...And you jumped in.
What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?
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3 Answers
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And you jumped in.
No, I'd refuse, You should do that Yourself. :=(
Do You want to "solve" this with or without friction by air?
Without friction, You would fall and reach maximum speed in the center of earth, going on until You reach the antipods, where You would stand still for a fraction of a second, then You would go down again. Very boring indeed and You should take some sandwiches and some drink with You.
With friction You wold accelerate up to a speed around 300 km/h, then fall down with this constant speed, slowing down when approaching the center, and go on some distance, fall down to center again and do that oscillation until all Your potential/kinetic energy is consumed by friction.
Because about a dozen of such holes were drilled here in physics.SE alone, You might find some company at the center of earth.
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2$\begingroup$ smile :). It was one of the first problems I had to solve in mechanics back when. $\endgroup$– anna vCommented Mar 21, 2011 at 12:27
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16$\begingroup$ Unless the hole goes pole-to-pole, you'll have to worry about effects of Earth's rotation as well as friction. Coriolis forces will press you against one side of the tube most of the time. As long as you're ignoring that friction as well as air resistance, the results are qualitatively the same. $\endgroup$– Ted BunnCommented Mar 21, 2011 at 14:15
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8$\begingroup$ One other fun exercise for those who haven't done it: Suppose that instead of going through the center of the Earth, the hole goes from one point to a non-antipodal point along a straight line (i.e., a chord of a circle rather than a diameter). Show that the time to fall from one end to the other is independent of the points chosen. (Ignore Earth's rotation and assume frictionless sliding.) $\endgroup$– Ted BunnCommented Mar 21, 2011 at 14:17
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7$\begingroup$ The last sentence just made me laugh.. $\endgroup$ Commented Mar 15, 2014 at 15:23
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$\begingroup$ Your frictionless answer is assuming that the mass density of the earth is the same throughout. This is untrue. So the position at which you "stand still" is not the antipode but before it given that the center is denser. $\endgroup$– ticsterCommented Jan 31, 2017 at 17:41
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I seem to remember Dr Karl on the Triple J radio station (Karl Kruszelnicki) explaining this one. In a zero friction environment, you would oscillate back and forth. It would take about 40 minutes to travel from one side of the earth to the other. An interesting side note was that if you were to dig the hole from any point in the Earth to any other point, it would still take the same amount of time to travel from one side to the other.
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1$\begingroup$ Read the comments from Ted Bunn "below". $\endgroup$– GeorgCommented Mar 21, 2011 at 18:58
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I'm not a Physics major but it seems to me that at the center of this planet you would have both little to no air and no weight. All direction would be equally down. If how ever you managed to git to one side then the gravity of that side would be half the gravity of the hole world minis the other half of the gravity that is reduced by the distance its source is from you. Gravity not being a constant but being reduced as the distance it is from its source increases. You would also feel the effect of centrifugal force that you could not tell was not gravity. There would be more air here as well but it might not be thick enough to breath. I think that you would feel that you were falling up after clearing the outer skin of the world. The effect of passing the center of gravity for the skin of the world.
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$\begingroup$ Yes, you'd be weightless at the centre, but the air pressure would be enormous. $\endgroup$– PM 2RingCommented Jun 19, 2018 at 3:12