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How long does it take to fall to the center of the earth?

  1. Nov 8, 2006 #1
    Let's assume that there are no other forces acting besides the gravitational pull of the earth. If a body started falling from the surface how much time would it take before it reached the center of the earth?
    It seems like an easy problem, but so far I have had no luck. So far I have only found acceleration as a function of distance (which is quite easy), which would be [tex] a=\frac{4G\pi \rho}{3}(r-s) [/tex] (rho: earth's density, r: earth's radius, s: traveled distance)
    But that doesn't help me since I need acceleration (or velocity) as a function of time and I have no idea how to proceed.
  2. jcsd
  3. Nov 8, 2006 #2

    Doc Al

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    Staff: Mentor

    Write the gravitational force as a function of distance from the center. Then see if it reminds you of anything.
  4. Nov 8, 2006 #3
    [tex] F=\frac{4G\pi \rho m}{3}s [/tex]

    still thinking...
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