# A cart of mass m moving at velocity v to the right collides with a stationary cart

1. Dec 12, 2012

### Lo.Lee.Ta.

"A cart of mass m moving at velocity v to the right collides with a stationary cart"

1. "A cart of mass m moving at velocity v to the right collides with a stationary cart of mass 2m on an air track, and the two stick together after collision.
What is their velocity after colliding?"

2. Okay, so this is inelastic collision, right? So KEi ≠KEf
But momentum is conserved.

So:

(m1)(v1i) + (m2)(v2i) = (m1 + m2)(final velocity)

(m)(v) + (2m)(0) = (m + 2m)(final velocity)
(m)(v) = (3m)(vf)
mv/3m = vf

...So wouldn't the 1 of the m's cancel out here, creating v/2m???

3. The answer is really v/3... Somehow. How is this?
How does the answer not even have an m?
How do you get this answer?

Thank you!!! :D

2. Dec 12, 2012

### lewando

Re: "A cart of mass m moving at velocity v to the right collides with a stationary ca

No. The m on top cancels the m on the bottom, leaving v/3 = vf.

If m were part of the result then unit analysis would not be consistent: v/2m => m/(s*kg) ≠ m/s

Last edited: Dec 12, 2012
3. Dec 12, 2012

### Lo.Lee.Ta.

Re: "A cart of mass m moving at velocity v to the right collides with a stationary ca

Oh, wow, Lewando! Thanks! :D

I get into problems when I make math errors! Sometimes I forget fundamental things like that...

But thank you SO much!
You're awesome! :D