Gravitational Potential Energy Problem

[brendan3eb]

[SOLVED] Gravitational Potential Energy Problem

Homework Statement

Suppose that the moon were at rest at its present distance from the earth, rather than orbiting it. With what speed would it strike the earth? (Take the Earth to be infinitely massive relative to the moon)

Homework Equations

Mass of Earth = 5.98x10^24 kg
Distance from center of Earth to center of moon = R = 3.82x10^8 m
Mean radius of Earth = Re = 6.37x10^6 m
Gravitational potential energy = -GMm/R
K1+U1=K2+U2

The Attempt at a Solution

K1=0
k2=(1/2)Mmv^2
U1=-GMeMm/R
U2=-GMeMm/Re
(1/2)Mmv^2-GMeMm/R=-GMeMm/Re
when I eliminate the mass of the moon and plug in all the numbers to solve I get 11.10 km/s, but I know the right answer is 9.8 km/s. Anyone see what I am doing wrong?

 

[BlackWyvern]

The radius of the moon?

 

[brendan3eb]

a-ha! Bingo! Thank you so much. The second potential energy distance would have be the sum of the radius of the Earth AND the moon! Let's see our numbers...yep 9.8 km/s!

Thank you so much!

 

[BlackWyvern]

No problem, glad to see you got it. :)