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Q & A: Hole through the Earth

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Most recent answer: 10/22/2007
Q:
If you could dig a hole deep enough into the earth so that you broke through to the other side of the planet, then you threw somthing into the hole, say a ball, would the ball fall up into the sky once it left the hole, or would it be stopped somewhere between the begining and the end of the hole.
- Anonymous (age 16)
Ohio
A:
In the really simple version of this picture, ignoring any friction, the ball would:

1. speed up until it reached the center
2. slow down as it approached the opposite side
3. start to fall back just as it reached the opposite side
4. return to where it started
5. repeat forever.

If you include a little air friction, then it would never get all the way to the other side. Each bounce would stay closer to the center, where it would ultimately settle.

If you include bigger friction with the sides, it will get stuck somewhere toward the middle.

The key principle in understanding this behavior is conservation of energy. The terms you need to keep track of are:

1. The kinetic energy, which is proportional to the square of the velocity.
2. The gravitational potential energy, which in this case is approximately proportional to the square of the distance from the center.
3. Thermal energy- miscellaneous energy sinks to which energy flows via friction.

Mike W.

You’d have to put some frictionless rails in the hole to keep a falling object from getting scraped up on the sides. One reason is that since the Earth is turning, and the ball’s moving with it. When the ball drops through the hole it is still going eastward as well as down. The eastward component of the hole’s velocity decreases as it falls in, and eventually the ball will collide with the wall. It has to lose angular momentum somehow on its way down because it has none when it goes past the center of the Earth and must get some again when it emerges on the other side.

Tom

(published on 10/22/2007)

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