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All right, last time we talked exclusively about completely inelastic collisions.

Today I will talk about collisions in more general terms.

Let's take a one-dimensional case.

We have here m1 and we have here m2, and to make life a little easy, we'll make v2 zero and this particle has velocity v1.

After the collision, m2 has a velocity v2 prime, and m1, let it have a velocity v1 prime.

I don't even know whether it's in this direction or whether it is in that direction.

You will see that either one is possible.

To find v1 prime and to find v2 prime, it's clear that you now need two equations.

And if there is no net external force on the system as a whole during the collisions, then momentum is conserved.

And so you can write down that m1 v1 must be m1 v1 prime plus m2 v2 prime.

Now, you may want to put arrows over there to indicate that these are vectors, but since it's a one-dimensional case, you can leave the arrows off and the signs will then automatically take care of the direction.

If you call this plus, then if you get a minus sign, you know that the velocity is in the opposite direction.

So now we need a second equation.

Now, in physics we do believe very strongly in the conservation of energy, not necessarily in the conservation of kinetic energy.

As you have seen last time, you can destroy kinetic energy.

But somehow we believe that if you destroy energy, it must come out in some other form, and you cannot create energy out of nothing.

And in the case of the completely inelastic collisions that we have seen last time, we lost kinetic energy, which was converted to heat.

There was internal friction.

When the car wreck plowed into each other, there was internal friction —

no external friction —

and that took out kinetic energy.

And so, in its most general form, you can write down that the kinetic energy before the collision plus some number Q equals the kinetic energy after the collision.

And if you know Q, then you have a second equation, and then you can solve for v1 prime and for v2 prime.

If Q is larger than zero, then you have gained kinetic energy.

That is possible; we did that last time.

We had two cars which were connected by a spring, and we burned the wire and each went off in the opposite direction.

There was no kinetic energy before... if you want to call it the collision, but there was kinetic energy afterwards.

That was the potential energy of the spring that was converted into kinetic energy.

So Q can be larger than zero.

We call that a superelastic collision.

It could be an explosion.

That's a superelastic collision.

And then there is the possibility that Q equals zero, a very special case.

We will deal with that today, and we call that an elastic collision.

I will often call it a completely elastic collision, which is really not necessary.

"Elastic" itself already means Q is zero.

And then there is a case —

of which we have seen several examples last time —

of inelastic collisions, when you lose kinetic energy, so this is an inelastic collision.

And so, if you know what Q is, then you can solve these equations.

Whenever Q is less than zero, whenever you lose kinetic energy, the loss, in general, goes into heat.

Now I want to continue a case whereby I have a completely elastic collision.

So Q is zero.

Momentum is conserved, because there was no net external force, so now kinetic energy is also conserved.

Today I will talk about collisions in more general terms.

Let's take a one-dimensional case.

We have here m1 and we have here m2, and to make life a little easy, we'll make v2 zero and this particle has velocity v1.

After the collision, m2 has a velocity v2 prime, and m1, let it have a velocity v1 prime.

I don't even know whether it's in this direction or whether it is in that direction.

You will see that either one is possible.

To find v1 prime and to find v2 prime, it's clear that you now need two equations.

And if there is no net external force on the system as a whole during the collisions, then momentum is conserved.

And so you can write down that m1 v1 must be m1 v1 prime plus m2 v2 prime.

Now, you may want to put arrows over there to indicate that these are vectors, but since it's a one-dimensional case, you can leave the arrows off and the signs will then automatically take care of the direction.

If you call this plus, then if you get a minus sign, you know that the velocity is in the opposite direction.

So now we need a second equation.

Now, in physics we do believe very strongly in the conservation of energy, not necessarily in the conservation of kinetic energy.

As you have seen last time, you can destroy kinetic energy.

But somehow we believe that if you destroy energy, it must come out in some other form, and you cannot create energy out of nothing.

And in the case of the completely inelastic collisions that we have seen last time, we lost kinetic energy, which was converted to heat.

There was internal friction.

When the car wreck plowed into each other, there was internal friction —

no external friction —

and that took out kinetic energy.

And so, in its most general form, you can write down that the kinetic energy before the collision plus some number Q equals the kinetic energy after the collision.

And if you know Q, then you have a second equation, and then you can solve for v1 prime and for v2 prime.

If Q is larger than zero, then you have gained kinetic energy.

That is possible; we did that last time.

We had two cars which were connected by a spring, and we burned the wire and each went off in the opposite direction.

There was no kinetic energy before... if you want to call it the collision, but there was kinetic energy afterwards.

That was the potential energy of the spring that was converted into kinetic energy.

So Q can be larger than zero.

We call that a superelastic collision.

It could be an explosion.

That's a superelastic collision.

And then there is the possibility that Q equals zero, a very special case.

We will deal with that today, and we call that an elastic collision.

I will often call it a completely elastic collision, which is really not necessary.

"Elastic" itself already means Q is zero.

And then there is a case —

of which we have seen several examples last time —

of inelastic collisions, when you lose kinetic energy, so this is an inelastic collision.

And so, if you know what Q is, then you can solve these equations.

Whenever Q is less than zero, whenever you lose kinetic energy, the loss, in general, goes into heat.

Now I want to continue a case whereby I have a completely elastic collision.

So Q is zero.

Momentum is conserved, because there was no net external force, so now kinetic energy is also conserved.

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