Classical Mechanics Problem: Particle in a Square Potential Well

[Jozefina Gramatikova]

Homework Statement

CLASSICAL MECHANICS

[/B]

Homework Equations

E=U+K[/B]

The Attempt at a Solution

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

 

[kuruman]

First off, find the range of mechanical energies. What could it possibly be if the motion is bounded? What does "bounded" mean classically?

 

[Jozefina Gramatikova]

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).

 

[BvU]

Any relevant equations linking kinetic energy to velocity ?

 

[Jozefina Gramatikova]

 

[Jozefina Gramatikova]

Could you tell me if this is true?

If U=-u , then E ≈ 0

if U=0, then E ≈ -u

 

[BvU]

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.

 

[Jozefina Gramatikova]

 

[Jozefina Gramatikova]

Is it -u<=K<0 ? and then v<0 ?

 

[Jozefina Gramatikova]

PLS help

 

[Gordianus]

Ah...the curse of negative numbers...
Please, remember K is always a positive number.

 

[kuruman]

Perhaps it might help if you considered a concrete example. Suppose $K= \frac{2}{3}u$ where $u>0$. What is $E$?