Time Period of pendulum on another planet? Given gravity

In summary, a simple pendulum on Earth with a period of 6.0 seconds has a length of 870 meters. Using the formula T=2pi * sqrt (L/g) and the acceleration of gravity on Jupiter (26 m/s^2), the period of the same pendulum on Jupiter would be approximately 3.7 seconds (option B). This is determined by solving for the length of the pendulum on Earth and then using that value to calculate the period on Jupiter.
  • #1
teggenspiller
94
0

Homework Statement



9. A simple pendulum on Earth has a period of 6.0 seconds. What would the period of this pendulum be on Jupiter, if the acceleration of gravity on the surface of Jupiter is 26 m/s2

A. 2.3 sec
B. 3.7 sec
C. 6.0 sec
D. 15.6 sec

Homework Equations


T=2pi * sqrt (L/g) Where L= Length of the pendulum

g=grav


The Attempt at a Solution



i know that 6.0s=2pi * (L/9.8) <-since that is the gravity on earth.
and T= 2pi* (L/9.8)

maybe, 6= 2pi * (L/9.8) ? But then ill be solving for L...
i have no idea what to do if anyone could please help me/explain the concepts.
 
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  • #2
They're asking you what T would be, so that is what you need to solve for under Jupiter conditions.

What changes on the right hand side when you move to Jupiter?
 
  • #3
maybe sub "6on Earth" somewhere, but i don't know how to word that into a mathmatical form. like present the ratio between Earth and Jupiter somewhere
 
  • #4
im doing 6= 2pi sqrt(L/26)

6^2=4pi^2 L/26

i keep getting 23. which is not an option.
 
  • #5
The period is 6 sec. on earth. It will not be 6 sec on Jupiter. Don't you have enough information to calculate the period on Jupiter? (Hint: use algebra)
 
  • #6
OKAY, cross multiply, try number 3:

6sec = Xsec x=15.91, which again, is not an option.
/9.8 / 26
 
  • #7
so now i have solved for the LENGTH of the pendulum on earth: L= 6^2/4pi^2 * 9.8

(i think that's right) and used 870, the Length and solved for T on Jupiter.

I get 36.34. Hmm, the squroot of 36.34 is 6. ahhh!
 
  • #8
In the formula for the period of the pendulum, you have enough data to determine the length of the pendulum based on its behaviour on earth. Taking the same pendulum to Jupiter, where the gravity is higher, what would the period of the pendulum be?
 
  • #9
is the length, 870, correct, you think? at least tell me tHat much. <?>
 
  • #10
thanks everyone for the help! Gotta 100 on the quiz!
 

Related to Time Period of pendulum on another planet? Given gravity

1. What is the formula for calculating the time period of a pendulum on another planet?

The formula for calculating the time period of a pendulum on another planet is T = 2π√(l/g), where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity on that planet.

2. How does the gravity of a planet affect the time period of a pendulum?

The time period of a pendulum is directly proportional to the square root of the acceleration due to gravity on that planet. This means that as the gravity increases, the time period of the pendulum decreases.

3. Does the length of the pendulum affect the time period on another planet?

Yes, the length of the pendulum does affect the time period on another planet. As the length of the pendulum increases, the time period also increases. This is because a longer pendulum will have a larger distance to travel, resulting in a longer time period.

4. How does the time period of a pendulum on another planet compare to Earth?

The time period of a pendulum on another planet will be different than on Earth due to the difference in gravity. If the gravity on the other planet is stronger, the time period will be shorter, and if the gravity is weaker, the time period will be longer.

5. Can the time period of a pendulum on another planet be measured using Earth's standard units of time?

Yes, the time period of a pendulum on another planet can be measured using Earth's standard units of time. However, the time period will be different due to the difference in gravity. It is important to use the formula specified for calculating the time period on another planet to get an accurate measurement.

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