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Forces (People and Earth) Problem

  1. Mar 23, 2005 #1
    There are about 6.3 billion people on the planet. Suppose that the world's population gather at one spot on the planet. Assuming each person takes up 1 m^2 of space on avg, the spot is 6.3 billion m^2. Assume that each person's mass is 70 kg on average. Suppose all those people jump at the same time. THe people, while pushing, are in contact with the earth for a time of 0.2 s and leave the ground with a speed of 5 m/s. The distance travelled by the people while pushing the earth is 0.5 m. Mass of the earth is 5.98x19^24 kg.

    Find the force with which the people push the earth.
     
  2. jcsd
  3. Mar 23, 2005 #2
    Thats a pretty cool problem. Find the force of one person, then multiply it by 6.3 billion people. I'm assuming your going to simplify the earth as flat.
     
  4. Mar 23, 2005 #3

    Doc Al

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    Staff: Mentor

    Hint: What impulse does the earth give to the people?
     
  5. Mar 23, 2005 #4
    Doc Al is correct. You have to use the impulse-momentum theorem =

    [tex]F \Delta t = \Delta p[/tex] where: [tex]\Delta p = mv_f - mv_i[/tex]

    So first, find your [tex]\Delta[/tex]momentum, then solve for [tex]F[/tex], and there you have it, your Force vector.

    Paden Roder
     
  6. Mar 23, 2005 #5
    Thank for the replies.
    I'm 100% sure this question is possible without momentum and impulse since we haven't studied those yet. My teacher did this question today in class and I understood it quite clearly but now I can't seem to figure out.
    I know first I have to figure out the weight of the people which would be equal to the Force pulling the earth up. I'm not sure where to go from here.
     
  7. Mar 23, 2005 #6
    Why is F = mv/t giving me an insanely wrong answer?
     
  8. Mar 23, 2005 #7

    Doc Al

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    Staff: Mentor

    You can always caculate the average acceleration of the people, then apply Newton's 2nd law.
     
  9. Mar 23, 2005 #8
    Thanks a lot, I got it :smile:
     
  10. Mar 24, 2005 #9
    Sorry for the slightly OT post (rather, a non-helpful reply), but that really IS a cool problem. I'm trying to picture a crowd of 6.3 billion people in "one place"...it would literally be an ocean as far as the eye can see.
    :bugeye:
     
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