Falling Through the Earth
Date: 05/27/2002 at 11:05:47 From: Josh Subject: Earth Question What if someone dug a hole straight down all the way through the earth and then jumped into it. What would happen when he came out the other side? Would he blast off into the sky or would he fall back down into the hole?
Date: 05/27/2002 at 15:42:02 From: Doctor Tom Subject: Re: Earth Question Hi Josh, It depends on where the hole is! Let's start with an artificial situation -- the earth is not spinning, and there is no atmosphere which would cause friction on the falling body. Then if you jumped in, you would fall faster and faster until you reached the center, at which point your speed would be greatest. As you continuted "up" the hole on the other side, you would slow and slow, and come to a stop exactly at the surface at the opposite end of the earth. If you didn't grab the edge and pull yourself out, you would then repeat the motion exactly, dropping to the center and returning to your same place. Without grabbing edges or friction, you would cycle like this forever. If there's friction, you would still speed up until the center, but more slowly, so when you got to the center, you wouldn't be moving so fast. Then you would rise up the opposite side, but not all the way to the top, where you'd stop and start falling again. Due to more friction, you would continue to lose speed on each cycle and would go back and forth from the center, each time stopping deeper in the earth. Eventually, you would stop in the center. The more atmosphere (and hence friction), the more quickly you would slow down. Now, with the actual case of the spinning earth, if there were no friction from atmosphere, you would cycle together if the hole were drilled from pole to pole, but from any other point, you would slam into one of the walls on the way down. To see why, imagine, that the hole goes from somewhere on the equator to its opposite point, also on the equator. At the surface of the earth, you are moving with it at about 1000 miles per hour. Without friction, you'll continue to move that fast, but half way down, the earth is only turning at 500 mph, so (if you got that far) you would be moving sideways in the hole at 500 mph (relative to the speed the hole was moving). So unless it was a very wide hole, you'd hit the side soon after jumping into it. With the actual atmospheric friction, you'd hit the wall, and your speed would be less than before. With atmosphere and jumping north pole to south pole it would be just like I described above for a non-spinning earth, but with atmospheric friction. - Doctor Tom, The Math Forum http://mathforum.org/dr.math/
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