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About gravity

  1. Aug 11, 2011 #1
    if a tunnel is bored through the centre of the earth and a pebble is dropped into it then the pebble will do what ?....A)stop at centre...b)perform s.h.m.
     
  2. jcsd
  3. Aug 11, 2011 #2
    SHM for a considerable period of time, given that it would have gained enough momentum to defy gravity and travel to the other end of the hole by the time it reaches the centre. And then gravity pulls it right back.


    [EDIT: And that's if the hole is drilled from pole to pole.]
     
  4. Aug 12, 2011 #3
    But you are neglecting the considerable air resistance. So it will not be close to SHM in the beginning.

    I'm of course assuming that molten rock/metal will not refill the hole when the drill is removed...
     
  5. Aug 12, 2011 #4

    Ryan_m_b

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    Staff: Mentor

    Assuming the tunnel was bored through a perfectly spherical Earth and was in a vacuum then it would SHM for quite a while if not indefinitely.
     
  6. Aug 12, 2011 #5

    HallsofIvy

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    IF you are ignoring air resistance then you will have harmonic motion- just as vhbelvadi says. Energy will be conserved so the pebble will accelerate until it reaches the center of the earth, decelerate so that it stops just as it reaches the surface at the other end of the tunnel, then repeat its motion.

    IF you are not ignoring air resistance, then Energy is not conserved. Depending upon just how much energy is lost to friction, the pebble may perform "damped" harmonic motion for several repetitions, eventually stopping at the center of the earth, as torquil says.
     
  7. Aug 12, 2011 #6
    thnx guys
     
  8. Aug 12, 2011 #7
    I was just wondering, if the hole drilled has a radius that is considerably small and we assumed a vacuum (so there's no question of air resistance) and the hole was drilled along the equatorial plane, would the pebble actually reach the other end at all or would it strike an inner wall of the hole because the Earth would have rotated quite a distance by that period of time?

    (I reckon it would take the pebble about 19min to reach the centre so roughly double to reach the opposite end of the tunnel which means the Earth would have moved thousands of metres by then.)
     
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