Calculating Mass and Gravity on Planet Newtonia

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SUMMARY

The discussion focuses on calculating gravitational acceleration (g) and the mass of the planet Newtonia using a simple pendulum. The pendulum has a bob mass of 1.00 kg and a length of 195.0 m, completing a swing in 1.40 seconds at an angle of 12.5°. The formula T = 2π√(L/g) is used to derive g, and subsequently, g is applied in the equation g = GM/R² to find the planet's mass. The angle of 12.5° is confirmed to have negligible impact on the calculations, as long as it remains within reasonable limits.

PREREQUISITES
  • Understanding of pendulum motion and the formula T = 2π√(L/g)
  • Familiarity with gravitational constant G and its application in physics
  • Knowledge of circumference and radius calculations for spherical bodies
  • Basic principles of angular displacement in pendulum motion
NEXT STEPS
  • Research the derivation and applications of the formula T = 2π√(L/g)
  • Explore the relationship between gravitational acceleration and mass using g = GM/R²
  • Learn about the effects of angular displacement on pendulum motion
  • Investigate the implications of using small angle approximations in pendulum calculations
USEFUL FOR

Physics students, educators, and anyone interested in gravitational calculations and pendulum dynamics will benefit from this discussion.

pdiddy94
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On the planet Newtonia, a simple pendulum having a bob with mass 1.00 and a length of 195.0 takes 1.40 , when released from rest, to swing through an angle of 12.5 , where it again has zero speed. The circumference of Newtonia is measured to be 51400 .

I solved for g using T = 2pi*sqrt(L/g) and then i used this g plus the constant G and the radius solved from the given circumference to calculate the mass of the planet from the equation g = GM/R^2 but can't get the answer, i don't know if its because I'm not taking the angle into account?
 
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welcome to pf!

hi pdiddy94! welcome to pf! :smile:
pdiddy94 said:
… takes 1.40 , when released from rest, to swing through an angle of 12.5 , where it again has zero speed.
…
… i don't know if its because I'm not taking the angle into account?

the angle makes no difference (so long as it's reasonably small, as 12.5° is),

but the period T is for two swings, isn't it? :wink:
 
ohh, thank you that makes sense
 

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