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California State Polytechnic University, Pomona

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Problem 68 Easy Difficulty

Three identical pucks on a horizontal air table have repelling magnets. They are held together and then released simultaneously. Each has the same speed at any instant. One puck moves due west. What is the direction of the velocity of each of the other two pucks?

Answer

Puck A's direction is 60 " north of east
Puck B's direction is 60 " south of east

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Video Transcript

{'transcript': "once again Welcome to a new problem. This time we have a three parks. Well, three parks the city on a table. It's a horizontal table. So going to call. But this one park, eh? Could be. And proxy? No. And then what's gonna happen is that, um is gonna be movement they held together before they're released. And each one of them has the same speed v. So speed? Oh, each broke It is his v. Um And so this park moves west ones to the negative direction you can have an ox is like this. So this is But why This is the X direction. This is for Stephen. That's positive. So that's what you've given l and they have a repelling magnets of each one of this parks as a repelling magnets of their We're telling each other they're repelling each other, so wanna know, like, this's this's the information that's given. So we want to know what's gonna happen to you to puck of B, uh, and A when we release sea to the West, to this side. Okay, so when we really see to the West, we want to know what's going to happen. Uh, to fuck, eh? And b, you know, that's that's the question. We have a break now, Um, so it's a It's a fairly obstruct problem, requiring us to kind of like used momentum. So the fasting we're going to do is we need to find the direction, Okay, Goal is to find the direction that A and B um, we're going to go. So you know, the first thing is to use the of the law off conservation, um, conservation off momentum, which says that the initial momentum is going to be equal to the final momentum. So a pinochle equals two p final. But remember, the parks are not moving, so that means the initial zero, and that's going to be equal to P final. They're all zero to get the momentum off the system. So the of the total, the total momentum off the system is the sun Is the sun off the mantle off each one who were something them up, soapy who momentum of a plus. Momentum will be plus momentum of see us to be zero. But remember, momentum is mass times of velocity. So, you know, lost you. Hey, uh, velocity of B and the last year of seeing Nicols to zero. We can divide everything by him that's going to cancel out these EMS. All of these, that soil the next page. We have a new relationship that say's the lost city of hay. Plus, the last year, the plus velocity of C equals to zero. And that just means that we can always write this to have a new equation. Um, But before we do that, remember, we say that for going east, that's positive accident. If we're going upwards, that's supposed to Why, that's not, um, using this equation. We can see that the now we can write this in terms of unit vectors. So right, uh, in terms unit vectors. So you're saying the last year a X was lost you This should be a wa a y Sorry. The velocity of a X and lost him here. Why? Um, a X I had in terms of Munich back turns a way. A jihad. Uh, we'Ll do the same thing for the be velocity of bees, or we split the velocity of be inter unit factors. And that's very valid. Um, And then we also split the velocity of C uh, inter unit vectors like that and that's all of that is gonna go zero on. Then we group them, you say, Let's put all the high in vectors together. We want to put all the eye vectors together, binding them and then want to put all the J vectors together. So we're combining them, Uh, j hard. That's equals to zero. And so this simply means that if if you are two things in their value zero, it means that either this one is going to be zero or that expression is going to be here. So then we save the day X plus V b x si x was to zero. And also we do the something here. The A y plus the B Y, um, must DC Why? Because two zero. Um, remember So in on the next page, remember, we had, you know, we had three parks. This was a BNC, and then the sea went west woods. So if you think about the c X and we see what they see, X has to be zero meters per second. Sorry. We see why has to be zero minutes for second because it's only moving west ones. Uh, V C X. Obviously it's going to be the same as the velocity, but in the negative direction. And then the sea X zero meters per second on a VC x B C Y zero meters per second. We see exes. Negative. So this is D C X, which is negativity. That's the only component of VC. Why obvious? We have has to be here with us for a second. Um and so, you know, going back and looking at this equation. We know that VC x zero. So that's going to give us a new equation ofthe X and B X vehicles to zero. So the X with the B X equals zero Andi also in terms ofthe the wise, you know, obviously we see why zero. And they told us that the two, uh of the two viel wie and B y those two are gonna equal zero faster ball. If you see you see that, uh, V c X his negative v. So you know, we have to change this. We have to change this L V c x this leg, davy. So we have X plus B p x plus V. C X equals to zero, but this one is V. So that changes that to zero. And so v x plus v b x it was to agree. And then also we have, uh, this part a y b y and see why a member of the C Y zero. So when we take of the A y plus b y plus we see why that's equals to zero. But remember, we see why is zero this is zero And so we'll have to be a y plus b Why? Because two zero That just means that the y equals two negative b y. So these are the component velocities for for X and Y And then something else happened. We get to see that the ex components off and be a person because the ex components ofthe n b a the same. So, um, in terms ofthe the white component. But these two are gonna have the same magnitude, different direction, but the same magnitude, Um, in the x components off since the A and B of the same magnitude, magnitude in the UAE, then they will, uh, soon magnitude in the acts. So by magnitude, we just mean that this portion off the equation is the same. The direction is different. That's the vector part for the movie to partisan same s O. That simply means that we X has to equal of the BX, and that's equal to the component off the velocity v X. And so, um, you know, if if both of them are the same, we can use this logic to solve this problem by saying by saying the ex plus the text it was to be in on the next page with Simplify that by saying to the X equals two. These are the X, which is a component off the tunnel velocities of the two, and that helps us compute the directions. Because remember, we have on the ex direction and we also have the wind direction. And so if you have a last divvied, it has a X component VX and white component the wide this stada. So it means that co sign off data has to be the X V. So our data has to be co signed inverse off the ax off the But then remember the exes be over two. So this is co sign in verse off the over to the V, which is just to say that these cancel. So this is like saying the coastline universal of one half. Come on. And that's gonna give us sixty degrees. You know, it's going to give a sixty degrees sign terms off uh, the components. Um, if if you go back and look att park envy, you can see that they have opposite directions, so they're moving in opposite directions. And so that simply means that one of them is going to go that way, and then the other one is going to go that way. So this is on this is nothing shoes soap is east Says with West. Um, so this is sixty degrees, and this one is also sixty degrees. So we'LL say talk, eh? This is fucking a And this is Bobby. Took a news sixty degrees no off east. And then park be moves sixty degrees. So East s So that's what we have in this problem. Hope you enjoyed it. No, we had three packs and they all had the same momentum. The initial momentum zero that helped us come up with an equation that would compare all the velocities and make them equal to zero and then we change that to unit vectors. That helps us helped us cancel out some of the velocities. And so if we look att for the four pack see, there was only moving westward. So the velocity in the wild zero but in the X equals negative B. So we came up with a new question which is this one simplifying of making the previous I had expression being equal to be because we replaced the X by negativity. And then we did the same thing for the Y V c. Why will zero? Because the park going to the west doesn't have a white component and so we're left with the air while being by being equal to zero. And so it shows us that the pack and be a moving in opposite directions, but they have the same magnitude. So they'LL have also the same magnitude in the X, and that's going to be the VX component off the velocity and then finally were able to show that to V X equals to VI. And the reason for that is you're replacing the X for these two right here. This is V X and that the XO simplify and come up with a different way of expressing VX. In terms of V that helps us to compute the co sign off Ada. In terms of the X and B, we replace the X by V over two, and then that's called sine cosine of us off one half. That gives sixty hope You enjoyed the problem. Feel free to ask any questions and have a wonderful day."}

California State Polytechnic University, Pomona
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