Comparing Gravity on Different Planets Using a Pendulum

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SUMMARY

The discussion focuses on calculating the gravitational acceleration on two different planets using a pendulum. An astronaut measures a 50 cm pendulum's oscillation period of 2 seconds on planet X, resulting in a gravity value of 493.48 cm/s². On planet Y, the same pendulum's oscillation period is 1.5 seconds, yielding a gravity value of 877.30 cm/s². Consequently, planet Y has the largest gravity, confirming that gravitational acceleration is higher on this planet.

PREREQUISITES
  • Understanding of pendulum motion and oscillation periods
  • Familiarity with the formula for gravitational acceleration: g = 4π²L/T²
  • Basic knowledge of unit conversions, specifically from centimeters to meters
  • Ability to perform calculations involving constants and variables
NEXT STEPS
  • Learn about the effects of gravity on pendulum motion in different environments
  • Explore the implications of gravitational differences on planetary science
  • Study the relationship between pendulum length and oscillation period
  • Investigate the use of pendulums in measuring gravitational acceleration on Earth and other planets
USEFUL FOR

This discussion is beneficial for physicists, educators, and students interested in gravitational studies, as well as anyone exploring the principles of pendulum mechanics in varying gravitational fields.

brayrbob
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Here is my problem that I have partly solved.

An astronaut visits planet x. She takes out a 50 cm pendulum and records a period of oscillation of 2 seconds. Then the astronaut visits planet y, takes out the same pendulum and records a period of oscillation of 1.5 seconds. Which planet has the largest gravity? What is the value of gravity on that planet?

g = 4pi^2(50)/2^2 = 493.4802201 for planet x
g = 4pi^2(50)/1.5^2 = 877.298169 for planet y
planet y has the largest gravity
Now I'm not sure how to find the value of gravity for planet y.
 
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brayrbob said:
Here is my problem that I have partly solved.

An astronaut visits planet x. She takes out a 50 cm pendulum and records a period of oscillation of 2 seconds. Then the astronaut visits planet y, takes out the same pendulum and records a period of oscillation of 1.5 seconds. Which planet has the largest gravity? What is the value of gravity on that planet?

g = 4pi^2(50)/2^2 = 493.4802201 for planet x
g = 4pi^2(50)/1.5^2 = 877.298169 for planet y
planet y has the largest gravity
Now I'm not sure how to find the value of gravity for planet y.
you've already calculated the gravity "g" for both planets.

(note: to obtain g in mks units, recalulate values using pendulum length of 0.5 meters instead of 50 cm.)
 
So the gravity for the planets is the vaule of gravity?
planet y has the vaule of gravity of g= 877.29cm/s^2
 
brayrbob said:
So the gravity for the planets is the vaule of gravity?
planet y has the vaule of gravity of g= 877.29cm/s^2
yes (at the location of the pendulum)
 

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