Classical Mechanics Problem: Particle in a Square Potential Well

  • #1
Jozefina Gramatikova
64
9

Homework Statement


CLASSICAL MECHANICS
upload_2019-1-20_12-29-4-png.png
[/B]


Homework Equations


E=U+K[/B]


The Attempt at a Solution


50288802_758179237899437_8167705243417575424_n-jpg-_nc_cat-106-_nc_ht-scontent-flhr4-1-jpg.jpg

Guys, can you please help me with part b) ? I am not sure how to find the velocity. Thanks
 

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Answers and Replies

  • #2
kuruman
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First off, find the range of mechanical energies. What could it possibly be if the motion is bounded? What does "bounded" mean classically?
 
  • #3
Jozefina Gramatikova
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Is it -u<E<0 ? The motion of the system is bounded if it begins at a point situated between two forbidden regions, the system’s trajectory will never leave the allowed region where it started (otherwise it would have to cross one of the forbidden regions).
 
  • #4
BvU
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Any relevant equations linking kinetic energy to velocity ?
 
  • #5
Jozefina Gramatikova
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upload_2019-1-20_22-42-39.png
 

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  • #6
Jozefina Gramatikova
64
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Could you tell me if this is true?

If U=-u , then E ≈ 0

if U=0, then E ≈ -u
 
  • #7
BvU
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No, I can tell you it is not true.
U is the potential energy
E is the total energy of the particle, an independent variable in this exercise.
As you almost say (well, guess) in #3, the given information tthat the particle is bounded leads to ##-u \le E < 0##.

With K the kinetic energy and, as you say, E = K + U you can write down the bounds of K and thereby the bounds of v. And derive the period of the motion.
 
  • #8
Jozefina Gramatikova
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9
7594_2276574659287142_7618848920235409408_n.jpg?_nc_cat=100&_nc_ad=z-m&_nc_cid=0&_nc_ht=scontent.jpg
 

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  • #9
Jozefina Gramatikova
64
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Is it -u<=K<0 ? and then v<0 ?
 
  • #10
Jozefina Gramatikova
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PLS help
 
  • #11
Gordianus
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Ah...the curse of negative numbers...
Please, remember K is always a positive number.
 
  • #12
kuruman
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Perhaps it might help if you considered a concrete example. Suppose ##K= \frac{2}{3}u## where ##u>0##. What is ##E##?
 

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