Particle bouncing between walls

In summary, the conversation discusses the formula for calculating the velocity of a particle after colliding with two stationary walls and the question of what happens to the velocity when colliding with a moving wall. There is also a question about the behavior of the velocity in the rest frame of the wall and its implications in a different frame.
  • #1
Josh0768
53
6
Homework Statement
A particle is situated between two walls that are closing in on each other. The particle is moving at 1.61 km/s in the -x direction, the left wall is moving at 1.01 km/s in the +x direction, and the right wall is moving at 2.51 km/s in the -x direction. What is the velocity of the particle after bouncing off of the left wall 10 times and the right wall 9 times?
Relevant Equations
Delta v = v final - v initial

Conservation of momentum

???
I thought it would be a good idea to pretend that the walls are stationary and that each time the particle hits a wall, it gets a velocity addition of the velocity of the wall it’s hitting. Using this I ended up at the formula

V = initial velocity of particle + n(velocity of left wall) + m(velocity of right wall)

where n and m are the number of collisions with the left and right walls, respectively.

Needless to say, this does not give me the right answer. Thoughts?
 
Last edited:
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  • #2
Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?
 
  • #3
Orodruin said:
Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?
Would you add twice the magnitude of the initial velocity to the initial velocity?
 
  • #4
Josh0768 said:
Would you add twice the magnitude of the initial velocity to the initial velocity?
What happens in the rest frame of the wall? What does that mean for a different frame?
 

1. What is particle bouncing between walls?

Particle bouncing between walls is a physical phenomenon where a small object, such as an atom or molecule, moves back and forth between two parallel walls due to collisions with the walls.

2. What causes a particle to bounce between walls?

A particle bounces between walls due to its own kinetic energy and the collisions it experiences with the walls. When the particle collides with one wall, it transfers some of its energy to the wall and changes direction, causing it to move towards the other wall. This process repeats, resulting in a back-and-forth motion.

3. How does the speed of the particle affect its bouncing between walls?

The speed of the particle has a direct effect on its bouncing between walls. A faster-moving particle will collide with the walls more frequently and with more force, resulting in a higher number of bounces and a shorter distance between walls. On the other hand, a slower-moving particle will have fewer collisions and will travel a longer distance between walls.

4. Can the distance between walls affect the bouncing of the particle?

Yes, the distance between walls can significantly affect the bouncing of the particle. A larger distance between walls will result in a longer travel time for the particle and fewer collisions, leading to a slower bouncing motion. Conversely, a shorter distance between walls will result in a faster bouncing motion due to more frequent collisions.

5. What are the real-life applications of particle bouncing between walls?

Particle bouncing between walls has various real-life applications, including in the field of nanotechnology where it can be used to control the motion and behavior of microscopic particles. It is also used in particle accelerators to study the behavior of subatomic particles. In addition, this phenomenon has applications in materials science, such as in the development of new coatings and adhesives.

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