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Unformatted text preview: 8 CHAPTER OUTLINE 8.1 Potential Energy of a System 8.2 The Isolated System—Conservation of Mechanical Energy 8.3 Conservative and Nonconservative Forces 8.4 Changes in Mechanical Energy for Nonconservative Forces 8.5 Relationship Between Conservative Forces and Potential Energy Equilibrium of a System 8.6 Energy Diagrams and the Potential Energy ANSWERS TO QUESTIONS Q8.1 The final speed of the children will not depend on the slide length or the presence of bumps if there is no friction. If there is friction, a longer slide will result in a lower final speed. Bumps will have the same effect as they effectively lengthen the distance over which friction can do work, to decrease the total mechanical energy of the children. Q8.2 Total energy is the sum of kinetic and potential energies. Potential energy can be negative, so the sum of kinetic plus potential can also be negative. Q8.3 Both agree on the change in potential energy, and the kinetic energy. They may disagree on the value of gravitational potential energy, depending on their choice of a zero point. Q8.4 (a) mgh is provided by the muscles. (b) No further energy is supplied to the object-Earth system, but some chemical energy must be supplied to the muscles as they keep the weight aloft. (c) The object loses energy mgh , giving it back to the muscles, where most of it becomes internal energy. Q8.5 Lift a book from a low shelf to place it on a high shelf. The net change in its kinetic energy is zero, but the book-Earth system increases in gravitational potential energy. Stretch a rubber band to encompass the ends of a ruler. It increases in elastic energy. Rub your hands together or let a pearl drift down at constant speed in a bottle of shampoo. Each system (two hands; pearl and shampoo) increases in internal energy. Q8.6 Three potential energy terms will appear in the expression of total mechanical energy, one for each conservative force. If you write an equation with initial energy on one side and final energy on the other, the equation contains six potential-energy terms. 215 216 Potential Energy Q8.7 (a) It does if it makes the object’s speed change, but not if it only makes the direction of the velocity change. (b) Yes, according to Newton’s second law. Q8.8 The original kinetic energy of the skidding can be degraded into kinetic energy of random molecular motion in the tires and the road: it is internal energy. If the brakes are used properly, the same energy appears as internal energy in the brake shoes and drums. Q8.9 All the energy is supplied by foodstuffs that gained their energy from the sun. Q8.10 Elastic potential energy of plates under stress plus gravitational energy is released when the plates “slip”. It is carried away by mechanical waves....
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