Earth's density and its gravity

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SUMMARY

The discussion centers on calculating the mass required to increase Earth's gravitational acceleration from 9.81 m/s² to a rounded value of 10 m/s², while maintaining the same density. The participant, Jack, seeks to understand the relationship between mass, density, volume, and gravity, specifically how to derive gravitational acceleration from density. Key formulas mentioned include the density formula p=m/v and the gravitational force equation. The conversation emphasizes the need to connect these concepts to solve the problem effectively.

PREREQUISITES
  • Understanding of gravitational force equations
  • Familiarity with the density formula (p=m/v)
  • Basic knowledge of Newton's second law
  • Concept of Earth's density and volume
NEXT STEPS
  • Research the derivation of gravitational acceleration (g) from density and volume
  • Study the implications of changing mass on gravitational force
  • Explore the relationship between mass, radius, and density in planetary bodies
  • Investigate methods for calculating Earth's volume based on its radius
USEFUL FOR

Students in physics, particularly those studying gravitational forces and planetary science, as well as educators seeking to enhance their understanding of gravity-related calculations.

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Homework Statement


Jack is tired of having to use 9.81 m/s^2 all the time to his calculations concerning gravity. He wants to use a round number 10 m/s^2. How much mass would have to be added to the Earth to make this happen? What would the new radius of the Earth be? Assume that the density of the Earth will remain the same. Where could you get the mass needed?


The Attempt at a Solution



All I have right now is the formula p=m/v. I know the volume of the Earth, its density and its mass, but I can't find the relationship between mass/density/volume and gravity.
I have to find the answer guided by the density formula only. I've tried to multiply the mass by the ratio of 9.81 and 10, but somehow the answer doesn't look right, and I won't know if it's right if I don't know how the 9.81 m/s^2 is derived from the density formula.

I'm not looking for the answer, just for hints as to how to approach this problem. Thanks!
 
Physics news on Phys.org
What equation do you use for gravitational force? If you think about that and Newton's second law, you can see where "g" comes from.
 

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