Elastic collision with 3 pool balls

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Homework Help Overview

The problem involves an elastic collision scenario with three pool balls, where one ball collides with two stationary balls. The objective is to determine the final velocities of all three balls after the collision, given specific initial conditions and assumptions about the angles and speeds of the balls post-collision.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish whether the two right balls should be assumed to leave the collision at angles of 45 degrees and -45 degrees. Some participants suggest that the balls should leave at the same angle and speed instead. The poster then presents equations derived from conservation of momentum and energy but expresses uncertainty about how to manipulate these equations to find the final velocities.

Discussion Status

The discussion is ongoing, with participants exploring different assumptions regarding the angles and speeds of the balls after the collision. Guidance has been offered regarding the assumptions to make, but there is no explicit consensus on the approach to derive the final velocities from the equations presented.

Contextual Notes

The original poster's equations rely on the assumption of equal speeds and angles for the two right balls, which is being debated. There may be constraints related to the specific setup of the problem that have not been fully articulated.

KaiserBrandon
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Homework Statement


A pool ball with initial speed v is aimed right between two other pool balls (looks like:

0 -> :


if the semicolon were two balls and were touching each other).

If the two right balls leave the elastic collision with equal speeds, find the final velocities of all three balls.

Homework Equations


k=1/2m(v^2)
p=mv

The Attempt at a Solution


All I need to know is if I should assume that the right balls have a final velocity at an angle 45 and -45 degrees to the horizontal.
 
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No, don't assume that. Just assume that the two balls leave at the same angle to the horizontal and at the same speed.
 
ok, so then with momentum and energy conservation, I get the equations:
v1=(2V)cos(theta) + v1f
and
v1^2=2V^2 + (v1f)^2

where v1 is the initial velocity of the incoming ball, V is the final speed of the two right balls, and v1f is the final speed of the first ball. I don't know how what I can do to get an expression for the velocities.
 
What do you mean you don't know how to get an expression for the velocities?
 

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