Why Is My Calculation of Final Velocities in an Elastic Collision Incorrect?

AI Thread Summary
The discussion centers on the calculation of final velocities in an elastic collision between two carts with given masses and initial speeds. The user initially calculates momentum and kinetic energy but ends up with an incorrect final velocity of 13.5 m/s for one cart. Despite attempts to adjust the equations, the user continues to receive a value that seems too high. Another participant confirms they reached a similar equation but obtained a lower final velocity, indicating a potential error in the user's calculations. The conversation emphasizes the importance of double-checking the equations used for momentum and kinetic energy conservation.
jubbly
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Homework Statement



Two carts with masses m1 = 0.8 kg and m2 = 1.2 kg are moving toward each other with
speeds v1 = 4.5 m/s and v2 = 3.8 m/s as shown in the diagram below. The two carts
collide elastically.

Some reason I'm getting too high of a value, don't know I'm doing wrong...

Homework Equations


momentum = m1v1 + m2v2 = m1vf1 + m2vf2

kinetic energy = .5m1v1^2 + .5m2v2^2 = .5m1vf^2 + .5 m1vf2^2

The Attempt at a Solution



So I found the momentum which came out to be -.96 = .8vf1 + 1.2vf2
Rearranged the equation to solve for vf2 = -(2/3)vf1 - .8
Then tried to find kinetic energy and got 8.1 + 10.83 = .4vf1^2 + .6vf2^2

Plugged in v2 and got 16.76 = .4vf1^2 + (4/15)vf1^2 + .64vf1 + .384
Subtracted 16.76 from both sides
Used quadratic equation

Came out with 13.5 m/s for vf1.
 
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jubbly said:
Then tried to find kinetic energy and got 8.1 + 10.83 = .4vf1^2 + .6vf2^2
Check the second term on the left hand side.
 
Doc Al said:
Check the second term on the left hand side.

Fixed it a little, but still getting a pretty high number. Is that really the answer?
 
jubbly said:
Fixed it a little, but still getting a pretty high number. Is that really the answer?
No. I got the same equation as yours, but got a lower answer.
 

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