- #1
psychicgerm
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Okay, first of all, sorry for not posting here, I unknowingly posted this q in the wrong section and got an infraction. Sorry again
Question : Calculate the change in gravitational potential energy of the moon, when the radius of it's orbit increases by 4cm.
Radius : 3.85*10^8 m
Mass of the Earth : 6*10^24 kg
Mass of the moon : 7.36*10^22kg
We were first told calculate the force between the moon and the Earth using
F = Gmm/r^2. Comes to around 2*10^20 N
We were then told to find the change in G.P.E when the radius increases using the force which we calculated.
F = GMm/r^2
GPE = GMm/r
Method I : Work done = Force * Distance. 2*10^20 * 0.04 = 8*10^18J
Now this is what my friend did, and why I think this is incorrect? Because he assumes that the force is constant as the radius changes, which clearly isn't. Why do I think he is correct? Because he does what was asked, he used the force to find the change in gpe.
Method II (This is what I did) : Potential energy of a mass m at a distance r is = -GMm/r
(Asked to calculate the change, hence i'll use the modulus of that and ignore the minus)
GMm(1/r2 - 1/r1) [Where r2 is 3.85*10^8 + 0.04 and r1 is 3.85*10^8)
When you go ahead and solve this using your calculator, you realize that the change in the radius is soooo less, even the calculator won't show up the change. Hence the value you get is 0J.
Why I think I'm correct? Because the change is the GPE shouldn't be much because the radius didn't change a lot. And because I used a perfect formula. (?)
Why I think I'm wrong? Because I didn't use the force to calculate.
My dilemma is clear, these are 2 extreme answers, 8*10^18 J and 0J.
Someone please help me out here!
Thanks a lot :D
Homework Statement
Question : Calculate the change in gravitational potential energy of the moon, when the radius of it's orbit increases by 4cm.
Radius : 3.85*10^8 m
Mass of the Earth : 6*10^24 kg
Mass of the moon : 7.36*10^22kg
We were first told calculate the force between the moon and the Earth using
F = Gmm/r^2. Comes to around 2*10^20 N
We were then told to find the change in G.P.E when the radius increases using the force which we calculated.
Homework Equations
F = GMm/r^2
GPE = GMm/r
The Attempt at a Solution
Method I : Work done = Force * Distance. 2*10^20 * 0.04 = 8*10^18J
Now this is what my friend did, and why I think this is incorrect? Because he assumes that the force is constant as the radius changes, which clearly isn't. Why do I think he is correct? Because he does what was asked, he used the force to find the change in gpe.
Method II (This is what I did) : Potential energy of a mass m at a distance r is = -GMm/r
(Asked to calculate the change, hence i'll use the modulus of that and ignore the minus)
GMm(1/r2 - 1/r1) [Where r2 is 3.85*10^8 + 0.04 and r1 is 3.85*10^8)
When you go ahead and solve this using your calculator, you realize that the change in the radius is soooo less, even the calculator won't show up the change. Hence the value you get is 0J.
Why I think I'm correct? Because the change is the GPE shouldn't be much because the radius didn't change a lot. And because I used a perfect formula. (?)
Why I think I'm wrong? Because I didn't use the force to calculate.
My dilemma is clear, these are 2 extreme answers, 8*10^18 J and 0J.
Someone please help me out here!
Thanks a lot :D