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$\cdot$ Three objects $A, B,$ and $C$ are moving as shown in Fig-ure $8.35 .$ Find the $x$ and $y$ components of the net momentumof the particles if we define the system to consist of (a) $A$ and$C,$ (b) $B$ and $C,$ (c) all three objects.

a) $-55 \mathrm{kg} \mathrm{m} / \mathrm{s}$b) 52 $\mathrm{kg} \mathrm{m} / \mathrm{s}$c) 0$-3 \mathrm{kg} \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

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in this problem were given three masses with mess or three objects with mass and velocity is described over here and using the convention of up being positive. Why and right Being Positive X were asked to find the total X and Y momentum of the system composing of objects and see in part a BNC and part B or all three in part C so we can simplify this question by first finding the X and Y momentum's of each object individually. So for object A. Since its velocity is entirely down with no components in the horizontal direction, all of its momentum is in the Y direction or negative y direction. And we can calculate that really easily. It's just equal to mass times velocity which we should remember, so momentum is equal to mass times philosophy. So the bass is 5.0 kilograms and the velocity in the Y direction is negative 11 0.0 meters per second. Because positive is up, that works out to be negative 55 kilogram meters per second in the Y direction in part B or rather, for object, be its. Its motion has both horizontal and vertical components, so We need to remember our trig functions here, so it's 60 degrees above horizontal. So if this angle is theta, then sign data is the adjacent over the high potty news, which in our case, is the X component over the total velocity. Well, science data is Theo opposite side over the high pot news which is thieve vertical component over over earthy, um, total philosophy. So with that knowledge, we can say that V X is equal to the total velocity Times Co sign of data, which is in this case, 60 degrees, while v y is V sign data, which is again 60 degrees. So, um, the momentum in the X direction then is equal to the mass times the velocity of be the mass. Sorry, I'll be, say, a massive B times the velocity of be in the X direction, which is in turn equal to, um, the master of B times the total velocity of B Times Co sign of data Sorry for the massive Be that should be M B like that. Plugging in the values we have. That's 6.0 kilograms. The velocity is 10.0 meters per second and, um, the angle is 60 degrees and all of this is equal to the expo mentum of the object. Be so plugging that all into a calculator, we finds that the X direction momentum of object B is 30 kilogram meters per second. Next we Duthie Why direction, momentum of object be and that's equal. Teoh. I'm gonna skip this first step because it's very similar. It's equal Teoh 6.0 kilograms times 10.0 meters per second times. Aziz, we showed down here rather than co sign. It's a sign of 60 degrees and putting this all into a calculator, we finds that that is equal to approximately 59.96 kilogram meters per second. Object C is simpler again, it's on. Lee has horizontal motion in the left directions. There's going to be negative x. It has no velocity in the vertical direction, so it's not going to have any why component to its momentum and in the X direction. We have mass of 10.0 kilograms times velocity of negative 3.0 meters per second because it's left not works out to be negative. 30 0.0 killer ground meters per second. Now for part A. We want to find the X and Y components of the total momentum of the system of a N. C. So, um, the total horizontal momentum is equal to simply the total horizontal momentum of object C, which is simply negative 30 kilogram meters per second and the Y component is simply three. The momentum of object A and that's going to be negative 55 kilogram meters per second. In part B. We have to use objects. BNC So, um, the X component of the total momentum is equal to the X component of, um, object bees. Momentum, plus the X component of objects sees momentum because they both have momentum in the X direction here. So that's going to be equal to, um, 30 kilogram meters per second, minus 30 kilogram meters per second. And that works out to be exactly zero um, further white components. Um, the object c has no velocity in the Y direction, so only the y component of object be counts only just realised a terrible mistake. This'd is incorrect. It's actually 51.96 meters per second kilogram meters per second, so the Y component of parts of object be is about 52 kilogram meters per second and that includes only the momentum in the Y direction of object. Be because objects see simply has none now. For part C, we need to add all of them together. So in the X direction, it's going to be the X direction momentum of object A, which is zero. It only has object. It only has vertical momentum. So it's going to be that of, um, object be plus that of objects e. And as we found out in part B, these cancel out and um, in the Y direction. Um, we includes the momentum from object A in the Y direction as well as the momentum from object be in the Y direction. However, object C does not have any momentum in the Y direction. It's all horizontal, so it is not included here, and that's equal to negative 55 kilogram meters per second, plus 52 kilogram meters per second and plugging that into a calculator or just doing it by hand. We find that it's negative three 0.0 kilogram meters per second. That's it for this question.

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