Is it possible to find the answer?

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SUMMARY

The discussion centers on calculating the time it takes to travel through a hole dug straight through the Earth, assuming a distance of 4000 miles. The gravitational acceleration is specified as 9.8 m/s², and the formula for gravitational acceleration inside the Earth is provided as g' = GMm/R³, where r is the distance from the center of the Earth, R is the Earth's radius, and M is the Earth's mass. The concept of simple harmonic motion is introduced, indicating that the motion through the Earth can be modeled similarly.

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  • Understanding of gravitational acceleration and its effects
  • Familiarity with the formula for gravitational acceleration inside a spherical mass
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  • Concept of Earth's mass and radius
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Homework Statement



if you dig a hole through earth, all the way through so you can see the other side is space. and you decided to jump into it. How long does it take for you to get to the other sisde of earth?

Homework Equations


the distance from top to bottom of Earth is 4000mi.


The Attempt at a Solution


I know that once you jump into the earth, gravity which is 9.8m/s will pull you down quickly. However, once you are directly in the middle of earth, you would stop accelerating. so is it possible to figure the answer? thank you for all help and inputs.
 
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Yes, it is.
In the middle of earth, no acceleration, but we still have velocity.
You can use gravitational acceleration inside of earth:
[TAB]g'=GMr/R^3
where r is distance from center of earth, R is Earth's radius, and M is Earth's mass.
It's just like a simple harmonic oscillation.
 

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