Effective Potential Energy from Central Force Motion

In summary, the conversation discussed the concept of potential energy in the context of central force motion, specifically in Marion's book. The concept of "Effective Potential Energy" was introduced, although there was disagreement about using the term "potential" due to its dimensions. However, it was explained that this term is commonly used and plays a similar role as potential energy. An alternative way to approach it was also suggested by considering the work needed to assemble the system.
  • #1
KT KIM
24
0
Hi, I'm studying undergrad mechanics, Central force motion, Marion's book in specific,
Here, the Potential Energy is defined weird way (in my opinion though)

(μ is reduced mass)
Mechanics1.png


So potential Energy becomes
Mechanics2.png

Called "Effective Potential Energy"

But, I can't agree with calling it potential just because it has dimensions of energy.
Mathematically it is right. But intuitively, I have no idea where it came from. little help please.
 
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  • #2
But, I can't agree with calling it potential just because it has dimensions of energy.
... well you don;'t have to agree, just make sure you understand that this is the term commonly used so that you will understand it in future.

It's called an effective potential energy (as opposed to a potential energy) because it plays the same role as potential energy so it is potential energy like in it's effect. Can you think of a better term for it?

You can also tackle it this way - keeping the central coordinate system - how much work would you need to do to assemble the system described by the model?
 

Related to Effective Potential Energy from Central Force Motion

1. What is effective potential energy in central force motion?

Effective potential energy is a concept used in physics to describe the energy of a particle moving under the influence of a central force, such as gravity. It takes into account both the kinetic energy and the potential energy of the particle, and is useful in analyzing the motion of objects in a central force field.

2. How is effective potential energy related to central force motion?

The effective potential energy is directly related to the central force acting on a particle. It is a mathematical representation of the force, and can be used to determine the trajectory and stability of the particle's motion.

3. What factors affect the effective potential energy in central force motion?

The effective potential energy is affected by the magnitude and direction of the central force, as well as the mass and position of the particle. Other factors such as external forces and the shape of the central force field can also impact the effective potential energy.

4. How is effective potential energy calculated in central force motion?

The effective potential energy is calculated using the formula E = ½mv² + V(r), where E is the total energy of the particle, m is its mass, v is its velocity, and V(r) is the potential energy function. This formula takes into account both the kinetic and potential energy of the particle.

5. What is the significance of effective potential energy in central force motion?

The effective potential energy is a useful tool in understanding and predicting the motion of objects in a central force field. It can help determine the stability and shape of orbits, as well as provide insights into the behavior of celestial bodies and other systems governed by central forces.

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