Perturbed circular orbit under central force motion?

AI Thread Summary
The discussion revolves around a confusion regarding the derivation of an equation in Kleppner and Kolenkow's "Introduction to Mechanics," specifically in the context of central force motion. The user initially struggles with understanding how to apply the second derivative of the effective potential energy, U_{eff}, and the substitution of a previously derived value for angular momentum, l. After some reflection and clarification, the user realizes the mistake of not substituting the value of l earlier in the process. The conversation highlights the common learning experience of grappling with complex mechanics concepts and ultimately finding clarity. The exchange emphasizes the importance of careful calculation and the learning process in physics.
physicsxlove
Messages
3
Reaction score
0
I am self studying Kleppner and Kolenkow's an Introduction to mechanics. But i have one doubt about how they got into the equation no 3 of the example problem 9.3 in Central Force Motion.
Please clarify my doubt.
 
Physics news on Phys.org
I suggest you quote it or give a link.
 
Here i have attached the photo graph of that page.
mathman said:
I suggest you quote it or give a link.
 

Attachments

  • IMG_0043.JPG
    IMG_0043.JPG
    58.5 KB · Views: 785
Seems pretty straight forward. Differentiate U_{eff} twice, evaluate it at r=r_0 and replace l by the one we obtained earlier. This should equal k, which is related to beta.
 
diegzumillo said:
Seems pretty straight forward. Differentiate U_{eff} twice, evaluate it at r=r_0 and replace l by the one we obtained earlier. This should equal k, which is related to beta.
Omg. I am so dumb. I just calculated the second derivative and then used to sit brooding over what to do next without plugging the value of l from equation 1. I am feeling embarrassed.

Anyway,,, thank you. I got it. Better late than never.
 
No problem :) This is just the peeking-over-the-shoulder effect.
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
View full post »

Similar threads

A Regular vs stable orbits in spherically symmetric potentials
Replies
4
Views
1K
B Confusion while trying to build intuition of centripetal force
Replies
15
Views
3K
Uniform Circular Motion vs Circular Orbit due to Gravity
Replies
9
Views
4K
Why is a negative sign included in Equation (6) for central-force motion?
Replies
2
Views
3K
Effective Potential Energy from Central Force Motion
Replies
1
Views
3K
A Puzzle Involving the Moon's Orbital Motion
Replies
19
Views
2K
Confused about Newton's 3rd law of motion
Replies
17
Views
2K
Confused in diffferent forces involved in circular motion
Replies
7
Views
7K
I Circular orbits aren't minimas of lagrangian for Kepler problem?
Replies
3
Views
1K
Motion under a force perpendicular to the velocity
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top