Potential barrier problem in mechanics

Click For Summary
SUMMARY

The discussion centers on the application of energy conservation principles in mechanics, specifically regarding the minimum velocity required for a ball to traverse points E, D, and B. It is established that while mechanical energy must be conserved at every point along the path, the minimum velocity at point E is critical for successfully reaching points A, B, and C. The concept of unstable equilibrium at point D is highlighted, indicating that just enough velocity to surpass D is sufficient for the ball's motion. Quantum mechanics is briefly mentioned as providing a more nuanced perspective on the problem.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly energy conservation
  • Familiarity with concepts of equilibrium, especially unstable equilibrium
  • Basic knowledge of velocity and its implications in motion
  • Introduction to quantum mechanics and its differences from classical mechanics
NEXT STEPS
  • Study the principles of energy conservation in classical mechanics
  • Explore the concept of unstable equilibrium and its implications in physics
  • Learn about the calculations involved in determining minimum velocity in mechanical systems
  • Investigate the differences between classical and quantum mechanics regarding motion and energy
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the nuances of energy conservation and equilibrium in mechanical systems.

Rhdjfgjgj
Messages
31
Reaction score
3
Homework Statement
Question:find minimum velocity so that the ball reaches A,B, and C .in the given figure
Relevant Equations
Energy conversion equation
IMG_20231012_194839.jpg

Here our sir said if I would apply energy conservation b/w initial point and B , we would get it wrong. But If I apply between initial point and D , we would get it right. He didn't tell why. Could anyone just explain why. One reason I thought was that since the question asked for minimum velocity and since D is a point of unstable equilibrium just giving enough velocity to get it past D is sufficient
 
Physics news on Phys.org
According to the diagram the initial point is at E. To get to B the ball must traverse D. The fact that B is lower than D does not matter according to classical mechanics. Mechanical energy must be conserved at every point along the path.
Quantum mechanics gives a slightly more nuanced answer.
 
Rhdjfgjgj said:
... One reason I thought was that since the question asked for minimum velocity and since D is a point of unstable equilibrium just giving enough velocity to get it past D is sufficient
I believe that your reasoning is correct.
Initial velocity at E should be the maximum minimum value that the ball will need to have to hit points A, B and C.

Edit: See post 4.
 
Last edited:
Lnewqban said:
Initial velocity at E should be the maximum value that the ball will need to have to hit point A
I do not undertstand what this means. Why is there a maximum limit??
 
@Lnewqban and @Rhdjfgjgj I think the problem seeks a calculated value for ##v_0## not the ensuing values at various points on the course. Am I misreading it?
 
hutchphd said:
I do not undertstand what this means. Why is there a maximum limit??
Correction appreciated.
Post 3 edited.
 
  • Like
Likes   Reactions: hutchphd

Similar threads

Replies
15
Views
2K
  • · Replies 14 ·
Replies
14
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
10
Views
2K
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
2
Views
1K
  • · Replies 7 ·
Replies
7
Views
1K