Unraveling the Mystery of the Gravity Train

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    Gravity Mystery Train
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Discussion Overview

The discussion revolves around the concept of a Gravity Train, specifically focusing on calculating the time it takes for a body to travel through a tunnel that passes through the Earth. Participants explore different approaches to this problem, including kinematic equations and the nature of acceleration within the context of simple harmonic motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant attempts to calculate the time for a Gravity Train using kinematics and presents an expression for acceleration as a function of depth.
  • Another participant questions the validity of the acceleration expression, noting that it yields an unexpected result when depth is zero.
  • A correction is suggested regarding the acceleration formula, proposing a different relationship that may be more appropriate.
  • Participants discuss the need to derive the correct kinematic equations for the motion, emphasizing that the acceleration is not constant and relates to simple harmonic motion.
  • There is a suggestion to start from Newton's second law to derive the motion equation, indicating that the problem requires a differential equation approach.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of acceleration and the appropriate kinematic equations to use. The discussion remains unresolved regarding the best approach to calculate the time for the Gravity Train.

Contextual Notes

There are limitations in the assumptions made about acceleration and the applicability of uniform acceleration equations. The discussion highlights the complexity of deriving motion equations for a non-constant acceleration scenario.

-Castiel-
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A few months ago I was surfing idly and found this little thing called a Gravity Train. For those who do not know what it is, see http://en.wikipedia.org/wiki/Gravity_railroad" .

After reading about it I thought maybe I should try and find out how much time it would take (42.2 minutes) but anything I tried did not work. Finally, when I decided to give up and sneak a peek I saw that they calculated it considering it as an oscillation (which in a way it is), but what I have been trying to do is calculate that time using kinematics.

I know the relation of 'a' with displacement (x), a = g((R-x)/2R) where g = 9.8, r = radius of earth, x = the depth to which the body is inside the earth.

Whatever approach I take from here leads me to a dead end. Any ideas how I should proceed?
 
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Start with what is wrong with your expression for a. If I put in x=0, I get a = g/2, which doesn't make a lot of sense.
 
-Castiel- said:
A few months ago I was surfing idly and found this little thing called a Gravity Train. For those who do not know what it is, see http://en.wikipedia.org/wiki/Gravity_railroad" .
.
I think you mean http://en.wikipedia.org/wiki/Gravity_train" .
 
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Ken G said:
Start with what is wrong with your expression for a. If I put in x=0, I get a = g/2, which doesn't make a lot of sense.

Sorry about that, it should be

a = g((R-2x)/R) where g = 9.8, r = radius of earth, x = the depth to which the body is inside the earth.

I am not used to writing formulae like this so...>_<

A.T. said:
.
I think you mean http://en.wikipedia.org/wiki/Gravity_train" .

Yes, I do.

On another note: No edit button?
 
Last edited by a moderator:
What do you mean by calculating time "using kinematics"?
First you need to find the (kinematic) equations of the specific motion. You cannot use the ones for uniform accelerated motion. The acceleration is not constant.
You can start with Newton second law which will provide a differential equation. You need to solve it to get the equation of the motion (position as a function of time).
This above mentioned equation happens to be the equation of a simple harmonic oscillator.
So the kinematic equations are these of the harmonic oscillator.
 

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