Why don't two colliding carts combine into one in momentum problems?

[haruspex]

I'm assuming we are to imagine the properties are the same in all of the various carts in all of the various examples.

Then don’t.
In the real (macroscale) world, nothing is perfectly elastic or perfectly inelastic. Even putty is a tiny bit elastic, but it is also sticky, so does tend to coalesce.
In physics problems, try not to assume anything about elasticity, but sometimes you are not given that information and are expected to make a reasonable assumption given the materials involved, like putty or billiard balls.

 

[paulb203]

The same two carts will always have the same type of collision (elastic, inelastic or totally inelastic) as long as the velocities are not so high as to break them to pieces or deform them over the elastic limit (in case of an elastic collision). But these are not situations you encounter in introductory physics examples. You are usually told what type of outcome to expect (move together or move separately) for a particular problem. Do you actually have an example where the nature of collision changes due to changes in initial velocities, without changing the nature if the colliding objects?

Thanks.
No, I don't have an example. I was incorrectly under the impression, from the outset, that all the carts were made of the same stuff, and that the sticking together or not was down to mass and/or velocities. I'm getting the hang now of doing the maths, of getting the correct answer, but will have to work on understanding what's actually going on :). Elastic and inelastic collisions haven't came up, as such, yet, in the course; I look forward to it.

 

[paulb203]

Thanks, guys. Really helfpul, as ever :)