Using Effective Potential to Describe motion of an object

In summary, the conversation discusses a question about an effective potential graph and its relationship to displacement and gravitational potential energy. The terms omega, g, and L are defined as angular velocity, acceleration due to gravity, and length of a rod respectively. The conversation also mentions two light rods and a point mass attached to one end. The terms E and Veff are defined as energy and effective potential respectively, with E missing the variables of mass and length. The definition of effective potential is not explicitly stated in the conversation.
  • #1
Junkwisch
31
0
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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  • #2
Can you define all the terms you are using?
 
  • #3
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
 
  • #4
What is E and Veff?
 
  • #5
E is the energy while Veff is effective potential
 
  • #6
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?
 

What is effective potential?

Effective potential is a mathematical tool used to describe the motion of an object in a conservative force field. It takes into account both the kinetic and potential energy of the object to determine its overall energy at any given point.

How is effective potential calculated?

The effective potential is calculated by taking the sum of the potential energy and the kinetic energy of an object. This can be represented by the equation V_eff = V(x) + 1/2mv^2, where V(x) is the potential energy function and m is the mass of the object.

What is the significance of effective potential?

The effective potential allows us to visualize and analyze the behavior of an object in a conservative force field. It helps us understand how the object will move and whether it will reach a stable equilibrium or continue to oscillate.

How does effective potential change with distance?

The shape of the effective potential function depends on the distance from the center of the force field. As the distance increases, the potential energy also increases, causing the effective potential to become more positive. This can affect the motion of the object and determine whether it will move towards or away from the center.

Can effective potential be used for non-conservative force fields?

No, effective potential can only be used for conservative force fields where the total mechanical energy of the system is conserved. For non-conservative force fields, the energy of the system is not conserved and other methods must be used to describe the motion of an object.

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