Solving a Central Force Motion Problem: Find E & L

AI Thread Summary
The discussion revolves around solving a central force motion problem involving a body of mass 1 kg moving in a circular orbit with a specified potential energy function. Participants emphasize the importance of calculating the force from the potential energy and balancing it with centripetal force to find velocity. The angular momentum and total energy can then be derived using the relationships between mass, velocity, and radius. While one user expresses concern about the tedious nature of the calculations, others suggest that the problem is manageable and can be solved efficiently with or without software tools. Overall, the consensus is that the approach outlined is correct and feasible for manual calculation.
anirudh dutta
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Homework Statement


a body of mass 1kg moves under the influence of a central force with potential energy question V(r)= -exp(-3r/2)/5r2
.it is found to move under a circular orbit of radius 2 m

Homework Equations


find the total energy and the angular momentum


The Attempt at a Solution

 
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You need to at least attempt to solve the problem if you expect help.
 
see, since i have the potential energy fn, i can calculate the force by calculating the negative of grad of V.
This force will be balanced by the centripital corce i.e mv^2 /r. from here i can cal the velocity, v.
thus the angular mom is simply mvr and total energy is P.E+K.E
 
Sounds good. So what is your question?
 
firstly the mathematical calculation is very tedious. So is there sm another meathod
 
I don't know of a better way. It doesn't look that bad. If you have access to software like Mathematica, it will be a snap, but even without that it should be less than one page.
 
Your method seems correct and it's not tedious at all. You should be able to do it with pencil and paper just fine.
 
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