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Mechanics Problem Rate Topic: -----

#1 3 February 2012 - 03:42 AM User is online  A Tripolation 


Atom
So, I had my first Mechanics II exam. There was one particular problem that drove me absolutely insane. I had no idea how to tackle it. Since I won't get the test back for another week or two, I decided someone here might be able to help me.

The question is (roughly): A particle is moving in an elliptical orbit. The ratio of the maximum angular momentum to the minimum angular momentum of the particle is 'n'. Prove that the eccentricity of the orbit is \epsilon = \frac{\sqrt{n}+1}{\sqrt{n}-1}.

So, what should I have done to start this problem? I'm thinking it has something to do with the relationship between the r0 or r1, but I'm not sure.
Why, Mr. Anderson, why? Why? Why do you do it? Why? Why get up? Why keep fighting? Do you believe you’re fighting for something? For more than your survival? Can you tell me what it is? Do you even know?
Is it freedom or truth? Perhaps peace? Could it be for love? Illusions Mr. Anderson, vagaries of perception. Temporary constructs of a feeble human intellect trying desperately to justify an existence that is without meaning or purpose.
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#2 3 February 2012 - 12:23 PM imatfaal 


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Primate
Firstly - hope you did well on the exam! Secondly - as a wild stab in the dark guess; could you use total energy conservation, the KE includes \omega^2 and the PE the two diffferent radii and you know that KE+PE at perihelion equals KE+PE at aphelio. It just seems that all the ingredients might be there - damned if I can see how to get to such a nice ratio though.

This post has been edited by imatfaal: 3 February 2012 - 12:24 PM

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#3 3 February 2012 - 01:01 PM doG 


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Kepler's laws come to mind...
doG


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#4 3 February 2012 - 02:44 PM User is online  swansont 


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Shaken, not Stirred
Angular momentum is mvr (or rp) and KE = p^2/2m, so it looks like you can cast work through and be able to put the radii in terms of n, and then put that into the eccentricity calculation
http://en.wikipedia....ity#Calculation
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#5 5 February 2012 - 08:04 AM User is online  A Tripolation 


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View Postswansont, on 3 February 2012 - 02:44 PM, said:

Angular momentum is mvr (or rp) and KE = p^2/2m, so it looks like you can cast work through and be able to put the radii in terms of n, and then put that into the eccentricity calculation
http://en.wikipedia....ity#Calculation


...that's it? That's all there was to it?

Sigh.
Why, Mr. Anderson, why? Why? Why do you do it? Why? Why get up? Why keep fighting? Do you believe you’re fighting for something? For more than your survival? Can you tell me what it is? Do you even know?
Is it freedom or truth? Perhaps peace? Could it be for love? Illusions Mr. Anderson, vagaries of perception. Temporary constructs of a feeble human intellect trying desperately to justify an existence that is without meaning or purpose.
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#6 5 February 2012 - 10:51 AM User is online  swansont 


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View PostA Tripolation, on 5 February 2012 - 08:04 AM, said:

...that's it? That's all there was to it?


I didn't work through the details, but that seems a logical way to do it. There may be a trick or two to getting it in the form that they asked for.
Minutus cantorum, minutus balorum, minutus carborata descendum pantorum

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