Elastic collision between two billiard balls

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Homework Help Overview

The discussion revolves around an elastic collision between two billiard balls on a frictionless surface, involving mass and velocity parameters. The original poster seeks to determine the final velocity and angles of the two balls after the collision, given initial conditions and constraints.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using conservation of kinetic energy and momentum to find the unknowns. There is a focus on deriving the angles from the momentum equations, with some expressing difficulty in managing the trigonometric relationships involved.

Discussion Status

Some participants have provided guidance on using conservation laws to approach the problem, while others are exploring the relationships between sine and cosine in the context of the equations derived. There is an acknowledgment of challenges faced in solving for the angles, indicating a productive exploration of the problem.

Contextual Notes

The original poster has indicated a specific difficulty with the angles, suggesting that the equations derived from conservation of momentum lead to a complex relationship between the trigonometric functions involved.

phyme814
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Homework Statement


Two balls collide on a frictionless surface. Mass m1 = .4 kg and Mass m2 = .3 kg . The initial velocity of m1 is 3 m/s. While m2 is at rest. After the collision the velocity of m1 is 1.5 m/s, θ1 above the horizontal. While m2 gains an unknown velocity of v2f, θ2 below the horizontal.
Find v2f, θ1, and θ2


Homework Equations



Conservation of kinetic energy
Conservation of momentum

The Attempt at a Solution


I can find v2f, but I am having trouble with finding the angles.
 
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phyme814 said:
I can find v2f, but I am having trouble with finding the angles.
Show what you did.
 
I presume you used conservation of energy to solve for v2f. Now use conservation of momentum to solve for the angles. (You'll get two equations and two unknowns.)
 
Yepp I used conservation of kinetic energy.
I was using the conservation of momentum equation for the unknowns of the angles but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
 
phyme814 said:
but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
Sine and cosine can be related by a trig identity.
 

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