00:01
Okay, so the key to answering this question is to understand that the momentum will need to be conserved and the total energy of the system will have to increase.
00:12
So if we look at the four cases, the first case being after they collide, the first, the original mass will stop and the second cart will continue at the same speed that the original mass was going at before.
00:29
And so in that case, in case a, the momentum is conserved, but the energy is also conserved, which means that this is not the right case because under that case, the spring is not adding any energy to our system.
00:52
So let's look at case b.
00:54
This is where they're both going to be moving forward at the same speed that is half a meter per second.
01:00
And this is also not the case because if they're moving forward at half meter per second, the total amount of energy is actually going down.
01:11
And so the original energy is one -half mv squared, where b is one, so it's just m over two joules.
01:19
This is your initial energy, the initial.
01:22
And if we have them both moving at 0 .5, 0 .5 squared is 0 .25.
01:29
And so we end up with less energy total than we started with.
01:35
So we'd end up with m over 4 joules of energy total, which would be fine if this was an inelastic collision, but we're told that that spring keeps them separated, so we can't have a reduction in energy.
01:52
We need to increase in energy.
01:54
So by a process of elimination, we know that it has to be c and d, but let's talk about those real quick...