TBR Physics Momentum Question (possible error in answer explanation)

[salsasunrise123]

---

Members don't see this ad.

Hello, My question is about the 1st passage of the 52 question test in momentum/torque chapter. It's the passage about the 2 figure skaters. Here's the relevant part of passage:

Khoi skates toward a stationary Jen at a constant speed of 2 m/s. They Collide and move together following the collision.

Question: Khoi and Jen have a final speed of V. Khoi and Jen now double their masses and repeat experiment 1 (see above). What is new final speed in terms of V.

50%V
100%V
141%V
200%V

The answer is 100% but I got 200%. I thought momentum of Khoi = (mass of k + mass of j)v. however, they reversed it and made it mass of jen = (mass of k + mass of j)v. I'm confused as to why the speed doesnt change even though both their masses increase. Can someone please explain?


ALSO, I find that I am missing a bunch of questions because the sub-content that these questions are testing was not covered in content section of chapter. Had it been addressed, I would have crushed them. Is this typical of TBR? for example, there are a few questions which compare inelastic collisions to elastic collisions and ask which one produces a greater final velocity. I didnt know that elastic collisions always produce greater velocity and change in momentum since it was not addressed in the content review ( it also wasnt addressed in TPR content review either).

 

[brood910]

Doubling their masses wont affect it as their mass ratio wont change.

 

[Odi]

2m(j)Vi(j) = [2m(k) + 2m(j)]Vf

You should notice here^ that all the 2's cancel out. If you don't see it simply expand the equation: 2m(j)Vi(j) = 2m(k)Vf + 2m(j)Vf

All the 2's cancel here^ and you're left with the original scenario. 100%.

I remember reading in their book that kinetic energy is conserved for elastic collisions--but it is not conserved for inelastic collisions.

 

[salsasunrise123]

My bad. I forgot to mention that K is 2x the mass of J. This was stated in passage

 

[Odi]

My bad. I forgot to mention that K is 2x the mass of J. This was stated in passage

It doesn't matter who had the initial momentum or if one of them was heavier... The mass ratios are increasing by the same factor... so the 2x increase or any factor you increase their masses by as long as it's an equal factor among all variables--it will cancel and it will have no effect.

I digress here but I think it's useful to know that many physics equations we learn early on involving mass such as conservation of energy: mgh = 1/2mv^2 ... free fall: mg = ma ... sliding on a ramp: mgsin = ma ... ramp kinetic friction: mgsin - umgcos = ma ... inelastic collision mv = (m + m)v and maybe others but these come to mind...

They generally have mass on each side with every variable which means mass cancels *most* of the time. I've noticed lots of passages preying on this concept simply because it goes against our normal intuition that doubling the mass of something should have an impact on acceleration... but it usually doesn't.