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# You and three friends stand at the corners of a square ISBN: 9780321675460 31

## Solution for problem 31E Chapter 7

University Physics | 13th Edition

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Problem 31E

You and three friends stand at the corners of a square whose sides are 8.0 m long in the middle of the gym floor, as shown in Fig. You take your physics book and push it from one person to the other. The book has a mass of 1.5 kg, and the coefficient of kinetic friction between the book and the floor is ???k = 0.25. (a) The book slides from you to Beth and then from Beth to Carlos, along the lines connecting these people. What is the work done by friction during this displacement? (b) You slide the book from you to Carlos along the diagonal of the square. What is the work done by friction during this displacement? (c) You slide the book to Kim, who then slides it back to you. What is the total work done by friction during this motion of the book? (d) Is the friction force on the book conservative or nonconservative? Explain. Figure:

Step-by-Step Solution:

Solution 31E Step 1 of 8: a)The friction force is constant during each displacement and The direction of the friction force can be different for different displacements. f = kmg 2 = 0.25 × 1.5 kg × 9.8 m/s = 3.675 N Direction of f is opposite to the motion. Step 2 of 8: When the motion from you to Beth the friction force is directed opposite to the displacement and W =1 f =s(3.675 N)(8 m) = 29.4 J Step 3 of 8: When the motion from Beth to Carlos the friction force is again directed opposite to the displacement and W = f = (3.675 N)(8 m) 2 s = 29.4 J W = W + W total 1 2 = 29.4 J 29.4 J = 59 J Step 4 of 8: b) s = 2(8 m)2 = 11.3 m f is opposite to s , so W = fs= (3.675)(11.3 m) = 42 J

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##### ISBN: 9780321675460

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