Probing Local Realism

Post Reply New Topic

A familiar question to first year physics students:

Assume the earth had a tunnel dug from both ends and disregarding any magma or anything in the way, what would happen if you dropped a ball into one end?

I know the answer to this question (for over 6 years), but I want to take this thread far beyond this.

disregarding gravity?

Unless no matter is present, you cannot disregard gravity.

ok. you said disregard anything in the tunnel that gets in its way..so since i'd think gravity would get in the way..
i'm not trying to be a smart ass. i've never heard the question, nor do i know where you're intending to go with it.

i would think that assuming it's not magnetic/or similar factors, and there was no material immediately in the way, nor falling/being drawn in the way, that it would go to the center of the earth.
yes?

ok. super cool. i just looked it up and as per http://www.askamathematician.com, you'd fall straight through back and forth and:
"the gravity at any point only depends on the amount of matter below you, and not at all on the amount of matter above you. "
i'm still contemplating this

Last edited by 100000fireflies on 27 Jan 2016, 2:45 am, edited 1 time in total.

It is not relevant in this case whether matter is up or down.

Hint: Here is the formula that is needed, d^2r/dt^2 + (g/a) r = 0

Edit: Just realized that some knowledge of differentiation is needed.

Last edited by Deltaville on 27 Jan 2016, 2:52 am, edited 2 times in total.

i still think that part was interesting. i mean it's kind of known..you're attracted to the mass below. but the rest of the concept of how it would feel dropping to a smaller and smaller surface combined with the fact of - that in the tube where there is no mass below as it's a tunnel...



anyway, you do spring as the website said and i got wrong? EDIT: you added the hint after i posted that, so i now figure no, that's not what you were getting at.

Last edited by 100000fireflies on 27 Jan 2016, 2:56 am, edited 1 time in total.

What do you mean spring?

Edit: Do you mean harmonic oscillation? Just realized this may have been your intention.

Doesn't it become a perpetual oscillator, like a pendulum? (If the tunnel is a vacuum at least. If there's air in there it would eventually come to rest in the center, I think.)

Well it cannot oscillate perpetually, unless you can breach the second law of thermodynamics; otherwise you are correct.

I think that's the pretty name for it, yes going back and forth from one end to the other.

If there's air in the tunnel the oscillation would eventually decay from friction. If the tunnel is a vacuum, however, what causes the oscillation to decay?

It would cease oscillating if air is present, that is what I meant.

My username is actually a parody of a famous German synthpop band.

This all assumes the Earth is not spinning too, i presume.

You said you wanted to take it further than the original question?

Interesting question op. I think since you are already "normalized" with the spin of the earth your momentum would just keep you going generally in the two directions (considering you didn't drop perfectly straight towards the "center") and considering friction you would slowly be pulled back and forth, a little less each time as you have less potential energy each time (thank friction for that) until you reached the center, where you would be basically suspended ( it would feel like that as all of the gravity of the earths' mass is pulling you equally in all directions). I think that your "bounceback" each time would be a little slower as you have less potential energy combined with less mass in the direction of the center and more mass "behind" you aka away from the center... if that makes any sense

Centrifugal force however is one I can't seem to factor in with any real coherency.... I imagine the earths spin would have no effect as it would be slowing your descent going in before speeding you up as you go out. My understanding is probably flawed.... If you happened to get unlucky with centrifugal force could you possibly gain too much energy going back out? Causing you to fly possibly even just 20-30- 40 feet or more the other direction? causing likely death

Maybe if you enter as the earth rotates in towards the sun and then exit as the earth rotates out, causing a whipping effect on you ? lol idk somebody with more physics knowledge should come in here and slay my hypothesis

edit: now I'm laughing, imagining the journey all the way through the center of the earth, some 10000 miles? Only to careen just barely too far the other way (thinking meters), to crash back and die lol