Hi. It’s Mr. Andersen and this is AP Physics essentials video 61. It is on linear momentum.
And I am going to start with a demonstration. I am going to drop a basketball and an apple
at the same time and watch what happens. So you can see the apple is going really fast
and where did that speed come from? Where did that velocity come from? Well it is the
momentum of the basketball. Momentum is equal to mass times velocity. And since the basketball
is much more massive than the apple it is transferring some of that momentum. And since
the apple has a small mass it gains a larger velocity. So let me play that video again,
but this time instead of watching the apple watch what happens to the basketball. So you
see it does not go very far. That is because it is transferring a lot of that momentum
to the apple. And so momentum is a product of two things. It is the mass of an object
times the velocity of the center of the mass that object. And that velocity and the momentum
are going to be in the same direction. And so if we are watching an object move, and
we will do this at the end of the video, as we watch that apple move we can calculate
its momentum by figuring out its velocity. And a good way to do that is using video analysis.
What I am doing is watching where that center of mass is changing over time. And since the
change in time is constant I can graph it and I get a graph that looks like this. And
so this is a graph of an object that has constant velocity. So I could calculate the slope of
that line, that is going to tell me the velocity of the object. If I know the mass, now I know
the momentum of the object. And so let me show you how to do that. And so we have two
spheres. They are 5 kilogram spheres. I have removed gravity and we are just going to let
the orange sphere collide with the green sphere. And watch what happens. So you can see we
are transferring some of that momentum from the orange to the green sphere. But the orange
is still moving so it did not transfer all of its momentum. So how do we calculate the
momentum of the sphere before the collision and after the collision? And so again we can
use video analysis. What I am going to do is put dots on the screen, but the distance
in time between those dots is going to remain constant. So let’s watch how that occurs.
So again you did not see the dots moving and that is because the green sphere was just
centered there for awhile. And so if we were to graph it now, we are going to get a curve
that looks like that. So we have two different parts. We have this part right down here before
the collision. It is not moving. And then we have this part after it collides and it
gets a velocity. And so if we want to figure out the momentum of that object before it
collides we have to figure out the velocity of the object in this area right here. Well
since the position is not changing over time we know the velocity is zero and it is not
moving. And so to calculate momentum it is simply mass times velocity. We have a mass
of 5 kilograms, a velocity of 0 meters per second, so how much momentum does it have?
It has 0 kilogram meters per second. It has no momentum before the collision. But let’s
watch what happens after the collision. It is going to move. And so if we can calculate
the velocity of the object after the collision we can figure out its momentum. So how do
we do that? You can see that it is a constant change in position over time. That means there
is a constant velocity. And so if we calculate the slope of that line, simply rise over run,
it is 1.4 meters moved over 0.95 seconds, we can calculate the velocity to be around
1.5 meters per second. So now I simply multiply the mass, 5 kilograms times 1.5 meters per
second. So how much momentum does that green sphere have? 7.5 kilogram meters per second.
That is how much was transferred to the sphere. Now let’s watch the orange sphere to start
with. How much momentum did it have before the collision? Well let’s watch. We are
again using video analysis. We could graph the position of that sphere at different times.
We are going to get a curve that looks like this. You can see this is the part where we
have constant velocity before the collision and then this is after. Again, it is not perfect,
but if we calculate the velocity during that period of time we can calculate the momentum.
It is going to be rise over run. It moves 1 meter in 0.5 seconds and so we could calculate
a velocity of 2 meters per second. So our momentum is going to be 5 kilograms times
2 meters per second. So it is going to be 10 kilogram meters per second. Now you could
figure out how much momentum we are going to have after the collision in one of two
ways. First of all you could calculate the slope of this line here, multiply it times
the mass. But if you know anything about conservation of momentum, we have this collision where
the green sphere now gets 7.5 kilogram meters per second. And so how much is that orange
sphere going to have at the end? Well it is the sum of the 2. The sum before the collision
is equal to the sum after. So it is going to have 2 kilogram meters per second after
that collision. That is why it is going about a third the velocity of that green sphere.
And so if we were to drop this apple, if I know the mass of the apple to be 0.5, we could
drop it, we could then do video analysis to calculate the velocity of that apple. And
so we could calculate the slope of this line right here. We know the mass of the apple
so we could figure out the momentum. How much momentum was transferred from that basketball
to the apple. So did you learn to calculate the momentum of an object. It is simply multiplying
the mass times that velocity. And then finally could you analyze data, like this? Could you
calculate the velocity and therefore calculate the momentum?
I hope so. And I hope that was helpful.