Orbiting particle with given potential. Find the total energy. Need help

AI Thread Summary
A light particle with mass m orbits a massive center under a potential V(r) = Cr^2. To find the total energy, it is shown that E = 2Cr^2 using circular motion equations. The discussion emphasizes applying the Bohr postulate, L = mvr = nh(bar), to derive an expression for the energy of allowed orbits. Participants suggest starting by calculating the force derived from the potential. The thread highlights the importance of understanding circular motion and potential energy relationships in this context.
PanosP
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Homework Statement



(a) A light particle of mass m orbits in a circular orbit around a massive attractive centre with a potential that is given by

V(r) = Cr^2

(b) Using the equations for circular motion show that the total energy of such a particle must be given by

E = 2Cr^2

Use the Bohr postulate for the quantization L = mvr = nh(bar) in combination with the answer to part (a) to arrive at an expression for the energy associated with the allowed orbits in terms of the mass of the particle n and other constants.


I have no idea how to even begin this!

ANY help would be deeply appreciated!

thanks!
 
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Welcome to PF!

Hi PanosP ! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)
PanosP said:
(a) A light particle of mass m orbits in a circular orbit around a massive attractive centre with a potential that is given by

V(r) = Cr^2

(b) Using the equations for circular motion show that the total energy of such a particle must be given by

E = 2Cr^2

I have no idea how to even begin this!

Find the force from V(r), then use good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" :smile:
 
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