SPEAKER 1: Ah, yes. So there’s a reason. It’s not because I am a

fan of a certain big box retailer that shall be nameless. All right. So what I’m going to do,

I have the little ball and I have the allegedly very

elastic liquid metal ball here. And I’m going to drop them. Probably very poorly, so we’re

going to think about it a lot before I actually screw up the demo. So I’m going to drop them, and

I think they’re going to fall, pretty confident on that score. So down they go. And if they fall the same

distance, then they’re probably going about the same speed. But the bottom ball will

encounter the floor first. And we’re going to say

for simplicity that it undergoes an elastic

collision with the floor. It’s cement. It’s pretty heavy. So it bounces up. If it was elastic and

it went down at v0, then does that imply that

it needs to come up at v0? Unless the earth is recoiling

with great velocity, right? OK. So we’ll pretend that the

earth doesn’t recoil a lot. Then the yellow one is still going down

at v0, and so they’re going to collide. And after the collision, well

maybe I don’t know for sure that the lower ball is

still going up, but I’m pretty confident that the

upper ball will be going up. And my question for you if all

the collisions are elastic, and if the blue ball’s mass is way big

compared to the yellow ball’s mass, then when the yellow ball

rebounds from the blue ball its speed will be most nearly which? All right. I’m terrible at this demo. So it may take a couple of

tries, and then I’ll give up. That’s about as good as

I’m ever going to do. So hang on one sec

before we explore that. So this one has four balls of decreasing

mass, and the top one can fly off. So let’s see– SPEAKER 2: But can the others? SPEAKER 1: No. Well they ain’t supposed to,

Yeah, that was really good. Let’s try this again, never fails. Get back there. All right, far away, here we go. Ah, missed her. All right. Thank you so much. So I will let you play with

these in recitation section. But I hope you noticed that

the little grape at the top actually got a lot of the kinetic

energy from the falling masses. So let’s now see if we can

understand the answer to this one. If fact, I think I heard

it right over here. Do you want to give it a shot? You’ve got this thing. Yeah, I know you do. I heard it. I heard the right answer. Go for it. SPEAKER 3: C, because since the

blue ball’s mass is a lot bigger than the yellow ball’s mass, the yellow

ball won’t slow the blue ball down. But the difference in speed

still needs to be the same. So– SPEAKER 1: So she says, OK. Correct me if I don’t get it right. So since the mass of the

blue ball is way big compared to the mass of the yellow, its velocity

isn’t really going to be changed much. It’s sort of like when the blue

ball collides with the earth, and the earth is effectively infinitely

massive compared to the blue ball, so the blue ball’s

velocity just reverses. So the blue ball is

going up at speed v0. And the yellow ball is coming

into this collision at speed v0. So what’s the relative speed? To v0, right. And then if we can approximate, because

this is so much bigger than that that the blue ball frankly doesn’t

care about the yellow ball. So it continues to move

up at speed about v0. Then in order for this to

be an elastic collision and preserve the relative

speed, then the yellow ball will have to be moving

up at 2v0 with respect to the blue ball, which

is moving up at v0. So therefore the yellow ball will

go up at 3v0, or thereabouts. Do you follow? I think she deserves

a round of applause. That was awesome. Any question on that? SPEAKER 4: Can we do

that a little bit slower? SPEAKER 1: Yes. Ian says, I want more chocolate,

or can you do that slower? All right. So here’s the large ball going up at v0. That’s too big. And the small one is coming down at v0. Now what has to be

conserved in the collision? Certainly momentum. So it is true that M, I’m going to

pick up as my positive direction. So initial momentum

would be Mv0 minus mv0. And the final momentum

will be M times, I guess I’ve got to make this a

big V going up, and a small v. Now I want to simplify this taking

into account that little m is puny compared to big M. So what if I

were to divide through by big M? Try to illustrate the little terms. No cheating yet, right? I didn’t divide by zero,

and then the world explodes. So in the limit that this is

huge compared to that, then I could maybe neglect this term. And I could neglect that term. And that implies that the

final v for the blue ball is the same as the initial v0. It’s not exact, but it’s close. And so if that’s the case, now

this one is moving up at v0. But the relative speed is

preserved in the collision. So this one has to go out

at some speed, v, such that v minus v0 is equal

well to the relative speed that we had before the collision, 2v0. Because here the relative speed is 2v0. Here the relative speed is 2v0. So therefore the outgoing speed of the

light ball, the ball with small mass, must be 3 times v0. About. OK now, I fudged things, right? I shouldn’t be putting–

this is a good equal sign. But by the time I get

down to here, it’s going to be relying on my ability to neglect

the difference between– that I can set the mass ratio to go to zero. There was a question. Yeah? SPEAKER 5: How is

kinetic energy conserved? SPEAKER 1: Ah. So she says, say it loud and proud. But then how is kinetic

energy conserved? Right? Because what would be the

kinetic energy before? Well it would be 1/2Mv0

squared, plus 1/2mv0 squared. And if we say that the big mass didn’t

change its kinetic energy, because it didn’t change its speed, then

we somehow manufactured energy. And that bugs you. Yeah. She says, yeah, that bugs me. So it can somebody help me out? Did we? Yeah? SPEAKER 6: So and then assuming that

big M is definitely [INAUDIBLE]. SPEAKER 1: So the

answer is, yeah we did. And he’s saying, well but in

the limit that big M is so much bigger than little m, all of the kinetic

energy in essence, is residing where? In the blue ball. And so even if we were to shave a

tiny little bit of its kinetic energy, it would still be moving

almost at v0, right? Because the top one is really light. So this is an approximate equals,

because I erased some terms in my momentum conservation. I did this. So my momentum conservation isn’t exact. But the approximation captures

the spirit of what’s going on. Because I mean if it’s true that big M

is this huge compared to little m, then almost all the kinetic

energy– so if you steal just a little

bit from the big one, you’ll hardly notice it’s slowing down. But you can shoot the little one up. So a little subtle

reasoning approximation.