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Universal gravity

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A sensitive gravimeter is carried to the top of Chicago's Sears Tower, where its reading for the acceleration of gravity is 0.00136 m/s^2 lower than at street level.

    Find the height of the building.

    2. Relevant equations

    F = GMm/(r^2)

    and maybe

    K + U = K_o + U_o

    3. The attempt at a solution

    don't know where to start!
     
  2. jcsd
  3. Mar 10, 2009 #2
    consider other units for m/s^2
     
  4. Mar 10, 2009 #3
    Well I think I could use (g - 0.00136) = g_t.

    I dont know how I could use this though.
     
  5. Mar 10, 2009 #4
    wait could I do this :

    (9.8 - 0.00136) = GMm/r^2 ?
     
  6. Mar 10, 2009 #5

    LowlyPion

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    Yes, so you can then write ...

    g*r12 = G*M= (g - .00136)*r22
     
  7. Mar 10, 2009 #6

    what happened to small m

    (9.8 - 0.00136)(r^2) = GM (m?)
     
  8. Mar 10, 2009 #7

    LowlyPion

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    m*g*r12 = G*M*m= m*(g - .00136)*r22

    If that makes you happier. It isn't a factor.

    F = m*g = GM*m/r2

    g = GM/r2
     
  9. Mar 10, 2009 #8
    so,

    let G_t = (9.8-0.00136);

    then,

    G_t*r^2 = GM

    M = G_t*r^2 / G

    and r is the radius of the earth and G is the universal gravity constant.

    m ~ 9.3579 * 10 ^ 17

    But what does this mean? This is the mass of th building and....
     
  10. Mar 10, 2009 #9

    LowlyPion

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    In case you didn't notice you don't need G and you don't need M and you don't need m.

    You just need re and g.

    Building height will be Δr = r2 - r1

    where r1 = re
     
  11. Mar 10, 2009 #10
    why is that?
     
  12. Mar 10, 2009 #11
    so

    (9.8-0.00136) r^2 = GM

    and GM is just dropped? why?
     
  13. Mar 10, 2009 #12

    LowlyPion

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    The answer is because you can.

    g*r12 = (g - .00136)*r22

    You just need re and g.

    Building height will be Δr = r2 - r1

    where r1 = re
     
  14. Mar 10, 2009 #13
    OK, i guess.

    so

    (9.8-0.00136) ( 6.37 * 10^6)^2 = R1;

    R1 - R2 = height of tower

    R1 ~ 3.976 * 10^14
    R2 = (6.37 * 10^6)

    right I got 6.37 * 10^6 as the radius of the earth from my book.
     
  15. Mar 10, 2009 #14

    LowlyPion

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    No.

    Try being more careful.

    (6378)2 km = 40678884

    now multiply by 9.81/(9.81 - .00136) = ...

    then take the square root. Then subtract one from the other. Keep as much precision as you can.

    Your answer will be less than a km. Multiply by 1000 for meters.
     
  16. Mar 10, 2009 #15
    (6378)^2 = 40678884

    ans * 9.81 / (9.81-0.00136) =
    40684524.26

    sqrt(ans) = 6378.44
    ??
     
  17. Mar 10, 2009 #16
    confused even more. Dont know where 6378 came from and why
    sqrt ( ans * 9.81/(9.81-0.00136) )
    ...
    ...
     
  18. Mar 10, 2009 #17

    LowlyPion

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    I used radius of earth as 6378 km. And g you recognize as 9.81
    Right.

    Now 6378.44 - 6378 = .44 km = 440 m = height of building.
     
  19. Mar 10, 2009 #18
    could you do it out in variables first so I can see what you have done.
    Sorry.
     
  20. Mar 10, 2009 #19

    LowlyPion

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  21. Mar 10, 2009 #20
    ok thanks
     
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