Particle bouncing between walls

Josh0768

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?
Homework 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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Orodruin

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Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?

Josh0768

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?

Orodruin

Staff Emeritus
Homework Helper
Gold Member
2018 Award
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?

"Particle bouncing between walls"

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