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PROFESSOR: Let's look at three interesting cases
whereby we go to extremes.
And let's first take the case that m1 is much, much larger than m2.
m1 is much, much larger than m2.
Or another way of thinking about that is that let m2 go to 0.
Extreme case, limiting case.
So it's like having a bowling ball that you collide
with a ping pong ball.
If you look at that equation, when m2 goes to 0, this is 0.
This is 0.
Notice that v1 prime equals v1.
That is completely intuitive.
If a bowling ball collides with a ping pong ball, the bowling ball doesn't
even see the ping pong ball.
It continues its route as if nothing had happened.
That's exactly what you see.
After the collision, the bowling ball continues unaltered.
What is v2 prime?
That is not so intuitive.
If you substitute in there, m2 equals 0, then you get plus 2, v1.
Not obvious at all.
Plus 2, v1.
It's not something I even want you to see.
I can't see either.
I'll do a demonstration.
You can see it really happens.
So now you take a bowling ball and you collide the bowling ball with the ping
pong ball and the ping pong ball will get a velocity 2 v1,
not more, not less.
And the bowling ball continues at the same speed.
Now let's take a case whereby m1 equals much, much less than m2.
Other words, in the limiting case m1 goes to 0 and we
substitute that in here.
So m1 goes to 0.
So this is 0 and so we see v1 prime equals minus v1.
v1 prime equals minus v1.
Completely obvious.
The ping pong ball bounces off the bowling ball and it just bounces back.
And this is what you see.
And the bowling ball doesn't do anything because m1 goes to 0 so v2
prime goes to 0.
So that's very intuitive.
And now we have a very cute case that m1 equals m2.
And when you substitute that in here, when m1 equals m2, v1 prime becomes 0.
So the first one stops but v2 prime becomes v1.
If m1 equals m2, you have two downstairs here and two upstairs.
And you see that v2 prime equals v1.
And that is a remarkable case.
You've all seen that.
You've all played with Newton's cradle.
You have two billiard balls.
One is still and the other one bangs on it.
The first one stops and the second one takes off with the speed of the first.
An amazing thing.
We've all seen it.
I presume you have all seen it.
Most people do this with pendulums, where they bounce these balls against
each other.
I will do it here with a model that you can see a little easier.
I have here billiard balls.
And if I bounce this one on this one then we have case number three.
Then you see this one stands still and this one takes over the speed.
Quite amazing.