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• 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.

Hi. It’s Mr. Andersen and this is AP Physics essentials video 61. It is on linear momentum.

# 線性動量 (Linear Momentum)

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Wayne Lin 發佈於 2021 年 01 月 14 日