brendan3eb
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[SOLVED] Gravitational Potential Energy Problem
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)
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
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?
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?