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Homework Statement
How much energy is required to move a 900 kg mass from the Earth's surface to an altitude 3 times the Earth's radius?
Homework Equations
[tex] \Delta U = GMm[\frac{1}{R_1} - \frac{1}{R_2}][/tex]
[tex] G = 6.67 x 10^{-11} Nm^2/kg^2[/tex]
[tex]R_1 = R_E = 6.37 x 10^6 m[/tex]
[tex]M = 5.98 x 10^{24} kg [/tex]
The Attempt at a Solution
I plugged in everything with [tex] R_1[/tex] = radius of earth
and [tex] R_2 [/tex] = 3(radius of earth) + 1 radius of Earth = 4 radius of earth...and got [tex] \Delta U = 4.23 x 10^{10}[/tex].
The answer is [tex] 3.76 x 10^{10}[/tex], where [tex] R_2[/tex] = 3(radius of earth).
Why don't you use the radius of the Earth plus the altitude (i.e. 4x radius of earth)? For the first potential energy, I use the radius as the radius of the earth, so I don't see why you use only the altitude for the second potential energy.
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