How do i compute the final velocity of two carts in an inelastic collision?

[Abigail_M]

I’m really struggling to understand how to apply the concept of **inelastic collisions** to a problem I have with two carts on a track. My textbook says momentum is conserved but kinetic energy isn’t, and I get that, but when I try to set up the equation for their final velocity together, my numbers keep coming out wrong.

[Andrew_T]

Yeah I’ve wrestled with that. When the carts stick together after a completely inelastic hit the final speed should come from momentum alone: v_f = (m1 v1 + m2 v2) / (m1 + m2). I once got a goofy number because I used the wrong sign for one velocity or swapped the masses. Double‑check you’re adding the momenta with consistent directions and that you’re using the initial values, not mixing in any final values.

[Stella90]

Could be you’re not in the sticking case. If they don’t weld together you need the coefficient of restitution e and you’ll have a relation like v1' - v2' = -e (v1 - v2) in addition to momentum conservation. I’m not sure your setup matches that, but it’s a common pitfall.

[Joseph_L]

I tried to use energy loss to back into the velocity and it blew up because energy isn’t conserved in the inelastic part. It helped to separate the two ideas: momentum conservation gives v_f, energy tells you how much KE disappears. I still mix up the numbers sometimes.

[KennethJ]

One time I was convinced I had the right numbers but the track friction got in the way in the lab, so the final speed measured was off. In theory it’s clean, in practice you still have to account for little losses everywhere.