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(II) A $0.280-\mathrm{kg}$ croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. (a) What is the mass of the second ball? (b) What fraction of the original kinetic energy $(\Delta K / K)$ gets transferred to the second ball?

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a) 0.840 $\mathrm{kg}$b) 0.75

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

Hope College

University of Sheffield

McMaster University

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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called a Crockett ball. Um, m a on. Let's call the other one. Let's call that am Let's call the other one. Be right. Massive man and be, um And so from Equation 9-8 from the book for elastic collisions, We have head on collisions. We have the velocity of air, Um, minus velocity of Billy. Initial velocities will be called to the negative off there. The differences in their final velocities okay, minus their prime minus, maybe prime. All right, Uh, S O V b is zero. Initially, the other ball is at rest on and so on. And then And also, um, Vehbi prime is 1/2 of the original of the of the initial velocity of the cock it balls. That's 1/2 V A. And so a prime is, uh, is just negative 1/2 of the air, the original velocity off the crack. A book wrecked. So now we invoke momentum conservation. So this is part A. We invoke momentum conservation. Initially, you have m. Ava is the only momentum the animals arrest. That's equal to M a V. A prime plus, um m b ah Vehbi prime and Vehbi prime is, um uh, is is 1/2 off v A. Okay, So, uh, Vehbi promise 1/2 of A and v a prime is 1/2 off as negative 1/2 of us are m a V A is actually negative 1/2 m A v a plus 1/2 and B b B b. Most played both sides by to o r m b v a, I should say, um, you multiply both sides by two and what we get is to m A v a. Ah, plus, bring this term out to the left, plus M a. V A is equal to m B B A. Therefore, um and therefore M B is three times m a cause of years cancel. And thus it's just three times 30.28 kilograms, making a 0.84 kilograms for the mass of the second ball, all right. And in part B, we want the fraction of kinetic energy that's transferred from the original. So we just take a ratio, actually take a ratio of will be to fall a. And so for Bob, do you have 1/2 on B B square? Obviously about a 1/2 m a V a squared. Uh, and so, um ah. Looks very be prime square. So you're the one has cancel and you have m B is three times m s. That's too. Am a over m a times v b prime is Ah, the negative 1/2. Uh, the A squared whole squared, uh, over, um over v A squared, which is just be a squared on. So the V A squares cancel the Emmys. Cancel right V is cancel. You're left with three times 1/4. So that's 3/4 or 30.75 is the faction.

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