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Newton's Laws of Gravitation

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Some people believe that the Moon controls their activities. The Moon moves from being directly on the opposite side of Earth from you to be being directly overhead. Assume that the Earth-Moon (center-to-center) distance is 3.82 multiplied by 108 m and Earth's radius is 6.37 multiplied by 106.

    (a) By what percent does the Moon's gravitational pull on you increase?


    (b) By what percent does your weight (as measured on a scale) decrease?


    2. Relevant equations
    F = (GMm)/r^2




    3. The attempt at a solution

    First I found the force of the gravitational force between me and the moon, then for me and the Earth. Then I set up a proportion and found the percent that the gravitational force between me and the moon is to the gravitational force between me and the Earth.

    F(moon) = (6.67e-11 * 7.36e22 * 70.76)/(9.55e7)^2 = 3.81e-2

    F(Earth) = (6.67e-11 * 5.98e24 * 70.76)/(9.55e7)^2 = 8.56

    F(moon)/F(Earth) = x/100

    x = [100 * F(moon)] / F(Earth) = .44
     
  2. jcsd
  3. Nov 9, 2009 #2
    the problem does not actually ask u to find earth's gravitational pull on you :D

    it does not hurt though ;)
     
  4. Nov 9, 2009 #3
    So the answer to the first one is just the gravitational force between me and the moon?
    I'm still confused lol.
     
  5. Nov 9, 2009 #4
    the distance between u and the moon is different for both cases :)
     
  6. Nov 9, 2009 #5
    Ok ya that makes sense. So the "r" in the equation would be different for each case. But do you think that I'm supposed to use my own mass for the problem?
     
  7. Nov 9, 2009 #6
    try it first with what we have so far :)
     
  8. Nov 9, 2009 #7
    Ok here we go..

    F(moon_opposite side) = (6.67e-11 * 7.36E22 * 70.76) / (3.82e8)^2 = 2.4e-3

    F(moon_overhead) = (6.67e-11 * 7.36E22 * 70.76) / (6.37e6)^2 = 8.56

    now proportion?
     
  9. Nov 10, 2009 #8
    u got the distances wrong :)
     
  10. Nov 10, 2009 #9
    oh lol so..let's see..

    is the distance for the "moon_opposite side" = 3.88e8?
    and the other distance is 3.82e8?
     
  11. Nov 10, 2009 #10
    done, give me cookies :D
     
  12. Nov 10, 2009 #11
    the other distance is 3.76 e8
     
  13. Nov 10, 2009 #12
    haha how'd you get 3.76e8?
     
  14. Nov 10, 2009 #13
    try drawing the diagram, u'll see :)
     
  15. Nov 10, 2009 #14

    Redbelly98

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    Homework Helper

    Yes.
    No, that's the distance from the moon to the center of the Earth. You would use that distance if you were located at the center of the Earth, which you aren't in this problem.
     
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