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Funny question in Physics

  1. Apr 19, 2010 #1
    Yesterday night, when I was on my bed, one of the funny question came to my mind and I'm posting it here before I forget.

    Suppose god come to earth and start making a big hole on the land of India. The length (or depth) of that hole is 12800 km. I mean it starts from India and end to America. (I'm not good in Geography and I considered that America is just opposite to India) That hole passes through the center of the earth. God was clever and so he coated that hole with a perfectly adiabatic material so that lava inside the earth crust should not trouble people traveling from India to USA using that hole. He also arranged oxygen on that hole. Now God went back.

    Some days later one man tried to get into America without having Visa to travel. He packed reasonable amount of food to take with him and jumped on that hole.

    Now take everything normal and tell whether that person can reach America or not and if he can reach how much time he will take to reach there.
     
  2. jcsd
  3. Apr 19, 2010 #2

    SpectraCat

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    :rofl: It is a funny thought, and I appreciate its relevance to the visa issue. But what do *you* think the answer is? Hint: think about conservation of energy and dissipative forces.
     
  4. Apr 19, 2010 #3
    In my view up to the center of the earth he will accelerate with acceleration equal to 9.8 m/s^2 and then he will start retarding with the same acceleration. It may be possible that his body will move back and forth on the hole for forever.
     
  5. Apr 19, 2010 #4
    if he travels with a speed of 20km/hr, then he might reach America in 26.66 days.

    Now, if the system is adiabatic, then it may be possible that there is no influence of heat into the so-called HOLE.

    But, the thing is, we can only imagine the severeness of heat in there.

    As for your geography,

    IT IS ALMOST IMPOSSIBLE !!
    :wink:
     
  6. Apr 19, 2010 #5
    I know it is impossible and therefore I started with a word "funny". And do you mean to make it possible we have to propel that person with initial velocity of 20 km/hr. .......?????
     
  7. Apr 19, 2010 #6

    SpectraCat

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    Not sure where that 20 km/hr came from .. I think you should ignore it, or do your own calculation.

    Two observations:

    1) Do you think the gravitational acceleration will be constant, or do you expect it to change?

    2) What about those dissipative forces I mentioned before? Didn't you say that the hole would be filled with air? Yes, that will be good so that your traveler can breathe, but might it also have other effects?

    Hmmm ... it seems you are thinking along the correct lines, but I wonder about the "forever" part (see comment 2 above).
     
  8. Apr 19, 2010 #7
    That is classic problem and it's fun to try and figure it out. Just a few hints:
    [tex]F=\frac{GMm}{r^2}[/tex]
    where G is the gravitational constant, m the mass of the person attempting the stunt and M the (partial) mass of the earth.

    I say partial mass, because at any given point in the earth you may neglect the outer shell of the earth that encloses it (the point). This may be done, because the forces of the outer shell cancel out.

    Hope I didn't give too much away :)

    On a similar note: Would anyone know how to calculate the pressure that the earth exerts on the tube in the middle?
     
    Last edited: Apr 19, 2010
  9. Apr 19, 2010 #8
    Don't forget that the person starts out with a horizontal velocity of about 1000 mph due to the earth's rotation. This will cause serious problems as one descends to a region of less rotation speeds. A curved (calculable) tunnel is required. God also has a sense of humor.
     
  10. Apr 19, 2010 #9
    that 20km/hr thing was just a supposition
    :tongue:
     
  11. Apr 19, 2010 #10
    that 20km/hr thing was just a supposition
    :tongue:
     
  12. Apr 19, 2010 #11
    But that tunnel will rotate with the same speed as the man because of earth's rotation. So how can it create a problem.

    @Spectracat, acceleration due to gravity increases as we go down toward center but after crossing center it will decrease with the same rate.
    And yeah, air resistance can create a big problem in calculation.
     
  13. Apr 19, 2010 #12
    If you are on the earth's surface, you travel 25,000 miles per rotation, or 25000 miles per day.
    a
    At a point 1000 miles from center you travel 2*pi*1000 miles per revolution or about 6,300 miles per day. So your horizontal velocity is only 1/4 of the velocity you had at the entrance of the tunnel. As a consequence, every time you started to free fall you would eventually crash into the wall of the tunnel, which has a slower horizontal motion than you do.
     
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