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Change in gravitation potential energy in space

  1. Nov 25, 2012 #1
    1. The problem statement, all variables and given/known data
    an object of mass 750 kg is lifted from the earth's surface to a height of 6.8 x 10^6 m above its surface. Calculate the change in gravitational potential energy for the object.


    3. The attempt at a solution

    I used this formula ΔEg = Eg2 - Eg1
    ΔEg = -(GMm/r2) - (-GMm/r1)

    Eg2 = -(GMm/r2)
    Eg2 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.8x10^6m)+(6.37x10^6m)
    Eg2 = -2.27 x 10^10 J

    Eg1 = -(GMm/r1)
    Eg1 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.37x10^6m)
    Eg1 = -4.7x 10^10 J

    ΔEg = Eg2 - Eg1
    ΔEg = -2.27 x 10^10 J + 4.7x 10^10 J
    ΔEg = 2.43 x 10^10 J

    Is my process correct?
     
  2. jcsd
  3. Nov 25, 2012 #2

    haruspex

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    Yes. But do be careful with parentheses: /(6.8x10^6m)+(6.37x10^6m):wink:
     
  4. Nov 25, 2012 #3
    Is in like when im adding them?
    Are all the calculation right.. i really had trouble with them...
    like adding the exponents above the 10... :frown:
     
  5. Nov 25, 2012 #4

    haruspex

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    Most likely you knew what you intended when you wrote /(6.8x10^6m)+(6.37x10^6m), and therefore treated it as /((6.8x10^6m)+(6.37x10^6m)) when you used it, but it's confusing for others (including examiners!), and might confuse you sometime.
    I did a sanity check. The altitude doubled the radius, and then some, so the energy should halve, and then some - which it did.
     
  6. Nov 25, 2012 #5
    so it is correct?
     
  7. Nov 25, 2012 #6

    haruspex

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    I believe so, but I did not check the arithmetic in detail.
     
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