Calculating Final Velocities in an Elastic Collision on an Air Track

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Homework Help Overview

The problem involves an elastic collision between two gliders on a frictionless air track, where one glider is moving to the right and the other to the left. The objective is to determine the final velocities of both gliders after the collision.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of momentum and kinetic energy in elastic collisions, questioning how to apply these principles to find the final velocities of the gliders. There is mention of setting up equations based on these conservation laws, but uncertainty remains regarding solving for two unknowns.

Discussion Status

Participants are exploring the necessary equations for solving the problem, with some suggesting the use of both momentum and kinetic energy conservation. There is recognition of the complexity involved in solving the equations with two unknowns, indicating a productive direction in the discussion.

Contextual Notes

Participants note the challenge of having two unknown final velocities and the need to apply both conservation laws to find a solution. There is an acknowledgment of the tricky nature of the calculations involved.

stevethepirat
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Homework Statement


A 0.147 glider is moving to the right on a frictionless, horizontal air track with a speed of 0.870 . It has a head-on collision with a 0.292 glider that is moving to the left with a speed of 2.20 . Suppose the collision is elastic. What is the magnitude of the final velocity of both
carts after the collision?

Homework Equations



M1U1+M2U2=M1V1+M2V2

The Attempt at a Solution


I can setup the equation and determine the direction both carts are traveling after the collision but with 2 unknowns for the final speeds I don't know how to find the exact speed each is traveling after the collision.
 
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If th collision is perfectly elastic, there is a 2nd equation you can use. What else is conserved besides momentum in an elastic collision?
 
Wouldn't Kinetic energy also be conserved?
 
stevethepirat said:
Wouldn't Kinetic energy also be conserved?
yes, sure
 
ok so I would set the initial kinetic energy equal to the final kinetic energy and solve for the velocity right?
 
stevethepirat said:
ok so I would set the initial kinetic energy equal to the final kinetic energy and solve for the velocity right?
you'd have to sove the 2 equations with 2 unknowns for the velocities...as I recall, it is a little tricky..but nonetheless, solvable.
 

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