Help with conservation of energy

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Homework Help Overview

The problem involves two billiard balls of equal mass colliding elastically at right angles in an xy coordinate system. Ball A moves upward along the y-axis, while Ball B moves to the right along the x-axis. The discussion centers on determining the final direction and speeds of both balls after the collision.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of momentum and energy in elastic collisions, questioning how to handle the two unknowns in the momentum equations. There are inquiries about the necessity of using trigonometric functions to find velocities and the method for determining the direction of Ball A.

Discussion Status

Some participants have provided guidance on using independent momentum equations for both the x and y directions, suggesting that finding the velocities of the balls in each direction could lead to determining the direction of Ball A. However, there remains confusion regarding the specific steps to take and the role of kinetic energy in the analysis.

Contextual Notes

Participants note the challenge of having two unknowns in the momentum equations and the need for additional equations, such as those related to kinetic energy, to fully resolve the problem. There is an acknowledgment of the complexity introduced by the elastic nature of the collision.

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Homework Statement


Two billiard balls move of equal mass move at right angles and meet at the origin of an xy coorindate system. Ball A is moving upward along the y-axis at 2.0m/s and ball B is moving to the right along the x-axis with a speed of 3.7m/s. After the collision, assumed elastic, ball B is moving along the positive y-axis . What is the final direction of Ball A and what is their speeds.


Homework Equations


Conservation of momentum :
MaVax+MbVbx=MaV'ax+MbV'bx

I know that the masses cancel as they are the same.
But that still leaves me with 2 unknowns in that equation. Do I have to use trig functions to fing the velociy of ball B and then use the momentum to find velocity of ball A?? but then how do i find the direction of ball A



The Attempt at a Solution

 
Physics news on Phys.org
In an elastic collision linear momentum and energy are conserved. You have two independent lines (x and y) so that gives you three equations ...
 
O right sorry I forgot to write out the equation for the momentum along y. so in the x equation for example Vax= 0 and simiarly for the y equation? and is the third equation the kinetic energy one?? But I am sill confused as too how i find the direction of the A Ball.
 
Don't worry about finding the direction of the A ball; if you find its velocity in the x direction and its velocity in the y direction ...
 

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