Energy to move mass (potential energy)

merced

1. The problem statement, all variables and given/known data
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?

2. Relevant 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]

3. 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.

nrqed

Your reasoning is entirely correct, [itex] r_f [/itex] {\em should} be [itex] 4 R_E [/itex]. If they used three times the radius of the Earth, they made a mistake, since "altitude" is defined to be measured above ground.

merced

Ok, If I only can tell my professor before the next test!

Thanks!!