a-150-kg-fish-swimming-at-110-ms-suddenly-gobbles-up-a-450-kg-fish-that-is-initially-stationary-igno

Name: a 150 kg fish swimming at 110 ms suddenly gobbles up a 450 kg fish that is initially stationary igno
Uploaded: 2019-06-24
Duration: 3 min 50 s
Channel: Numerade
Description: 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?

Question

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?

Ben Nicholson · Accepted Answer

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&#x27;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&#x27;s, uh, find the final speed of our fish. It&#x27;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&#x27;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&#x27;ve lost 2.10 Jules, and this is always the case, and we have a totally an elastic collision or any collision that&#x27;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&#x27;ve got the result that matches what we had to expect, and so everything is good.

Zulfiqar Ali · Answer

Well, we have to. Fish is a and B the big ones masses 15.0, uh, kilogram. So I m OK, that&#x27;s the mass off big big one. And it&#x27;s equal dude, 15.0 kilogram, right? And the small ones mass is 4.5 kilograms. So small wounds Man sees 4.5 cereal kilogram Well taken. The initial direction is the positive direction we have the big piece of lost e before the collegian. Well before the cook Origen the lost ease the A one and that is equal to 1.10 Me too per second and the small our fish were lost before the collision is we B one and that is equal to zero meters per second. Well, we know that in collision off all kinds, since there is no external net force on the system are the total momentum before the collision. Nichols. The total momentum are off the religion. Therefore be one is equal to be to right momentum before collision is equal to momentum after collision. Well, if the collision is between two particles and be, then we could B one right? Let&#x27;s speed be one is equal to be into less speedy, too. Must be be to where the momentum off particle is given by so momentum off particle is given by most times velocity. But let&#x27;s call this equation of a one. Now we can write the courtroom religion, the question in the following form. Let&#x27;s write down here Marcel&#x27;s In times we a one bless Marcelo b times we b one, and that is equal to Marcelo Dinz. We ate too less muscle being times we be to. And let&#x27;s say this is equity number to this equation is equity number two Right now? Let&#x27;s to party. So we depart in well, neglecting what Straight in fact means that there is no external net force. So the momentum is concerned also after the collision the big fish it&#x27;s the small one. So they have the same final velocity. So we have be a to is equal to we be too is equal to we to now we plug our values for M A M be re Evan and we be gone and substitute for we two in three. Question number two. So we have 15.0 15 points. It&#x27;ll into one point once you don&#x27;t this 4.5 Sydell in 20 that is equal to 15 multiply by. We do this 4.5 cedar times we do and solving for we to We two is equal to 15.0 times 1.10 divided by 15.0, this 4.5 CDO and that is equal to zero point 846 Me, too, per second. And now we do part being well, let&#x27;s calculate the Connecticut before the religion. So care one is equal to okay, a one escapee, one its kinetic energies okay, and be how then is equal to one divided by two into 15.0 into 1.10 Hold square. Ah, bless Zito, and that is equal to 9.75 Julie and the kinetic energy after the collision is given by so kinetic energy after the collision is scared to and get two is equal to key to less baby to on that is equal to one divided by toe into ah, 15.0 this 4.5 into zero point it 46 old square, and that is equal to six point 981 Jewell and no change in kinetic energy. Physical took a to minus K one that is equal to six point buying it one minus 9.75 that is equal to minus 2.94 Jules. Since the fishes are in the water, there is always a force exerted by water opposite to gravity, so we can neglect the gravitational potential. Energy for the kinetic energy is all the mechanical interceding for the disparaged mechanical energy. Giving this Tom meal is 2.94 Jewell. So it is, he added, mechanical energy is equal to 2.9 or jewels.

Ben Nicholson · Answer

problem. 7.67. We have a three kilogram fish that&#x27;s on the end of a spring. With the spring constant of 900 newtons per meter, the spring is neither compressed or nor stretched initially. And so the position of the fish zero initially it&#x27;s then released from rest. And we&#x27;d like to know what? What is it? Speed after it&#x27;s descended five centimeters. And what is the maximum speed of the fish as it&#x27;s descending? So we use energy conservation. Uh, so the initial kinetic energy is zero initial potential. Energy is mg. Why? Why is distance It&#x27;s descending. So we&#x27;re going to call 0.5 meters below the initial position. Y equals zero, and then so its initial position is y equals five centimeters. Okay, uh, so that why is that? Its position above that point? And then the kinetic energy at the point of interest is 1/2. I have he squared. Potential is 1/2 okay, y squared because the spring will be stretched by why. And it&#x27;s at the point where we said that the gravitational potential energy is equal to zero. So we know why. And we know most of these other things aside from V So we saw this for pour que tu. We know that this is equal to M g y minus 1/2 k y squared. And if you put the numbers in, this has a value of zero point 34 five jewels and then we can put this into an expression we can get from from this for a V two or no, actually, we don&#x27;t even need to do that. We just know that we know that Que tu, whose number numerical value we know is equal to one, have m b squared. And so this is equal to K two over m. That should be a capital K. So this is equal zero point for a zero meters per second four you meters. Now for part B, we want to know what is what is the maximum speed fish has. And that&#x27;s when a two is at its maximum. And so we take the derivative okay to with respect toe, why find where what the y value is, where the the kinetic energy is maximized. We can put that into here to find its numerical value and then use this equation again. So It&#x27;s a derivative with respect. Why is mg minus K? Why? So that implies that why here is equal 20 point 32 Sorry, 2.0 32 67 meters. And now this means that K too has using this has a value. Those your point for eight 01 Jules. And then this supply implies that me too, which again is equal which the square twice the kinetic energy divided by the mass is equal to zero point by 66 meters per second. And our answer for part B is higher than it is for party, which is good because this being the maximum value, Uh, if this were higher than that, whether this wouldn&#x27;t be the maximum, so we would be in some kind of trouble and we have to go back and figure that out. But this is the way we did. This is sort of fool proof, and the two results since this is less than or equal to this one, uh, sort of help indicate that nothing has gone awry.

Ren Jie Tuieng · Answer

it is good. So we have fish. It&#x27;s a test every spring, a little part of the spring. And this is initially at incredible Dentist. The spring is not stretched or compressed and it said is natural length and subsequent ages Fishes then released We got to find what s t speak. When is that a distance off? Your point is your five meet us from the initial position after yes, moved down by 2.5. Now we know that some of this energy right which is basically the gravitational potential Energy is converted into kinetic energy and the elastic potential energy off the spring. So we can find the kinetic energy by taking Subedi gravitational potential minus away the elastic potential energy they stopped in the spring. The gravitational potential energy We just think she times the distance Height, the s traveled elastic potential energy half times thespian constant time. See, Mr Study, spring is stretched square solving For this value, we substitute all the very sensible men&#x27;s off our fish. This tree k g, the screen constant is 900. You turn me too. So we should get your point five. Jules, you create this toe half MV Square. So we should be able to get What is Sophie fighting? The message. The fish over. Just refugee by two and ticking. He scribbles off everything we should catch for its just a second. No, to find you get maximum kinetic energy. This is, uh, not s simple. It&#x27;s We will have two little Getty entire expression for kinetic energy based on previous, uh, explanation right, Which is close to the gravitational potential energy minus away. The elastic potential on is you dare speak store But this energy x minus off K X squared Now we don&#x27;t know with X will be you will give us a maximum kinetic energy. So your news who is two different ship Kennedy and she refer Specter X if you could just cereal to find where he makes the kinetic energy will be a maximum 40 value affects. So differentiating the kinetic energy Thanks to get em, rightness kicks close to zero. So it is at a point where good the force from spring is equals to the gravitational force my body it and so we can software X king empty over key. So it is the extension, and at this point, a good extension. Okay. Substitute to solve for the connect energy. 90 constants ask you the same. K is 900 massive street kinetic energy for this case is for each 21 juice and Saudi lost he Are you quitting this toe off every square? Can&#x27;t self off Stevie to be is your 0.5 66 meters per second.

Mayukh Banik · Answer

daughter Energy is given by the amount of work done. It is power Times get ready equals three K g times. Do what Part of kilogram times? 22 hours, 22 days times 24 hours Times 3602nd All together, this would be Jews on this will come out to be 1.14 times 10 to the seven. Jewell. Now the mass of the fact barn Very. Um So the fact mosque that is getting barn is given by the efficiencies. It&#x27;ll 0.8 times the daughter energy 1.14 times 10 to the seven jewels Delighted by people are eight times 10 to the four Jewell Bar kilogram. It was 2 40 grand now, initially massive. The fact is, 0.15 times 3000 graham equals 4 50 g. So final massive. The fact is, for 50 minus 2 40 gram equals two, then

Ronald Prasad · Answer

for part A. Let&#x27;s calculate the potential energy of the diver at the apex of the dive relative the surface of water to calculate the potential energy that&#x27;s equal to M G. H. The mass is 52 0 kg, G is 9.8 meters per second squared and the height is 10.8 m. This works out to five 503 point six eight jewels. We report this answer in Kill a Jules, this&#x27;ll would be 5503 Killah jewels round up 35.50 four Kill jewels for part B Assuming that all the potential energy of the diverse converted to kinetic energy At what speed will the diver enter the water so kinetic energy to call the one half and b squared. And so this would be 5504 jewels. Pe&#x27;s equal the kinetic energy one half 52.0 kg B squared solving for V C song For the velocity Here we find that this is equal to 14.6 m per second would be the speed that the devil would end to the water. And for part C does the diver do work on entering the water. So when the diver enters the water, all its potential energy is converted to kinetic energy and some of its energy is released as heat. Therefore, work he has done by the diver.

Problem

Two fun-loving otters are sliding toward each oth…

Problem 33 Easy Difficulty

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?

Answer

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

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

University Physics

Elyse G.

Andy C.

Liev B.

Jared E.

Math Review - Intro

Algebra - Example 1

Hugh D. YoungUniversity Physics

Elyse G.

Andy C.

Liev B.

Jared E.

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

Hugh D. Young

University Physics