth due to Io's stronger gravitational pull. On Earth, a pendulum with a length of 1 meter has a period of approximately 2 seconds, while on Io, it would have a period of about 45 minutes.

## 3. Does the period of a pendulum on Io vary at different locations on the moon?

Yes, the period of a pendulum on Io would vary at different locations on the moon. This is because the strength of gravity is not constant on Io, as it has varying topography and mass distribution.

## 4. Would the period of a pendulum on Io be affected by other factors besides gravity?

Yes, the period of a pendulum on Io may also be affected by the moon's orbital eccentricity, which could cause slight variations in gravity at different points in its orbit.

## 5. How would the period of a pendulum on Io be affected by the moon's volcanic activity?

The period of a pendulum on Io would not be significantly affected by the moon's volcanic activity. Although volcanic eruptions may cause temporary disturbances in Io's gravity, these effects would not be significant enough to alter the period of a pendulum in a noticeable way.

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