What Are the Final Velocities in a Perfectly Elastic Collision Problem?

AI Thread Summary
In a perfectly elastic collision problem involving two carts, cart1 (1 kg, initial velocity 2 m/s) collides with cart2 (2 kg, initial velocity 0 m/s). The conservation of momentum and kinetic energy equations are used to find the final velocities of both carts after the collision. The user has derived two equations: 2 = V1f + 2V2f and 4 = V1f^2 + 2V2f^2, but is struggling with the substitution method to solve for the final velocities. A suggestion is made to isolate one variable in the first equation and substitute it into the second to solve the resulting quadratic equation. This approach is expected to yield the correct final velocities for both carts.
southernbelle
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Homework Statement


In an isolated system, cart1 (with mass = 1 kg and vi1 = 2) has a perfectly elastic collision with cart2 (with mass = 2 kg and vi2 = 0). Find the velocity of cart1 and the velocity of cart2 after the collision.
I have to solve this using kinetic energy and momentum equations.


Homework Equations


m1vi1 + m2vi2 = m1v1f + m2v2f
1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2


The Attempt at a Solution


I have gotten to this point:
2= V1F + 2V2F
4= V1F2 + 2V2F

but I cannot get the numbers to work out correctly.
Using another equation I know that V1f = 2/3 and V2f = 4/3

I am doing substitution wrong or something.
Please help!
 
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southernbelle said:

The Attempt at a Solution


I have gotten to this point:
2= V1F + 2V2F
This makes sense.
4= V1F2 + 2V2F
How did you get this?
 
I got that by solving the kinetic energy equation.
I mutiplied both sides by 2 to get rid of the halves.

It is actually supposed to read:

4 = Vif^2 + 2V2f^2
 
southernbelle said:
It is actually supposed to read:

4 = Vif^2 + 2V2f^2
That's good.

Take the first equation and solve for one of your variables. Then substitute that into the second equation. Solve the quadratic.
 
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