Momentum Conservation Question

[justadream]

See the picture.

I'm confused because I think that in elastic collisions when the 2 masses are the same, the first object completely transfers it's speed to the second one. Thus, in the first situation, all the KE is transferred (assuming it's elastic - but I'm not sure if I can assume that).

But I also know that in collisions where there is "recoil", more momentum is transferred.

Can someone clarify these concepts?

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[DrknoSDN]

Thus, in the first situation, all the KE is transferred (assuming it's elastic - but I'm not sure if I can assume that).

Yes, you can assume that.

In another thread (here) I replied to a momentum question and used tables from ExamKrackers to help. The Examkrackers books go into a lot of detail about conservation of momentum and do a pretty good job of explaining it. If you want to these diagrams are from page 56 of the current edition.

(Shameless plug for EK because I feel bad posting their image, but have not found anything online that is as well organized)

The left diagram shows an elastic collision where m1 (projectile) is either lighter, the same as, or heavier than an object it is striking.
If the masses are the same the initial projectile velocity (vo) goes to zero and the velocity of the target ends up at the velocity the projectile started at.

For the right diagram y axis shows equal masses and everything left of zero is when the projectile is less massive than the stationary object (m1 < m2)
The red dotted line shows the trend of "recoil" of momentum where the projectiles original velocity +Vo approaches -Vo as m2 becomes much more massive.
Essentially if a projectile strikes a target that has way more mass, and the collision is elastic, the projectile will bounce off with almost an identical velocity in the opposite direction. The target would have a new velocity that was still "almost" zero.

If i remember correctly, the footnote for the right diagram said something along the lines of "if you don't understand this diagram don't worry about it, it's not super important conceptually" (paraphrased)

 

[justadream]

@DrknoSDN

Thank you for the response!

So to apply that graph to my question*, in the second situation (bottom one) from my picture, since block C still has some velocity after the collision, the collision must be partially elastic. Since the graph shows that at the y-axis, V2 for partially elastic < V2 for fully elastic, I can conclude that for my original question, Va> Vc?

*I'm using the situation at the y-axis where m1 = m2. How do I know if I can use this in my picture (where the initial momentum is just denoted by "B")?

 

[Mantis Toboggin]

I'm sorry if I'm oversimplifying, but if momentum and KE are conserved then that would mean that because vf of the ball is 0,all the velocity was transferred into block A, whereas only a part of it was transferred to block C

My Kaplan tutor two years ago was talking about what Drko was saying, but is it necessary to understand those situations explicitly? Can I not reason it out just like I did here, or should I commit to memorizing the EK chart?

Point 3 should be correct.