What Is the Variation of Force With Respect to Radius in Circular Orbit?

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SUMMARY

The discussion centers on determining the variation of force (F) with respect to radius (r) in a circular orbit, specifically finding the exponent n in the equation F=kr^n. The correct answer is established as -5, while one participant initially calculated -3. Clarifications regarding the variables and the diagram used in the problem were requested, as confusion arose from the interpretation of the force's behavior as the particle approaches point p on the circumference. The conversation highlights the importance of clear variable definitions and accurate diagram representation in solving physics problems.

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  • Understanding of circular motion dynamics
  • Familiarity with force equations, specifically F=kr^n
  • Knowledge of angular motion and its relation to radius
  • Ability to interpret and create diagrams for physics problems
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Samsmith47
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Homework Statement
The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Relevant Equations
F=kr^n
Da/dt= l/2m
Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Answer is -5
But I am getting -3
 

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Samsmith47 said:
Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n
Da/dt= l/2m

Answer is -5
But I am getting -3
Your diagram is too messy to decipher, so I do not know what your variables represent.
Please post a clearer diagram and (as text, not an image) definitions of your variables and consequent working.
 
Is it possible that your sketch is a misinterpretation of the problem description? If p is on the orbit, when the particle comes around to the location of p, the force would become infinite (with n being a negative exponent). I am assuming that r is the distance to p. And in that case, I can not see why the particle has a circular orbit. Could it be that p is on the circumference of some other circle? Clarify.
 
sojsail said:
when the particle comes around to the location of p, the force would become infinite
Not sure that that is a problem in this artificial scenario.
 
Samsmith47 said:
But I am getting -3
I can see how you would get that if you were to confuse the angular rate of orbit about the centre of the circle with that about P.
 
Thanks for seeing my response I will draw the dia neatly and send again
Sorry for the late reply
And also I got the answer thanks for trying I am really greatfull
 

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