Inelastic Collision: Cart of Mass m Hits Stationary Cart of Mass 2m

[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

 

[lewando]

mv/3m = vf

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

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

 

[Lo.Lee.Ta.]

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