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Math Help - Very Difficult Calc Question!

  1. #1
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    Very Difficult Calc Question!

    Our professor gave us this one question for "bonus" marks last week and nobody got it. Just wondering how to solve this:
    If two masses m1 and m2 (in kg) are a distance d (in m) apart, then the force F (in N) of gravity is F = Gm1 m2 /d2 , where G = 6.6710^-11 Nm2 /kg2 . If the mass of the Earth is 5.9710^24 kg and the radius of the Earth is 6380 km, calculate the work required (in J) to send a mass of 1 kg to the edge of the universe. Be careful with units and note that this will involve an improper integral.
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  2. #2
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    I think GM/R = 6.24 x 10^7.
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  3. #3
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    Quote Originally Posted by calculuskid1 View Post
    Our professor gave us this one question for "bonus" marks last week and nobody got it. Just wondering how to solve this:
    If two masses m1 and m2 (in kg) are a distance d (in m) apart, then the force F (in N) of gravity is F = Gm1 m2 /d2 , where G = 6.6710^-11 Nm2 /kg2 . If the mass of the Earth is 5.9710^24 kg and the radius of the Earth is 6380 km, calculate the work required (in J) to send a mass of 1 kg to the edge of the universe. Be careful with units and note that this will involve an improper integral.
    F = \frac{6.67\times 10^{-11} \times 1 \times 5.97\times 10^{24}}{(6380\times 10^3)^2}

    W = \int F\, ds
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  4. #4
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    What will the interval of the integral be?
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  5. #5
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    Quote Originally Posted by calculuskid1 View Post
    What will the interval of the integral be?
    I would have thought from the radius of the earth to infinity?
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  6. #6
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    Dear calculuskid1,

    If the 1kg mass is r distance away from the surface of the earth, the force on it is given by,

    F = \frac{6.67\times 10^{-11} \times 1 \times 5.97\times 10^{24}}{((6380\times 10^3)+r)^2}

    Therefore the work done when moving it to the edge of the universe is given by,

    W=\int_{0}^{\infty}\frac{6.67\times 10^{-11} \times 1 \times 5.97\times 10^{24}}{((6380\times 10^3)+r)^2}dr

    I think e^(i*pi) made a slight error in taking the force when the 1kg mass is at the earths surface.
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