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$\bullet$ $\bullet$ You and three friends standat the corners of a square whosesides are 8.0 $\mathrm{m}$ long in the mid-dle of the gym floor, as shownin the accompanying figure.You take your physics book andYou take your physics book andpush it from one person to theother. The book has a mass of$1.5 \mathrm{kg},$ and the coefficient ofkinetic friction between thebook and the floor is $\mu_{k}=0.25$ . (a) The book slides from youto Beth and then from Beth to Carlos, along the lines connect-ing these people. What is the work done by friction during thisdisplacement? (b) You slide the book from you to Carlos alongthe diagonal of the square. What is the work done by frictionduring this displacement? (c) You slide the book to Kim whothen slides it back to you. What is the total work done by fric-tion during this motion of the book? (d) Is the friction force onthe book conservative or nonconservative? Explain.

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(a) $-58.8 \mathrm{J}$(b) $-41.58 \mathrm{J}$(c) $-58.8 \mathrm{J}$(d) From part (c), since the total work done during a complete round trip is not zero, therefore the friction force on the book is nonconservative.

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

Lectures

03:47

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.

04:05

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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so we know that you can create worked, and due to friction, Wharton should be called toe negative of friction Times s where s is the displacement and the reason this will be negative is because if an object is sliding along the right, then the friction force will be acting on the left. So the displacement of the frictional force are exactly opposite to each other. So let's say this is the displacement. So that's why there's a negative sign over here. So Walton is always mind self times s If that's your opinion of friction and for the friction. We know that if we're given the coefficient ofthe kind of dick friction, then frictional forces equal toe nuclear times and where and is the normal force acting on the object? So if we say the normal force is this where and that should be equal to the gravitation force acting on the object. So from there, we can say that Norman forces equal to M g, which gives us mu k times mg as our, uh, fiction, of course, no. For our problem, Mu K is given a 0.25 The weight of the book is 1.5 kg. The gravitational acceleration is 9.8. We never second spread using those. We get the frictional forces 3.675 new tenants now. Right? Okay. Now, what were given here is the following. We are sliding a book from us to bet and then from bed to Carlos. So we don't have to worry about these two signs. Let's say these Green Arrow's denote the displacement of the book. So if the book is going falling the green arrow, then the force of friction let's market with ah, red arrows. So this will read a force. Do the displacement if we call the displacement as s. So the green arrows will be the displacement and the force. Affection is the force due to the displacement, as we can see that they're opposite in direction. So for the total, Wharton, let's let's say from you two bed. We have w one as our worked and from Beto Carlos, we have the veto as our work done. So w one for the equal to negative F s, which is native 3.675 Nunes times the displacement which has given us eight meters using that we see the blue one is negative. 29.4 Jules. Similarly, for W toe, everything is same. The frictional force and the displacement. So this will be 29.4 Jews as well. So the total work done will be w one plus w two. That is roughly negative. 59 George, you for part B. Now the book has been displaced from you too, Carlos. Directly. It's not falling. It's not going to bet it's going directly to Carlos. So that means will be using the same equation. But here the displacement will be along. No, this arrow if we call, that s so let's call. It s our prime just toe. Do you know that this is different from these two? Because this is longer than this s displacement. So then the frictional force will be acting on the opposite side again. So what will happen here is well, it's spotted as prime. So s prime will be a squared plus eight squared. So we're using Pythagorean theorem here to find out s But Andi is 11.3 meters a cz. We say that the fiction, of course, is acting opposite to the displacement. So and also, the friction force is always constant in our case, because we are, um um And then the normal force is always seen. And the candidate? Ah, the coefficient of friction in same as well. So this guy right here will be 63.675 You so that only friction force our stolen weren't on duty. The frictional force will be for individuals here. A Zoe. As you can see, that if his same here. And we took this prime as our distance. And that gave us 42 jewels now for part. See, the book is book goes from you two came, and then Kim passes you back So again that the displacement is s for both of the cases. And as we can assume, you see that the forces opposite of the displacement. So the warrant, Danny's again negative s, which is 29.4 Jules. So this is when the book goes from YouTube came. And when Kim passes it back, it will be the same because the displacement isn't it is the same. And the friction is always off. So the negative things, always there for the whole world will be this w plus this is the yeah, the W Martine Black and the W. Martin Green. So if we add those weaken negative 15 angels. So the final points is that whether the force, the frictional forces kinds of real evil nonfans video. So to do so, we must remember that a force if a force is conservative, then what happens is if you bring and I'll take back then. But only four should be zero. But as you can see that when the object has been passed from you two came. And when Kim passes object that to you all the book in our days, then we have some non zero force over here. Also, that's one of the evidence is that the friction force might be known conservative, and then we have another hint. Or another rule for a conservative force is if the final point and the final point and the initial point. So that's the final point and that's an initial point are the same then for conservative force. The work done will be the same no matter what part you take. But that's not the case here because a Z can see that when the book has been passed through Bet and the worked on wass Negative five negative 59 jewels. But when the book was directly past from You, too, Carlos, then the world is negative. 42 jewels, which is not equal, So that means the forces non conservative. So that's what we wrote here. If ah so we see that but and be toe shows two different parts from U. N. Carlos. Although that worked and where the friction is different and party shows that the study in ending points are seen by the total work is not zero. So that means the frictional force is not a conservative. Thank you.

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