Why do bar magnets have zero velocity after collision?

[TomK]

Homework Statement

ENGAA 2018 (Section 2, Question 4)

Relevant Equations

Conservation of momentum

I don't understand the reasoning of this question's answer. The answer is velocity = 0 (option A).

A while ago, I was told that, since the magnets were held at-rest (before being let go), they must have no velocity after the collision. What about the velocity which they had just before the collision? It is stated that the larger magnet has velocity v.

If you try to use conservation of momentum, you end-up with too-many unknown variables, meaning you must make an assumption about conservation of energy to get an answer.

 

[etotheipi]

The total momentum of the system comprised of the two magnets is conserved! Since both magnets start from rest (both have zero initial velocity), what is the initial total momentum of the system?

Once they have coalesced, the total momentum of the system after the collision is $(m_1 + m_2)V$, if $V$ is the final velocity. What must $V$ be?

 

[TomK]

The total momentum of the system comprised of the two magnets is conserved! Since both magnets start from rest (both have zero initial velocity), what is the initial total momentum of the system?

Once they have coalesced, the total momentum of the system after the collision is $(m_1 + m_2)V$, if $V$ is the final velocity. What must $V$ be?

Why do we use the initial velocities of zero when you could use the velocity immediately before the collision (i.e. X has velocity v)? How do you know which to use? I understand the momentum calculation, but I don't understand why you don't use the velocities right before the collision.

 

[etotheipi]

For this scenario the momentum of the system is conserved for all $t\geq 0$, so the total momentum right when you release them, 0, will be the same as right before they collide, 0, and will also be the same as after the collision, 0.

If you weren't given that they both start from rest, they you could not deduce the total momentum of the system given only the speed of magnet X before the collision, because you don't know the speed of magnet Y! In which case you wouldn't be able to work out the final speed.

The question setter is just trying to throw you off by giving you unnecessary information, don't be misled!

 

[TomK]

For this scenario the momentum of the system is conserved for all $t\geq 0$, so the total momentum right when you release them, 0, will be the same as right before they collide, 0, and will also be the same as after the collision, 0.

If you weren't given that they both start from rest, they you could not deduce the total momentum of the system given only the speed of magnet X before the collision, because you don't know the speed of magnet Y! In which case you wouldn't be able to work out the final speed.

The question setter is just trying to throw you off by giving you unnecessary information, don't be misled!

That makes more sense now. Thank you.