Hi. It’s Mr. Andersen. And this is AP Physics essentials video 93. It is on the conservation
of linear momentum. Remember momentum is a sum of the mass of an object times the velocity
of an object. The bigger it is or the faster it is going the more momentum that it has.
And I am going to give the blue sphere on the left a little bit of momentum by removing
the platform and it bounces off the other sphere and then it comes back again. And so
is linear momentum conserved? Yes, it is always conserved in every collision. I have momentum
on the left side. I am transferring that to the right side. And then it is simply coming
back again. And this only works if they both have the same exact mass. But what would happen
if I made it out of a different material. Let’s say I made it out of clay. Watch what
happens here. Instead of just bouncing off they become connected to each other. And so
what is really lost? We are loosing some of that speed. We still conserve our linear momentum
but we have lost some of that kinetic energy. And if we loose kinetic energy we call that
an inelastic rather than an elastic collision. And so conservation of momentum remember is
always maintained in any collision. So if I have two objects running into each other,
the momentum that we have before the collision equals the momentum that we have after. So
let me set up a little elastic collision like that. We are transferring momentum, in this
case, from one object to another. We would call this an elastic collision. Why is that?
Not only have we maintained the linear momentum but we have also maintained our kinetic energy.
We have not lost any of that speed. In other words the kinetic energy that came into the
collision equalled the kinetic energy that came out. Now we could also have another type
of collision called an inelastic collision. At that is when one object hits another object
and they loose some of that kinetic energy. Maybe they become connected or it could just
run into a wall where they both eventually come to a complete stop. We would then call
that an inelastic collision. Did we maintain conservation of linear momentum? For sure.
We always do in every collision. Did we maintain kinetic energy? No. We have lost some of that
speed. Did we maintain energy? Is there a conservation of energy? We did. Where did
that energy go? It went to the internal energy inside the objects involved in that collision.
And so an example of this, if I drop a basketball with an apple on the top of it, we are converting
some of that momentum from the basketball, which is bigger, to the apple. We are increasing
its speed. Now the best way to verify this is through experimentation. So we are using
a simbucket simulation. We have these carts that are going to collide with one another
and it will show us what their velocity is after the collision. And so what we will do
is figure out is the linear momentum maintain? And then is kinetic energy maintained, to
figure out if it is elastic or inelastic. And so linear momentum remember, p1 plus p2
equals p1 prime plus p2 prime. In other words the momentum of those two objects before has
to equal the momentum after. And so let me start this collision. You could see in this
simulation that both of them have a 1 kilogram mass to begin with. Initial velocities were
5 meters per second on the left, negative 5 meters per second on the right. And you
can see that those speeds are reversed after the collision. And so if we set up our equation,
m1 v1 plus m2 v2 equals m1 v1 prime, and that is after the collision, plus m2 v2 prime.
So I can just plug in my values and what I find is that the momentum before and after,
again of the system, not of individual objects, but of the system itself, the momentum was
0 before and 0 after. Linear momentum is maintained. Now is kinetic energy maintained in this collision?
Kinetic energy before and after is going to be equal, well if we do that collision, it
looks like the speeds are not changing very much. And so I then have to get to the math.
And so I am going to plug in kinetic energy. This looks scary but again it is 1/2 m v squared
plus 1/2 m v squared of the objects before the collision and then after the collision.
So if I plug in those values, what I find is that we had 25 joules of kinetic energy
before and 25 joules after. And so is this an elastic or inelastic collision? It is elastic.
We have not lost any of that kinetic energy. Let’s try another one. Now the one on the
left has 10 meters per second. So it has a greater speed than the one on the right. They
both are 1 kilogram masses. You could guess as far as what is going to happen when they
collide with each other. You can see the speeds are going to be swapped. And so if I were
then to plug that into my linear momentum equation I would find that the momentum we
had before is equal to the momentum that we had after. Now it is not 0 anymore. What is
it? It is a positive value. That indicates that we have a shift. In other words those
momentum, the overall momentum is to the right in this system. Now, is kinetic energy maintained?
Again we used that formula, kinetic energy before, kinetic energy after. If I plug those
values in what I find is that we have 62.5 joules before, 62.5 joules after. Now we have
more kinetic energy because one of those cars is going faster. But is it an elastic collision?
For sure because we have maintained kinetic energy. Now let’s go to a different kind
of a collision. Instead of bouncing off of each other, they are becoming connected. And
so you know right away this is probably going to be an inelastic collision. If I plug in
my linear momentum values I find that the momentum we had before, 20 equals the momentum
we have after. Again, it is always going to be maintained. But then if we look at the
kinetic energy before and after, and we figure out our values, you can see that we have less
kinetic energy after. If I plug in those values, 200 joules before, 50 joules after. And so
we have lost 150 joules of energy. What does that indicate? This is an inelastic collision.
In other words we have lost some of that kinetic energy. But you might be thinking to yourself,
where did it go? Well think about a car accident. When two cars run into each other they had
kinetic energy before. Where did it go? It became the internal energy after that collision.
And we can even have a super elastic collision. So if we have an explosive device in the middle,
it is all internal energy. So what is the momentum and this point? There is no momentum.
There is no movement. But if I were to let that explosive go, what is going to happen?
We are going to convert all of that internal energy to kinetic energy in an explosion like
that. So did you learn to make qualitative predictions about momentum and how it is transferred?
Could you apply the principle of conservation of momentum? Remember p1 plus p2 equals p1
prime plus p2 prime. Did you then figure out how to design an experiment? So using carts
and colliding them is the best way to do this. And then finally did you figure out, how do
you classify this as elastic or inelastic. Remember in any collision conservation of
linear momentum is going to be maintained. But only in an elastic collision are we also
going to have the conservation of kinetic energy. So I hope that made sense. And I hope
that was helpful.