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The Gravitational force

  1. Oct 5, 2009 #1
    A Space traveler weighs 695N on Earth. What will the traveler weigh on another planet whose radius is 3 times that of earth and whose mass is 2 times that of earth?

    So for this problem I got the mass and radius of the earth
    Mass of earth= (5.98 *10^24)
    Radius of Eath- (6.38 *10^6)
    Since it says mass of earth is twice of earth I multipled it by two (5.98 * 10^24)*2= 1.196*10^25
    and I multiplied the radius of earth by three (6.38*10^6)*3=19140000

    Then I plugged it into the Newton's law of universal gravitation formula
    F=G(m1*m2/R^2)
    G=6.674*10^-11

    F=(6.674*10^-11)((1.196*10^25)/(19140000^2))=2.898*10^-10
    but its wrong what did I do wrong. Thank you!
     
  2. jcsd
  3. Oct 5, 2009 #2

    Doc Al

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    Staff: Mentor

    Two problems:
    (1) You forgot the traveler's mass.
    (2) You messed up the exponent.

    Rather than do all that number crunching, just use ratios. Much less chance of error that way.
     
  4. Oct 5, 2009 #3
    Ratios...How would i set that up?

    Would i just put (695*2)/3?
     
  5. Oct 5, 2009 #4

    Doc Al

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    Staff: Mentor

    Almost, but not exactly. (The radius should be squared.)

    Try this:
    Weight on earth = GmM/R^2 = 695 N
    Weight on planet = Gm(2M)/(3R)^2 = ?

    Compare those two expressions.
     
  6. Oct 5, 2009 #5
    so I plugged the formula in:
    ((6.67*10^-11)(695)((5.98*10^24)*2))/(((6.38*10^6)^2)*3)=4540.244
    I plugged that in as the answer but it's still wrong...Am i missing a step? or is my calculation wrong?
     
  7. Oct 5, 2009 #6

    Doc Al

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    Staff: Mentor

    Two new problems:
    (1) 695 is the traveler's weight, not his mass. Find his mass.
    (2) You multiplied the demoninator by 3 after you squared the radius instead of before.

    But this is still the hard way. I'd still play around with the suggestion for using ratios that I gave in my last post:

    Hint: Weight on planet = Gm(2M)/(3R)^2 = 2/(3^2) * GmM/R^2
    (And you already know what GmM/R^2 equals.)
     
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