Hi. It's Mr. Andersen and today I'm going to be talking about momentum. The
equation for momentum is this. P = mv. Or if we were to write that out, momentum, which
is P is equal to mass. And we always measure mass in kilograms. So it's mass times velocity.
And we have to measure velocity in meters per second. So momentum is simply the product
of mass times velocity. So let's say an object has no mass. What is its momentum? The right
answer would be 0. Let's say an object has no velocity. What would its momentum be? Right
answer would be 0. And so that's a pretty easy one. We'll do a question in just a second.
And so this is a famous application of that. This is a train that was coming into a train
station in Paris. And the brakeman was trying to save a little bit of time. And so he didn't
pull on the brake soon enough. And that train had so much momentum, it had so much mass
that it just kept going and going. It went through a giant wall and then crashed off
this terrace. Surprisingly nobody was killed in this accident except a woman who happened
to be sitting right below. But that's momentum. So what are some typical problems that you
might get as far as momentum goes? This would be a typical one. This is the first car that
I ever had. This is a 1981 Honda Civic. And so let's say Mr. Andersen's 1981 Honda Civic
has a mass of 1200 kg and a top speed of 38.6 m/s. Calculate the maximum momentum of this
car. Well, first thing we have to do is right out the equation. So remember P = mv. In this
case momentum then equals the mass. And so the mass in this case is 1200 kg. And we're
going to multiply that times the velocity. And the velocity is 38.6 m/s. Now we want
to make sure that the mass is in kilograms. And that the velocity is in meters per second.
If it isn't you're going to have to convert it to that. And then we simply multiply those
two values. And if I multiply those two values together on my calculator I get 46320 kg m/s.
That's the units for momentum. Now the next thing you want to do is look back and check
your significant digits. If we look at 1200 kilograms, that's going to have two significant
digits. If we look at 38.6, that's going to have three significant digits. And so my answer
can only have two. And so the way I would write this is momentum equals 4.6 times 10
to the 4th kilogram meters per second. So that would be the right answer and the correct
number of significant digits. Remember though if that Civic isn't moving then it would have
momentum of zero. And so you could have an object that's much smaller than that. In other
words if that car was going at that speed, and I were to throw and object that has a
mass much smaller than that, straight at it with an incredible velocity I could actually
stop it if those momentums were to match. So that's what momentum is. Next thing you
should understand is that momentum is conserved. Now one of my favorite toys as a physics teacher
was this. It's called Newton's cradle. And I don't have mine right here. But what you
can do is you can lift up one ball and that will hit the balls. And the other ones will
go flying up on the other side. I don't have an actual one today. But I do have a virtual
Newton's cradle right here. And so what I can do is I can lift up on this ball on this
side. There's a slight pause there. But what happens is the balls on the other side are
going to move up. And so what's happening to the momentum? The momentum is just moving
back and forth and back and forth. Now to get one of these to work, it's actually pretty
hard. You have to make sure that all of the balls have the exact same mass. And you have
to make sure that they're all the same height. Let me try to grab that for a second. So next
thing I could do is lift up two. And so if I have two balls now, I've doubled my mass.
It's going to have the same velocity. So when I let it down that momentum is going to be
transferred back and forth again. So that's cool. The one thing you want to play with
as you do this is then what happens with three? So if I lift three up like this. Let me get
those stopped for a second. There we go. Okay. If I lift three up on this side what's going
to happen there? Well the momentum is going to be the same. And so how am I going to get
three balls to go up on the other side? Well let's just try it. So what happens is two
will maintain their position. And then that momentum is transferred back and forth. And
so momentum remember is conserved in any kind of a collision. So solving problems with one
object is really easy. And so is solving problems with two objects. And so let's say we have
object one now and object two. And object one is an eight ball. And so let's say this
is before the collision. And so we can figure out its momentum. We'll call that mass one
times velocity one. Plus mass 2, this is the cue ball now, times the velocity 2. And so
the momentum of this ball plus this ball before the collision is going to equal the same after
the collision. And so this would be mass one. Its mass isn't going to change. Times its
velocity after the collision. Plus mass two times it's velocity after the collision. And
so if we say that this is a collision where object two strikes object one, and object
two remains stationary, in other words if it doesn't move. So how would we solve this?
Well if you think about it, let's do this. Let's call this case one where the cue ball
just stops. And so in case one, what's its velocity before the collision? Let's call
that zero. And what's the mass of the cue ball before the collision. Well let's add
some numbers to it. Let's say that a typical cue ball has a mass of 0.2 kilograms. And
to make this easy let's say it's going 6 meters per second. And so we could take it's mass
and velocity before the collision. So that would be mass of 0.2 times 6 meters per second.
And so it's momentum before the collision would be 1.2 kilograms meters per second.
And so after the collision, let's say that this cue ball starts moving now. And this
one stays stationary. So we'd say well its momentum is going to be zero now. And so all
of that momentum is going to be transferred to the other object. And so as long as this
eight ball, and I think they all have the same mass, has a mass of 0.2 kilograms then
it's going to move with the same velocity. And so it's going to be a velocity of 6 meters
per second. In other words the momentum would be conserved. Let's call that case one. And
now if we make it a little trickier. Let's do case two now. So in case two let's say
those two objects become linked. in other words let's say this ball hits this ball and
they both move forward. In other words they don't move. Well how would we do that? We've
got mass. The first one has a momentum of 0. This one we said has a momentum of 1.2
kilograms meters per second. Now after the collision the mass of this one is going to
be 0.2 times the velocity. And I'm just going to call this v. Because the velocity is going
to be the same. Plus the mass of the other one, 0.2 times v, because we're saying the
mass or the velocities are going to be the same. So 1.2 kilogram meters per second now
equals 0.4v. And so the velocity at this point would equal 3 meters per second. In other
words if this ball comes in and it has a velocity of 6 meter per second, since their velocity
of 6.0 meters per second. Since their masses are exactly the same it's going to leave with
a velocity roughly half that. Or of about 3 meters per second. And so that's how you
do momentum problems if you have two objects. Now another thing that I failed to mention
before that's really important is that momentum is a vector. And so to solve momentum problems
the other thing that you want to have is a direction as well. And so most of the problems
I've done before are just linear. But if we're breaking, so this is a pool ball. Let's say
we have the cue ball here and we break the balls, there's going to be a lot of different
vectors of velocities that are created by that. And so the sum of all of those velocities
is going to equal the sum of that first momentum of that first cue ball. And so momentum is
conserved. Momentum is also relative. And now we get a little bit deep. But it's not
that deep. And so let's say you're this person right here. Let's say you're person A and
you're watching an object come by. Let's say this is an elevator. And it has an apple in
it. And the elevator and the apple are both moving at a constant velocity. Well when you
look at that object, it's going to have a certain momentum that we could calculate.
So let's say the apple has a mass of 0.2 kilograms. And it's going at a speed or a velocity of
20 meters per second. Then we can figure out exactly what the momentum of that object is.
But let's say we put you inside. And we sometimes refer to this as Einstein's elevator. Let's
say we put you inside. And now that elevator is still moving at a constant velocity, but
your reference has changed. And so when you look at this object, it's not moving. It's
moving with you. And so we would say that its momentum now is 0. And the reason why
is that we've shifted your time or your reference point. Where you're observing it from. And
so does it have a momentum here when you're watching it? Yeah. Does it have no momentum
here when you're watching it when you're in the elevator? Yeah. And so that's relativity.
Or that's a little bit of relativity. And so I hope that's helpful.