Collision between snooker balls

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Homework Help Overview

The discussion revolves around a problem involving the collision of three identical snooker balls, where two balls are initially at rest and a third ball collides with them. The collision is specified to be elastic, and the participants are interested in determining the resulting velocities of all balls post-collision.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of momentum and energy in the context of the collision. There are attempts to clarify the distinction between scalar and vector quantities in the equations governing the collision. Questions are raised about the representation of velocities in terms of their components.

Discussion Status

Some participants have provided guidance on visualizing the problem through diagrams and simulations. There is an acknowledgment of the complexities involved in breaking down the momentum into components, and a suggestion to use a simulation tool to explore the collision further. The discussion appears to be productive, with participants engaging in clarifying concepts and exploring different aspects of the problem.

Contextual Notes

Participants note the absence of friction and the symmetry of the collision, which may influence the resulting velocities. The original poster expresses a desire to understand the resulting velocities, indicating a focus on the outcomes of the collision without providing a complete solution.

hmparticle9
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Homework Statement
Two identical frictionless balls are symmetrically hit by a third identical ball with velocity v_0i. Find all subsequent velocities.
Relevant Equations
Conservation of mass and conservation of momentum.
Two snooker balls are at rest and a third collides with the two of them. There is no friction and all balls are identical. The initial velocity of the ball (1) is ##v = v_0 i##. I can understand the direction that the balls go in after the collision. But I want to know the resulting velocities of all the balls in play. The collision is elastic.

Here is my attempt
Math - page 1.webp
 
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hmparticle9 said:
Homework Statement: Two identical frictionless balls are symmetrically hit by a third identical ball with velocity v_0i. Find all subsequent velocities.
Relevant Equations: Conservation of mass and conservation of momentum.

Two snooker balls are at rest and a third collides with the two of them. There is no friction and all balls are identical. The initial velocity of the ball (1) is ##v = v_0 i##. I can understand the direction that the balls go in after the collision. But I want to know the resulting velocities of all the balls in play. The collision is elastic.

Here is my attempt
View attachment 361361
Energy is not a vector. It only can be taken to be conserved overall, not separately per direction.
 
Last edited:
A fun simulation to try out is the PHET collision lab - you can define coefficient of restitution, give initial velocities, and set up collisions - choose the 2D model:

https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab_all.html

Screenshot 2025-05-22 195844.webp


For your equations, energy is a scalar quantity, but momentum is a vector. Can you draw a picture of the x and y components for your mv's?

You should have
Σmvx = ...
Σmvy = ... (no initial vy, after collision one flies up and the other down)

Draw picture of velocities after the collision, break everything into Vx and Vy
 

Attachments

  • Screenshot 2025-05-22 195358.webp
    Screenshot 2025-05-22 195358.webp
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Last edited:
Got it! Thanks :D

Quick sheets - page 1.webp
 

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