Using Effective Potential to Describe motion of an object

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Discussion Overview

The discussion revolves around the use of effective potential to describe the motion of an object, specifically in the context of a system involving rods and a point mass on a rotating turntable. Participants explore definitions, equations, and the graphical representation of effective potential in relation to gravitational forces.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant describes the motion of an object using effective potential, detailing a cyclical process of movement influenced by gravitational potential.
  • Another participant requests definitions for the terms used in the discussion, indicating a need for clarity on the concepts involved.
  • A participant outlines the physical setup involving two rods and a point mass, specifying the parameters such as angular velocity and gravitational acceleration.
  • Questions arise regarding the definitions of energy (E) and effective potential (Veff), with one participant providing a basic definition of these terms.
  • Concerns are raised about the absence of mass (m) and length (L) in the equation for energy, prompting further inquiry into the definition of effective potential.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants seeking clarification on definitions and equations without reaching a consensus on the effective potential's application or the completeness of the equations presented.

Contextual Notes

Participants express uncertainty regarding the definitions and relationships between variables in the context of effective potential, indicating potential limitations in the provided equations and assumptions.

Junkwisch
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Hey guy, this is one of the question in my uni work (I'm not sure whether my answer is correct or not, please have a check). The attachment consists of what the effective potential graph look like.





"It starts from a low point where it move downward to the lowest point. It then move upward to the highest point then to the lowest point parabolically. It then move upward to the low point (where the motion start) and restart the entire process again."



I treat the effective potential as the displacement of the object in Y, since the only potential energy acting in here is gravitational. Omega represent angular velocity, g= acceleration due to gravity and L represents the length if the arm.


Best Regards
Naphat Veraphong
 

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Can you define all the terms you are using?
 
Two light, inextensible rods OP and PQ are joined at P by means of a frictionless hinge. The
rod OP stands vertically. Its base O is glued to the centre of a rotating turntable. The rod PQ
makes an angle θ(t) with respect to the vertical, which changes as a function of time t, with
0 ≤θ(t) ≤ pi . Both rods rotate around the axis OP with constant angular velocity Ω. A point
mass m is attached to the free end Q of the rod PQ.

L is the length of rod PQ, g is uniform acceleration due to gravity
 
What is E and Veff?
 
E is the energy while Veff is effective potential
 
Not sure why the mass m and length L terms are missing from the equation for E.

What is the definition of the effective potential?
 

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