What are the velocities of the carts after a perfectly elastic collision?

AI Thread Summary
In a perfectly elastic collision between two carts, cart1 (1 kg, initial velocity 2 m/s) collides with cart2 (2 kg, initial velocity 0 m/s). The momentum equation yields 2 = V1f + 2V2f, while the kinetic energy equation results in 4 = V1f² + 2V2f². The initial calculations provided V2f = 2 and V1f = -2, but these values do not satisfy both equations. Confirmation of the correct velocities requires ensuring that both conservation laws are upheld. The discussion emphasizes the importance of checking calculations against fundamental physics principles.
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.


Homework Equations


1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2

m1vi1 + m2v2i = m1v1f + m2v2f


The Attempt at a Solution



I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f2 + 2V2f2

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2
 
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southernbelle said:

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.


Homework Equations


1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2

m1vi1 + m2v2i = m1v1f + m2v2f


The Attempt at a Solution



I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f2 + 2V2f2

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2
You could check your answers yourself. Do they satisfy both the kinetic energy and momentum equations?
 
No, they don't. You're right that was an easy way to check myself.
 

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