Now that we've discussed what momentum is
and what some of the derived quantities are
related to momentum, including the impulse,
we can go to collisions.
What we'll do with collisions is first give an overview of collisions
and what they are,
and then we'll do an example of an elastic collision
and then an example of an inelastic collision.
So let's see what those are.
First of all, an inelastic collision is a collision in which the objects,
if it's a totally inelastic collision, stick together.
So they come in and then they actually stay together
as opposed to an elastic collision.
So, here's how an elastic collision works, right here.
For an elastic collision, two objects come in,
and then they perfectly bounce.
So, that's what the use of the word elastic is there.
What we mean is they actually completely bounce off each other.
So think in your head of the word elastic
like an elastic rubber band
or something stretchy or bouncy,
unless the idea here is that they bounce,
they just sort of reflect off of each other.
So we say a perfectly elastic collision,
is a collision in which the objects bounce
and in which their kinetic energy is conserved.
So for a situation where objects are bouncing off each other,
we say that the initial kinetic energy that they have coming in
will be equal to the final kinetic energy that they have going up
because the bouncing process conserve that -- it just reflected it.
We also have an inelastic collision, which I just mentioned,
where the objects actually stick together completely.
So for example a clay object or something
if these two things run into each other and stick together,
then you have a single mass
which is the sum of the two masses
and then this single mass will go off
with its own velocity of the prime.
In this case, when objects stick together like this,
what happens is they deform
and then they stuck to each other.
And so you can have lost energy in your collision
because of the deformations of your object.
So it could have been friction, or sound, or any other source of energy
leaving your system when objects stick together.
We'll see examples of the velocities
and the loss of energy is coming up shortly.
But first, let's summarize some of the important things
about these completely inelastic and elastic collisions.
For a completely inelastic collision,
where the objects stick together,
the momentum is conserved,
So, the P or momentum initial
is equal to P momentum final.
You also have that the final mass is a single mass.
It's a single collective object
whose mass is sum of the two masses that collided.
Finally, it has a velocity after the collision
that is just a single number.
So you only have one variable to try to find in this problem
because the final object that you have is a single object
so it will have a single velocity.
We can call that velocity v prime.
Well, prime just means we put a little notation above the letter,
as you can see here. We call it prime.
So, we have v1 and v2, collide, becoming 1 object.
That object has a total mass of m1 plus m2
and it has a velocity of v prime.
For elastic collisions, however,
we still do get the conservation of momentum,
which is always going to be the case.
However, instead of getting one object
that sticks together as a single object,
we instead get the energy is conserved because again
once these things bounce off of each other
the total kinetic energy initally and finally will be the same.