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Two pucks travel along frictionless; flat surface towards one another with the same momenta but the puck traveling towards the right has 30% greater mass than the p...

Question

Two pucks travel along frictionless; flat surface towards one another with the same momenta but the puck traveling towards the right has 30% greater mass than the puck traveling to the left: If the puck on the left initially was traveling at 8.0 m/s, half to the kinetic energy of the system was lost after the collision; and each puck is deflect 30* from their original direction of travel after the collision, what are the final speeds of the pucks? (2 points) [7.36 m/s]30.030.0"

Two pucks travel along frictionless; flat surface towards one another with the same momenta but the puck traveling towards the right has 30% greater mass than the puck traveling to the left: If the puck on the left initially was traveling at 8.0 m/s, half to the kinetic energy of the system was lost after the collision; and each puck is deflect 30* from their original direction of travel after the collision, what are the final speeds of the pucks? (2 points) [7.36 m/s] 30.0 30.0"



Answers

$\bullet$ A hockey puck $B$ rests on frictionless, level ice and is struck by a second puck $A,$ which was originally traveling at 40.0 $\mathrm{m} / \mathrm{s}$ and which is deflected $30.0^{\circ}$ from its original direction. (See Figure 8.39 .) Puck $B$ acquires a velocity at a $45.0^{\circ}$ angle to the original direction of $A$ . The pucks have the same mass. (a) Compute the speed of each puck after the collision. (b) What fraction of the original kinetic energy of puck $A$ dissipates during the collision?

Since the initial momentum of the system is zero, we have, Yeah, one point, um times the initial equals M times leaf, 10 m per second. So we find that the initial is 8.33 m per second. Now, this is for the particle. Be so that's put V B I. So now final diabetic energy equals half am V g squared just half times one point, um, times V b squared. Yeah, which equals G. I equals half M times 10 square, plus half times 1.2 times 8.33 squared equals half times m types. 1 83. Okay, now finally kind of energy is half of the initial energy, So there is a half over here. So this times have on this times have so we can cancel out the amps and we can find that V g Square plus 1.2 VB square. It was 91.7. Conservation. Off moment on leads M V. G. It was 1.2 m v b. So v g is 1.2 vb Now Put that in here and solve this equation, you will find V G equals 7.7 middle per second. Yeah, the speed of the Green Park for the Blue Park V V will come out as 5.89 m per second.

Welcome today, we'll be talking about collisions and momentum. So we have um two packs a blue and a green, they go in opposite directions. And then after colliding we'll go both at 30 degree ingles and actually it's the other way around. Yeah so it'll look something like this, the angles being 30 degrees. And also we know that the mass of the blue puck is 20% greater than the mass of the green one. Mm If we call this green one M. One there then M. Two must be equal to M. One but times some sort of factor. And because it's 20% greater we can write that it's 1.2 um of M. One and this means it's 20% greater. So from there you can start by writing down the momentum in the X. Direction and in the Y direction. So we will have that mass one. We won and this will be minus last two V. Two because the second one has a negative velocity, how's it going? In the opposite direction? And they should be equal two. Um One you one final and again minus M two V two final because it's still going in a negative direction. And from here we can write M. One V one minus um Yeah 1.2 and one Me too is equal to M. One we want and we know view this is view one final and it has an X. Component of why? So we can write it as the one final coast of 30 degrees minus 1.2. Me too Final coast of 30 degrees because there's also 30 degrees and here the M one's all cancel out and there should be someone here and this cancels out. So we can call this we can just simplify having 10 which is initial speed. The first one we one is equal to 10 minus 1.2 Me too is equal to khowst 30 you want final minus 1.2 MI two final. Now you can call this equation one for equation too, we'll have it in the Y direction and why we will have zero as they as neither of the initial velocities have a white component and this will be equal to the mass of the first times velocity final in the UAE minus one point um mass to Mhm me too final in the UAE and this is negative again because this is going in the negative direction for the Y component, so we'll have isolating for view on final and substituting first we'll have mass one. The one final sign of 30 is equal to 1.2 M one Me Too. Finals sign of 30 and here both the M one's and assigns cancel out. So we'll be left with the one final is equal to be too final multiplied by 1.2. So from there, if you want to substitute this into here, we saw three unknowns. So we can't do that. But we can use the fact that the final kinetic energy is one half of the initial kinetic energy. So because half is lost, that means half remains. So we can write that. This will be equation three. That key final is equal to one half K initial. So from there we'll have that one half and one you one final squared is equal I mean uh huh plus one half M two V two final squared is equal to one half. One half M one the one initial squared plus one half M two V two initial squared in here. You can factor out the one half and these will cancel out. And also we'll be able to cancel the M one's by replacing the M two s with 1.2 M one. So these will cancel and we'll be left. The one final squared plus V two final squared is equal to one half. Yeah, Here there should be the 0.1 as well. I mean 1.2 Eagle, one half View, one squared cost one half, 1.2. Me Too Final square do initial square. So now we have three equations and three unknowns and we can start to solve some of the problems here we can our number one, we'll replace equation substitute into one and we'll get the 10 minus 1.2. Be to initial is equal to Khowst 30 and we'll substitute the one final is equal to V two final times 1.2 to hear. So we'll have 1.2 V two final minus 1.2. Me Too. Final and this will cancel. This will be zero, so we'll have 10 is equal at 1.2. Me too. And this is the speed, not velocity because we already took account it's negative and we will get the V two is equal to 10 divided by 1.2. This is 8.3 three m per second. This is the speed. And from there we can replace two into three and substituting in our value for V two to find B two final. And from there we'll find view one final so we'll have you and finally the two final squared multiplied by 1.2 squared plus 1.2. The final of two squared is equal 2.5 of 10 squared plus one half, 1.2 in V two is 8.33 square. Now we want to isolate for V two. So first we can factor out the V two. You need, your final squared is equal 2.5. 10 squared plus one half, 1.2, 8.33 squared and everything divided by 1.2 squared plus 1.2. This is because we factor out the V two and to get rid of this two, well just square everything. And this will give us a value for V two final and this will be approximately 5.89 m per second. So this is one of the answers. This is the second answer. And now using equation too where you know V one final is equal to 1.2. The two final. We'll get the view one final Geico to 1.2, 5.89 And this will give us a value view on Final is equal 27 0.7 m per second. And this will be your answer for the final speed of the third of this first. Look, this is the final speed for the second part, and this is the initial speed of the second park. So thank you for listening and have a great rest of the day.

So in this exercise you have to hockey bucks A and B off Rico masses. And in the beginning, the hockey puck A has initial velocity V one off 15 m per second and hockey puck too is at rest right after the collision. Hockey Puck Chew gains a velocity, uh, pointing upwards and making a 25 degree with its initial direction. Access, which is this X axis here, and the hockey book be also gained a below Stevie B. So, in the security size, what we want to find is what is the magnitude off the final velocity off book? A. We also want to find the magnitude off, uh, the velocity of book be and we want to know what angle does the book be makes with book A. So I want to know this that I'm drawing here in green, which is what is five plus 25 degrees. Okay, so the exercise states that the collision between the bucks is perfectly elastic, so we have conservation off linear momentum and kind of energy. So it's starting with the conservation off linear momentum. We have that the components ex and why off the linear movement are conserved. So it's starting with the X component we have that the mass of Pak Wan times initial velocity V one has to be equal to the mass off back to Sorry, the mass of pack Juan times the X component off the final velocity which I'll call V H two x. Sorry if this is confusing plus the mass off rugby times the final velocity off book be in the X direction. Okay, so from here we have that the projection off V off D eight books velocity into the X Direction V A X two Uh, it's just the magnitude of the H two times the consign off 25 degrees and we can also cancel out this term. So we have that, um, the A one So is equal to V H. Two times Cool sign off 25 degrees plus B the big X, which is the be times consign off I okay now going thio the conservation on the Y direction we have that there is no initial velocity in the Y direction on in the X. So we have that zero has to be equal to am V A to why so the y direction off the final of velocity off book. Um, A plus M v b y. So this cancel and we have that v b y has to be equal to, um V A to sign off 25 degrees. Okay, so let's keep this expression for a second. Let I'll call it one. Now we have we can apply the condition off conservation off kinetic energy. So we have that the initial kinetic energy is, um the A one squared over two is equal to also put em in evidence. So over to p A two squared plus V b squared. And from this, we can cancel out am over to, and we have another relation between the three velocities, which is being a one squared is equal to V two squared, plus the big squares. Okay, so way can expand this. So have that expression to Zvi a one squared because you ve a two squared plus so I can express V b squared in terms off the X component off P and the Y component. So this is equal to V b X squared plus V b y squared. And we know that Phoebe, why is just this expression one so we can express it has in terms off v A and the angle that we know. So this is a good choo create You squared sine squared off 25 degrees. Okay, We can also rewrite be vb X from the conservation off the X component to remember that this is just V b X, and we can express it s o isolating this V a one minus v a to good sign. 25 degrees. Okay, so let's put it this here. So I'll write it in red. So we have Sorry. The A one squared plus V H two squared. Who sign squared off 25 degrees plus two times V A. One V two. Because sign off 25 degrees. Okay. This is just Do you want Bliss G two Good. Sign off. 25 degree squared. Okay. Just this thing squared. Sorry is the minus. So we have a minus here minus And also you might assign here. Okay, so So from expanding vb x and V I X. We have that this term. Very one squared from B X squared will cancel out with this. Okay? And we also have that this term here will sum up with this so we can rewrite everything as V A two squared plus v A to so squared sign squared off 25 degrees plus consigned squared off 25 degrees. Um, sorry miners to V A. One V A to consign off 25 degrees. So notice that from the trigonometry populations we have that this is equal to one. So this term sums up with this term, and we have that, uh, and all of this is equal to zero. Sorry, I forgot to write, so we can put, um so we have to v a one V H u go sign of 25 degrees is equal to two V A to squared so we can divide both sides by V two and we also divide by two. So if I found a expression off V A to in terms off things that we know, which is the initial velocity, which we know is 15 m per second and could sign off 25 degrees. And from this, we find that the magnitude of the final velocity of book A has to be equal to 13.6 meters per second. Okay, so we can use this result to find the magnitude off books Book B's Final Velocity. So going back to conservation off kinetic energy we had we had the expression that is V A one squared is equal to V A two squared plus V b squared. Okay, now we know what v a two squared iss so we can isolate VB. So you have that VB is equal to the square root off 15 squared which is V one squared minus vhe squared. So 13.6 squared and we find that the magnitude off the final velocity off books be after the elastic collision has to be equal to 6.34 m per second. Now the only thing left is to find the angle between the velocity of book A and the velocity of book. Be on. Well, since we already know V h u M v b, we can just go back to this expression here, for instance, so expression one. So we still to the values we already know. So let's go back from this is from conservation off the Y component off linear momentum so we can find the angle that puck bees makes with the horizontal from the conservation off the components off the momentum or the X component. But I'm going to take the way components So p y we had the following equality B b. Why equal to v H u sign off 25 degrees. We know vey chew, and we can express V B y as the magnitude of the B times the sign it makes with the horizontal. And for the more we can isolate uh, the angle by taking the ark sign off this term. So I have that fire is going to be deep arc sine of V A to over Phoebe time sign of 25 degrees on which VH you is just 13.6 and BB we found to be six point 34. So we find Dingle to be equal to 65 degrees. Now I want to find what is the angle phi plus 25 degrees. So 65 plus 25 is you go to 90 degrees. So we found that particles be that the book be makes a 90 degree angle with books A after the collision. So this concludes the exercise

Yeah in this question the following theater rooms the initial and final velocities of the no as the plot these initially act less and hence the initial velocity of what It was 20 and the masses of what works and we are equal so on applying low off conservation of and energy eager even equals A. That means while divided by and even Be a one square Was one divided by two. And even people are gonna be even where Equal to one divided by two. And it do be able square less one divided by and we do the you do yeah now here we substantive zero for we be well therefore bigger we even square it was you the IT to distress plus we B two square let's see right this for we be too therefore we get we be to equal so despaired of we everyone is square minus he a two is spared no applying no of conservation mm momentum how long origin and bigger we even plus we even once will be if you was 25 degrees plus we you need to was to no experience the situation for bruschetta therefore Wall street to equal still we Ayman plus we evil minus we you do was depart degree. Do I buy B B mm Now we named this as equation one now on applying no of conservation. Well momentum along were people I think that we need to Sign 25 Degree. It wants to me video All right here Now next really is the situation for scientific that was scientific equals two the do sign 25° divided by we be too. Now we consider this as equation. No no on standing and adding situation one and oh bigger we we do square equal to be everyone is scrapped plus B. It is square minus two. We even my diploma but we a new course 25 degree. Now here we substitute be even square minus we ate to scrap what we be to strap. Therefore begin being even square minus we A two square equal to we A one square less the au square minus to B. Even our people will be able to Post 25 Degree. So from a bow very we two equals two. The even Was 25 daily. Now here we substitute 15 m per second for we haven therefore figured me A two equals two 15 mighty level was 25 degree. Therefore be a. It was still 13.59. Make that for a second And the velocity of a is 13 1 59 m per second quarter. Approximately 13.6 m for a second. No. Uh huh. Island velocity. Uh uh huh. B is calculated by VB two. It was to straddle of we even the square minus will two square. Now here we substitute 13.59. Meeting for a second for viator And 15 we can for a second for the area. So we get we be to it wants to the square root or 15 only square -13.59. So we got we we do is it will do 6.329. Meet up for 2nd. Or we can write this. We'd be to equal to 6.4 m second. Hence the velocity of part B. It was to 6.34 metre but second now we have to find out the direction of velocity of being so on. Up line. Law of conservation. Well America alone, the our people bigger the A. Two sign 25 degree equals two. We we to sign kid rock. Now on the appearance in the public question for tita bigger T. Type where you sign in verse the E. Two signed 25 degree divided by we be you now here for substituting 13.59 m per second for Vh two and 6.339. Made up for a second for B. B. Two ego cheetah It was to sign in verse our team 0.59. My people I was signed and define divided by 6.3 T nine. So we got tita it was too 65. I agree Before the direction of publicity of P. It was 265 dignity


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