How to Solve an Elastic Collision of 3 Balls with Frictionless Motion?

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Homework Help Overview

The problem involves an elastic collision of three balls, where one ball with an initial speed collides with two identical stationary balls. The scenario is set in a frictionless environment, and the balls are arranged such that the centers of the two stationary balls are in contact and aligned perpendicular to the direction of the incoming ball's motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply conservation of momentum and kinetic energy equations to analyze the collision, considering both x and y components of velocity. They express confusion over the angles involved and the resulting velocities after the collision.
  • Participants question the assumed directions of motion for the balls post-collision and discuss the implications of the elastic nature of the collision.
  • One participant seeks clarification on the problem and expresses a desire for a solution, indicating they are facing similar challenges.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem setup and the resulting motion of the balls. Some guidance has been offered regarding the components of momentum and energy, but no consensus or resolution has been reached.

Contextual Notes

Participants are navigating the complexities of the collision dynamics, including the angles involved and the assumptions about the direction of motion after the collision. The original poster has expressed difficulty in managing the variables and equations related to the problem.

baubletop
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Homework Statement


A ball with an initial speed of v1 = 21.5 m/s collides elastically with two identical balls whose centers are on a line perpendicular to the initial velocity and that are initially in contact with each other. The first ball is aimed directly at the contact point and all motion is frictionless.
>What is the speed of ball 1 after the collision?
>What is the speed of ball 2 after the collision?

Homework Equations


m1v1i + m2v2i = m1v1fcos(θ) + m2v2fcos(θ)
KE = 1/2 mv12 + 1/2 mv22

The Attempt at a Solution


So I know that the velocities have two components, x and y. I also know that at the collision point, the angle of the centers of mass are 30° (since the balls form an equilateral triangle).
For the x-component, I tried using the conservation of momentum equation above with cos(30°) and using the KE equation to substitute for unknown values of v1 and v2.
For the y-component I tried doing the same, but since the original velocity in the y-component is 0, I used
0 = m1v1sin(θ) + m2v2sin(30). For θ I tried 30, 60, and 180, but none of them worked.
Now I'm a bit stuck and I'm getting confused from all the variables I'm trying here. Any direction is appreciated!
 
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hi baubletop! :smile:

what directions are you assuming for the three balls after the collision? :wink:
 
Should the first one go backwards since it's an elastic collision?
 
i'm not worried about backwards or forwards, just the line :wink:

(and now I'm off to bed :zzz:)
 
This is the diagram that came with the problem:
prob04a.gif


So the first ball would go forward, and the other two would move outwards 30° from that straight line, right?
 
(just got up :zzz:)
baubletop said:
So the first ball would go forward, and the other two would move outwards 30° from that straight line, right?

(forwards or backwards)

yup! :smile:

ok, now do components of momentum in the forwards direction, and energy :wink:​
 
I have exactly the same problem.
Can someone please explain and solve this? Please?

(baubletop have you ever solve this?)

Many thanks.
 

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