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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)

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Solution re(2): part 1: another method; another answer (wrong assumption) | Comment 7 of 22 |
(In reply to re: part 1: another method; another answer (wrong assumption) by np_rt)

Yes, you're correct; I had given the wrong proportionality for the acceleration due to gravity.  The corrected line is

acc = acc0 * r

The resulting corrected table is

  100  162.407     8126.67
  200  323.297    32430.79
  300  481.167    72685.34
  400  634.543   128514.35
  500  781.992   199396.34
  600  922.137   284669.20
  700 1053.668   383536.44
  800 1175.357   495074.56
  900 1286.067   618241.69
 1000 1384.764   751887.35
 1100 1470.526   894763.16
 1200 1542.552  1045534.55
 1300 1600.169  1202793.15
 1400 1642.840  1365070.04
 1500 1670.164  1530849.39
 1600 1681.888  1698582.65
 1624.63 1682.365  1740006.97
 27.07708333333333

Giving 1624.63 seconds or 27.077 minutes as the answer to part 1.  This confirms my first answer, using the argument from a circular orbit of the moon.  I had been wondering why the two answers did not match.


  Posted by Charlie on 2004-11-23 00:06:41
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