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(II) Mass $M_{A}=35 \mathrm{kg}$ and mass $M_{\mathrm{B}}=25 \mathrm{kg} .$ They have velocities $($ in $\mathrm{m} / \mathrm{s}) \vec{\mathbf{v}}_{\mathrm{A}}=12 \hat{\mathbf{i}}-16 \hat{\mathrm{j}}$ and $\vec{\mathbf{v}}_{\mathrm{B}}=-20 \hat{\mathbf{i}}+14 \hat{\mathbf{j}}$ Determine the velocity of the center of mass of the system.

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$-1.3 \hat{\mathrm{m}} / \mathrm{s}-3.5 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

Lectures

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In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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of the center of mass of the system was given by this formula. Uh, the C M is one over total mass times to some of the individual masses product the products of the individual masses, uh, and velocities individual components, masses of velocities. Right. And remember, velocities vector here, so that is important s so in this case, it will be one times one over, um m a plus m b uh, times m a times v a factor plus m b times Vehbi factor on. So this is one over 35 plus 25 kilograms about 60 kilograms times 35 uh, programs times via is 12 I hot minor. 16 j hot meters per second. Uh, plus 25 kilograms. Um, times V b is negative. 20 I hot plus 14 jihad meters per second. Okay. And so you have one of those 60 kilograms times. Ah, so we're equating the I had a J had portion. So for the i heart, you have 35. That's actually not right, Units. The step just be comes a 35 times, uh, 12 from, um from M A plus 25 uh, times negative 20 from m B. Um and so that's in the eye. Had direction? Uh, plus in the J had direction, you have 35 times negative. 16 uh, plus 25 times 14. Um, looks, um and that's, um no que out. That's j hot direction. Uh, and so you do the arithmetic there, and what you get is you see, added equals one over 80 kilograms times our lips. One over 60 kilograms. It should be 60 uh, one over 60 kilograms. Times negative. 80. I had a minus 2 10 cat. So therefore you get negative 1.3. I hat. By the way, these are both and kilograms meters per seconds. That telegram could cancel. So you get negative one pointy. I hot, uh, minus 3.5 j hat kilometers per second. Whoops. I meant meters per second. Ah, the velocity. And it is a vector. So that's it.

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