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A 15.0-kg fish swimming at 1.10 m/s suddenly gobbles up a 4.50-kg fish that is initially stationary. Ignore any drag effects of the water. (a) Find the speed of the large fish just after it eats the small one. (b) How much mechanical energy was dissipated during this meal?

A. $0.846 \mathrm{m} / \mathrm{s}$B. $-2.10 \mathrm{J} .2 .10 \mathrm{J}$ of mechanical energy is dissipated.

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

Cornell University

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

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problem. 8.33. We have one fish swimming up and eating a smaller fish that is stationary originally and what we want to know. We're neglecting any effects of drag in the water, so the momentum of this system is going to be conserved. So we want to know what the speed of the larger fish is going to be after it eats the smaller one. And then we want to know how much mechanical energy is lost. In this case, the only energy mechanical energy of is this system here is the kinetic energy of the moving fish. So first, let's, uh, find the final speed of our fish. It's call the big one, eh? I wanna be. So may the initial equals m a plus m b time. Be fine. So we just divide both sides. By the summer of their masses, we get the final speed every over M A plus and B times the initial speed. And so putting the the numbers in for that finders. This is 0.8 or six meters per second. Now the change in the kinetic energy, of course, is the final kinetic energy which is of the fish that's eaten the other fish times the final speed squared minus the initial energy, which just comes from a larger fish moving and then putting the numbers into that, we find that we've lost 2.10 Jules, and this is always the case, and we have a totally an elastic collision or any collision that's an elastic. But in this case, you can think of this is being a slightly odd inelastic collision because both, uh, both masses in this case fish are stuck together or one is inside of the other after the collision or engulf mint. I guess so this is how you do it, and we've got the result that matches what we had to expect, and so everything is good.

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