Hi. It’s Mr. Andersen. And this is AP Physics essentials video 94. It is on elastic and
inelastic collisions. Let’s say we take a ball that has 10 joules of potential energy
and then we simply drop it on a table. Now it probably is not going to do that, but if
it did it would be a completely elastic collision. We converted that potential energy into kinetic
energy and as it bounced off the table it returned all that kinetic energy back into
the ball so it was able to make it back again. Completely elastic. Now let’s say we take
another ball, it is made of different material and drop it. It also has 10 joules of energy,
but it does not bounce at all. We would call that a completely inelastic collision. Now
where did that energy go? Where did those 10 joules of energy go? They became internal
energy in the table and the ball itself that collided. Now we know that most balls are
going to be somewhere in the middle. Somewhat elastic in their collisions. And so during
any collision, which could be elastic or inelastic we are going to maintain linear momentum.
In other words the momentum of the objects before the collision is going to equal the
momentum of the objects after. In an elastic collision not only do we maintain linear momentum,
we also maintain kinetic energy. The speed before the collision equals the speed after
the collision. Again, it is rare that that is going to occur. In an elastic collision
we are still maintaining linear momentum but we have lost some of that kinetic energy.
Where did the energy go? It became internal energy into the objects themselves. And so
let me show you a collision between some matchbox cars. Okay. So we saw two collisions there.
And so one of those is elastic and one of those is inelastic. Did you figure out which
one? So we call that an elastic and this an inelastic. So we know in an elastic collision
we maintain all of that kinetic energy. In an inelastic collision some of that energy
goes into the internal energy of the objects itself. If you think about two real cars running
into each other, there is a lot of damage done inside those car. And that is internal
energy. It used to be kinetic energy that is doing damage inside the car. Let’s start
by studying some elastic collisions. And we are using a simbucket simulation where carts
will collide with each other. You can see on the left side that we have a 1 kilogram
cart is traveling at 5 meters per second. That means it is going to the right. And then
we have a 1 kilogram cart that is traveling in 2 meters per second to the right. And they
are going to bounce off of each other. And now we have some new velocities after that
collision. And so was linear momentum maintained? Well it is always maintained in a collision.
But let’s study that. If we look at the conservation of linear momentum, p1 plus p2,
in other words the momentum of those two objects before, has to equal the momentum after. So
m1 v1 plus m2 v2, so if we were to say m1 is a 1kilogram cart going at 5 meters per
second and then a 2 kilogram cart going at 2 meters per second, so this is the momentum
before, does it equal the momentum after? Well if I multiply that out, it is 9 kilogram
meters per second on both sides. A positive value indicates that the overall momentum
of the system is towards the right, but it is equal. And it always will be equal in every
collision. But did we maintain kinetic energy? To do that we are going to have to use a different
formula. Kinetic energy in has to equal kinetic energy out. It is a unwieldy formula. And
so again it is just 1/2 m v squared. That is kinetic energy remember. This would be
of object one and two. Before and then after the collision. So if I plug in those values
here what we find is that the 16.5 joules that we had before the collision equals the
16.5 joules that we had after the collision. This is an elastic collision. They are just
bouncing off of each other. We are not losing any of that kinetic energy. But let’s say
we deal with an inelastic collision. Remember in an inelastic collision, in this case let’s
say it is completely inelastic, these two carts are going to come connected to each
other when they collide. Then this formula, conservation of kinetic energy is useless
to us. It does not help us at all. But what is neat is since they have a shared velocity
after they collide we can use the conservation of linear momentum to figure out, you know,
where is that energy going? And so if we write it out like this, this would be momentum before,
and then momentum after, you can see that in this case those two carts are going to
become connected. And so the velocity of both of them after is going to be exactly the same.
They are going to become connected and so I have written that as v3. This is our new
shared velocity of the two. And so what I can do is I can plug in my values. We had
a 1 kilogram cart going at 5 meters per second before the collision. And 2 kilogram cart
going at 2 meters per second after. The masses do not change. And so I can solve for that
v3. I can solve for a velocity of 3 meters per second. And so if it is an inelastic collision,
since they are connected that shared velocity allows me solve for the change in linear momentum.
Let’s make sure that that works. Yep. They both have 3 meters per second. It is going
to the right. And so did you learn to predict the outcome of either an elastic or inelastic
collision. Remember elastic is when we do not lose any of that kinetic energy. Could
you plan data collection? I am using a simulation, but you could use carts colliding as well.
Did you learn to classify a collision as elastic or inelastic? If we lose that energy then
it is going to be inelastic. And then finally could you apply the conservation of linear
momentum to instance where we have an inelastic collision? To solve, for example, to solve
for its final velocity? I hope so. And I hope that was helpful.