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Homework Help: Help with gravity Question

  1. Jan 23, 2009 #1
    1. The problem statement, all variables and given/known data
    How high above the surface of the earth should a rocket be
    in order to have 1/100 of its normal weight? Express your answer
    in units of earth radii.


    2. Relevant equations
    F=GMm/r2
    F=mg


    3. The attempt at a solution
    r = √(( 6.67 x 〖10〗^(-11) x 5.97 x 〖10〗^24 )/0.098)
    then divide by 6.37*106

    I asked for help from one of my friends and he emailed me this but I think he might have messed somthing up. I keep getting a really big number.

    I also know the answer its 9 radii but i dont understand how to get that answer.
     
    Last edited: Jan 23, 2009
  2. jcsd
  3. Jan 23, 2009 #2

    mgb_phys

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    You don't need to use the actual mass of the Earth or the value of G.

    You know that the weight is F = GMm/r^2
    You know 'GMm' doesn't change,
    So all you are asking is what do you have to do to 'r' to make 'r^2' 1/100 as big

    ps. Careful with the final answer, r is from the centre of the Earth but the question asks for height above surface.
     
    Last edited: Jan 23, 2009
  4. Jan 23, 2009 #3
    So i have to make r^2=1/10 of r^2?
     
  5. Jan 23, 2009 #4

    mgb_phys

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    yes - it migth help to label them rinitial and rfinal to avoid confusing yourself !
     
  6. Jan 23, 2009 #5
    so how do i do that i tried r^2/10 its not right.
     
  7. Jan 23, 2009 #6
    i think i got it, so I did r*10 then subtract 1 to get distance from earths surface not its center. Thnx for the help.
     
  8. Jan 23, 2009 #7

    mgb_phys

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    More formally you would write
    ri2 = 100 rf2

    Take square root of both sides, it also helps to know that sqrt(ab) = sqrt(a) * sqrt(b)
     
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