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Two skaters collide and grab on to each other on frictionless ice. One of them, of mass 70.0 kg, is moving to the right at 4.00 m/s, while the other, of mass 65.0 kg, is moving to the left at 2.50 m/s. What are the magnitude and direction of the velocity of these skaters just after they collide?

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Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

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sign this new problem. We have two people skating on frictionless ice. Okay, so, uh, you know, we have two people that escaping on frictionless ice and you know, that just means that we're gonna have to use the law of conservation of energy. The fast one has a mass off on seventy point zero kilograms. So this is the information that's given has a Marcel's seventy point zero kilograms, and they're moving with the initial lost E towards the right, So that's going to be positive or four point zero zero meters per second. So they're moving this way. This is positive towards the right, and then the second skater has a mass off sixty five kilograms and they're moving in the opposite direction. So they're moving to the left, meaning that have lasted the initial velocity will be negative. So that just means that they're moving in the opposite direction to the to the fast skater. So they're skating and and so this is initial. The last year off be happens to be negative, uh, two point five meters a second. So that's the information we were given. And then the second part of the problem. This is what happens before. And then afterwards they're gonna collide and stick together with a common velocity. So they'll they'LL collide and stick together with a common blast. We don't know if they're going to end up going to the to the right of the left, but if they go to the right, that's positive. Quickly go to left. That's negative. So we have the final, the final Kamen velocity for both of them when they collide with each other. So you know, that's that's what we're gonna be looking for. So we want to find the final final Kamen blast you. And when they collide with each other again, you know it's friction less so they're not losing their no losses off energy. Momentum is conserved the law ofthe conservation of momentum. Using the law of conservation off momentum, I get to see that the initial momentum off the system equals to the final momentum of the system. Want to solve for the final last? So we switched those positions off the momentum and so way have their sticking to each other. So it's almost like they have a common mass or m e m be No, the but you know the moss is different, but then you combine them together. So we have a plus and then you have a final velocity. Or you can do this. You can look at them as distinct and then combined them using DCF. Final velocity is a factor. And then on the initial side, we have Marcel and then initial velocity off a plus mass of being an initial velocity off Be okay, So we are the initial velocity of B. And so we want to solve for the final Kamen velocity. If we saw for that, we end up getting Emmy of the A I That's the momentum off the fast skater and then ah, plus m b Phoebe, I, um you know, and then we divide both sides by I a muscle a plus muscle B. So we're gonna plug in the numbers. Remember the the final velocity off B, Or rather, the initial blast of Pisa is a negative. So don't forget that part off the problem. And so you know, when we plug in these numbers, we get Emmy seventy point zero kilograms plus old times initial velocity of here, which is forty four point zero zero meters per second. We have a minus because the initial lost Eun Bi's a minus put the masks right there on DH, then two point five meters per second. And then we divide all of that by the Marcel's huge, which is seventy points of kilograms plus the Marcel's B, which is sixty five point zero kilograms. When you run your numbers, you end up getting, you know, the final velocity, the common final lost. He has positive zero point eight zero meters per second. So once again remember that you want to keep the variables up until the end on. That helps you with not just simplifying the problem solving process, but also making sure that you make few mistakes when you're solving the problems. Okay, just make sure that you having fewer mistakes because you're focusing more on the concept unless on the on the actual numbers that going to the bar variables hope you enjoyed the video. Feel free to ask any questions on looking forward to seeing you in the next video. Thanks and have a wonderful day. Okay, Bye.

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