Uncle Patrick's Science Quiz

Discussion in 'Science and Technology' started by Patrick2, Jul 30, 2011.

  1. Patrick2
    Offline

    Patrick2 Senior Member

    Joined:
    Jul 12, 2011
    Messages:
    1,576
    Thanks Received:
    104
    Trophy Points:
    48
    Ratings:
    +104
    Suppose you could dig a tunnel through a diameter of the earth. On one end, you drop a ball in the center of the tunnel opening. What happens next?

    Assume:

    - spherical, gravitationally homogeneous earth
    - no coriolis effects
    - no molten interior - solid all the way through
    - no magnetic field effects
    - to tidal interactions with the moon, sun, etc.
    - a vacuum in the tunnel - no aerodynamic effects
     
  2. American Horse
    Offline

    American Horse AKA "Mustang"

    Joined:
    Jan 23, 2009
    Messages:
    5,741
    Thanks Received:
    892
    Trophy Points:
    153
    Location:
    The Hoosier Heartland
    Ratings:
    +938
    it would go all the way to the other side and begin to repeat the same cycle again
     
  3. Patrick2
    Offline

    Patrick2 Senior Member

    Joined:
    Jul 12, 2011
    Messages:
    1,576
    Thanks Received:
    104
    Trophy Points:
    48
    Ratings:
    +104
    Good, but give more info. Describe velocity and acceleration. Time for one cycle?
     
  4. American Horse
    Offline

    American Horse AKA "Mustang"

    Joined:
    Jan 23, 2009
    Messages:
    5,741
    Thanks Received:
    892
    Trophy Points:
    153
    Location:
    The Hoosier Heartland
    Ratings:
    +938
    Come on now! It's enough to say that the cycle times will be the same, and the time from the center of the earth to either surface the same; It is an interesting phenomena to think about.

    You tell us the specifics; I'm sure you have something interesting for us.

    ASK RDEAN!
     
    Last edited: Jul 30, 2011
  5. Toddsterpatriot
    Offline

    Toddsterpatriot Gold Member

    Joined:
    May 3, 2011
    Messages:
    26,082
    Thanks Received:
    3,643
    Trophy Points:
    280
    Location:
    Chicago
    Ratings:
    +10,043
    The only high speed rail that wouldn't require billions in subsidies.
     
  6. flacaltenn
    Online

    flacaltenn USMB Mod Staff Member Gold Supporting Member

    Joined:
    Jun 9, 2011
    Messages:
    30,034
    Thanks Received:
    4,659
    Trophy Points:
    1,130
    Location:
    Hillbilly Hollywood, Tenn
    Ratings:
    +13,351
    There's another potential energy (pun) source of energy in this thought game...

    I Give you atmospheric pressure of 30.00in on one side of the tube and about 29.90 on the other.. Call it a 3ft diam tube.. Kinda an expensive wind tunnel.. But I bet it would beat the reliability of regular surface wind power..
     
  7. Patrick2
    Offline

    Patrick2 Senior Member

    Joined:
    Jul 12, 2011
    Messages:
    1,576
    Thanks Received:
    104
    Trophy Points:
    48
    Ratings:
    +104
    The ball would accelerate all the way to the center of the earth (the speed at the center turns out to be 17,700 mph) and decelerate all the way to zero on the other end. One cycle turns out to last about 84 minutes.
     
  8. American Horse
    Offline

    American Horse AKA "Mustang"

    Joined:
    Jan 23, 2009
    Messages:
    5,741
    Thanks Received:
    892
    Trophy Points:
    153
    Location:
    The Hoosier Heartland
    Ratings:
    +938
    I remember something from the past that the speed at the center of the earth would be equal to escape velocity for orbiting....?
     
  9. Patrick2
    Offline

    Patrick2 Senior Member

    Joined:
    Jul 12, 2011
    Messages:
    1,576
    Thanks Received:
    104
    Trophy Points:
    48
    Ratings:
    +104
    Well first, escape velocity isn't an orbital velocity. Escape velocity is the initial velocity required to leave the surface of the earth, and end with a velocity of zero at infinity. It's about 25,000 mph. You can also look at it as the terminal velocity (neglecting aerodynamic effects etc) of an object dropped from an infinite distance with an initial velocity of zero (actually, you'd need a tiny nudge) when it strikes the earths surface.

    This problem is different: the falling body experiences less and less acceleration as it falls to the center, because the spherical shell farther out than the current depth of the ball provides no attraction. Hence the terminal velocity is much less than 25,000 mph.
     
    Last edited: Jul 31, 2011
  10. HUGGY
    Offline

    HUGGY I Post Because I Care Supporting Member

    Joined:
    Mar 24, 2009
    Messages:
    33,727
    Thanks Received:
    3,805
    Trophy Points:
    1,140
    Location:
    Seattle, in a run down motel
    Ratings:
    +6,285
    As described by others the ball would be in perpetual motion falling..accelerating to whatever speed you said..then gradually slowed to a stop and falling back in the opposite direction. In a perfect vacuum it should repeat this alternate falling and accelerating / decelerating forever.
     

Share This Page