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Moon Experiment (Posted on 2004-11-22) Difficulty: 5 of 5
Assume the moon is a perfect sphere and a straight tunnel has been drilled through the center. How long would it take a 1kg ball dropped from one end of the tunnel to reach the center? Ignore all resistances.

If a second 1kg ball is dropped 10 seconds after the first one, when and where in the tunnel would they first meet?

Idealized Moon Stats:
- Diameter: 3480 kilometers
- Mass: 7.38x10^22 kilograms (uniform density)

See The Solution Submitted by Brian Smith    
Rating: 2.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Further to Andy Comment 22 of 22 |

I dont see that the ball, on reaching the centre of the Moon would suddenly stop. It would carry on because of momentum, but now decelerating as it travelled "up" the other side. As this momentum is gradually used up,  the ballīs kinetik energy is converted to potential energy, as it approaches the surface of the far side. On this ideal Moon there has been no loss to friction &c, so the ball would just exactly reach the other surface,before falling in again (potential back to kinetik..)<p>

Meanwhile the second ball having gone through the same process is shortly behind, and as the first ball begins its second fall it meets the second ball just below the surface of the far side of the moon.<br>

The balls recoil slightly on impact (their speeds at this point is not great) , the second ball giving up all its remaining outward kinetik energy in the collision. Both balls then fall together to the centre and beyond. <br>

The process continues as an oscillation many times, with the only energy seepage being the "click" of the balls together, progressively less and less near the surfaceof each side of the Moon. Eventually they settle together at the centre, and live happily ever after!


  Posted by John on 2005-12-27 08:58:14
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