A question about central-force movement

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In summary, the conversation is about a particle moving under a force of the form F(r) = -Ar^3 (r-hat). The questions asked are to find and draw the effective potential and determine if the particle can reach r=0, find the velocity v0 for the particle to move in a circle, and calculate the frequency of small movements around a certain radius. The attempt provided includes a sketch of the graph and equations for the different scenarios, but there are some errors that need to be corrected.
  • #1
sapz
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Homework Statement



Hi there! Could you please help me with this question? Am I doing it right?

A particle is moving under a force of the form F(r) = -Ar^3 (r-hat). The particle begins its movement at a distance r0 and velocity v0.

A. Find and draw the effective potential. Can the particle arrive at r=0?
B. Find the velocity v0 so that the particle will move in a circle.
C. What is the frequency of the small movements (w0) around that radius?

Homework Equations





The Attempt at a Solution


The attempt is attached as an image.
 

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  • #2
To sketch the graph, determine the asymptotic behaviours as r tends to 0, infinity, and find any local maxima and minima. Can it reach r = 0?
In B, you made an algebraic error going from the first line to the second. This propagated into your work in C.
In C, you left out centripetal acceleration in the second equation.
 
  • #3
Thanks!
 

FAQ: A question about central-force movement

1. What is central-force movement?

Central-force movement is a type of motion that occurs when an object is acted upon by a force that always points towards a fixed point, known as the center of force. This type of movement is commonly seen in systems with gravitational or electromagnetic forces.

2. What are some examples of central-force movement?

Some examples of central-force movement include the motion of planets around the sun, the orbit of satellites around the Earth, and the motion of electrons around an atomic nucleus.

3. How is central-force movement different from other types of motion?

Central-force movement is different from other types of motion because the direction of the force acting on the object always points towards a fixed point, causing the object to move in a curved path. This is in contrast to other types of motion where the force may be applied in different directions, resulting in straight or more complex paths.

4. What is the role of centripetal force in central-force movement?

Centripetal force is the force that causes an object to move in a circular path in central-force movement. It is always directed towards the center of the circle and is necessary to keep the object from moving away from the center due to its inertia.

5. How is central-force movement related to Newton's laws of motion?

Central-force movement is a direct consequence of Newton's laws of motion, specifically the law of gravitation and the second law of motion (F=ma). These laws explain how objects move under the influence of a central force and how this force affects the object's acceleration and velocity.

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