1
$\begingroup$

I was solving the following problem and the explanation to it confused me.

There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and collides with the other object that is initially at rest. If the collision is elastic, what is the velocity of the object with mass $M$ right after the collision? Friction is negligible.

My understanding is, for these kind of collision problems momentum is conserved so,

$$mv_{m} +Mv_{M} =mv'_{m}+Mv'_{M}$$

or in other words,

$$mv_m=mv'_{m}+Mv'_{M}$$

Since the initial velocity is 0 for the object with mass $M$.

In addition, elastic collision means that kinetic energy is conserved and intuitively, I am imagining that the smaller object (say, $m$) will "bounce" to the opposite direction as its initial velocity while the bigger object starts moving in the direction that is as same as the initial velocity of $m$, just a little slower.

However, the answer explanation tells me that right after the collision the momentum is preserved, so

$$mv_m=(m+M)v'_{m+M}$$.

I thought that this equation represents the situation where the collision is completely INELASTIC and the objects stick to each other.

Does it have to do with the wording "right after the collision" ?

Or, is the explanation not making sense ?

$\endgroup$
2
  • $\begingroup$ What you say sounds reasonable, so maybe there is just a typo in your source. $\endgroup$
    – akhmeteli
    Nov 15, 2013 at 20:06
  • $\begingroup$ If you neglect friction, it does not matter if you look at velocity right after collision, or a few days after collision. In the absence of friction, the velocities remain constant. Regarding the momentum conservation, your statement is correct. The second equation is valid for inelastic collision $\endgroup$
    – pho
    Nov 15, 2013 at 20:15

1 Answer 1

-1
$\begingroup$

There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and collides with the other object that is initially at rest. If the collision is elastic, what is the velocity of the object with mass $M$ right after the collision? Friction is negligible.

This is an old question but it may still interest someone: the velocity of mass M, according to the formula will be: $$v'_M = \frac{\sqrt{8gl}}{m+M}$$

$\endgroup$
1
  • $\begingroup$ You're not helping him. Just providing the answer won't let him figure out how it was derived. $\endgroup$ Jul 26, 2015 at 3:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.