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316    Chapter 7  Conservation of Energy and an Introduction to Energy and Work

                                                converted back into kinetic or potential energy. In many cases the amount of dissipated
                                                energy will be small enough that we will choose to ignore it. If all of the kinetic energy
                                                got stored in the compression of the ball, then the ball would have the potential to come
                                                flying off the wall with the same speed and exactly the same shape it had when it first
                                                struck the wall. We call this energy stored in the reversible changes in a configuration of
                                                the system (in this case the compression of the ball) potential energy.
                                                Conservative and Nonconservative Forces

                                                To use potential energy instead of force to describe and predict motion for a system, the
                                                force must be like that exerted by an ideal spring or the gravitational force: The work
                                                done by the force does not depend on the path taken (the total distance), just the dis-
                                                placement of the point of contact of the force. Such a force is called a conservative force.
                                                Another way this is often stated is that if a force exerted on an object does no net work
                                                during any closed loop (zero displacement but not zero distance), then the force is said
                                                to be conservative. If the net work is not zero, the force is said to be nonconservative. (In
                                                Chapter 8 we’ll more fully develop this term.) By contrast, the kinetic friction force is an
                                                example of a nonconservative force for which we cannot use the concept of potential
                                                energy. The reason is that unlike the force exerted by an ideal spring, the “work” (the
                                                quotation marks are intentional and will be explained soon!) done by the kinetic friction
                                                force does depend on the path taken from the initial point to the final point.
                                                    In Figure 7-15a we slide a book across a tabletop from an initial point to a final
                                                point along two different paths. Along either path the kinetic friction force has the
                                                same magnitude and points opposite to the direction of motion. Hence the kinetic fric-
                                                tion force does more (negative) “work” along the curved path than along the straight
                                                path. Because the “work” done by kinetic friction depends on more than just the initial
                                                and final positions, we can’t write it in terms of a change in potential energy. That’s
                 WATCH OUT  !                   why there’s no such thing as “friction potential energy.”
                                                    Remember, potential energy is associated with reversible changes in a system’s
                 Conservative forces have two   configuration, so there is an equivalent way to decide whether a certain kind of force
                 defining properties.           is conservative: If the work done by the force on a round trip (that is, one where the
                                                initial and final positions are the same) is zero, the force is conservative and we can use
                   For a force to be conservative,   the idea of potential energy instead of using the force to describe or predict motion.
                   it must (1) depend on        This is the case for the gravitational force. If you toss a ball straight up, the gravita-
                   a reversible change in       tional force does negative work on the ball as it rises and positive work on the ball as
                   configuration, such as a             y  = y , then W  =−mgy  + mgy  = 0. The same is true for the spring force:
                   change in length of a spring   it falls. If  f  i  grav  2  f 2  i
                                                                           1
                   or a change in separation    If x f  = x , then W spring  =  1 2  kx f  − kx i  = 0. But if you slide a book on a round trip on a
                                                       i
                                                                           2
                   between Earth and an object,   tabletop, the total amount of work that you do on the book is not zero (Figure 7-15b). To
                   and (2) involve no dissipation   keep the book moving, you have to do positive work on the book as you push it.
                   of energy by the system          If there were no kinetic friction, you would have to push the book to get it going,
                   exerting the force.          push it again if you wanted to change its direction, and push it again to stop it. Getting
                                                it going and stopping it in each direction would require equal magnitude and opposite
                                                amounts of work (pushing in the direction of motion, and then opposite the direction

                 Figure 7-15  Nonconservative   (a)                                 (b)
                 forces Because the amount of energy   Friction dissipated more energy along   The book makes a round trip that begins and
                                                    path 2 than along path 1. Since the
                                                                                        ends at this point. As you push the book
                 dissipated by kinetic friction depends   “work” done (energy dissipated) by   around the path, you decide where to push
                 on the path, it is a nonconservative   friction depends on the path, we conclude   the book and where to stop and start it, and
                 force. Any force that does nonzero   that friction is not a conservative force.  you have to use your own internal energy. So
                 net work on a round trip or requires                                   we can conclude that force exerted by a
                 internal energy is nonconservative.                                    person is not a conservative force.

                                                       Path 1
                                                                 Path 2
                                                                                          Path 1    Path 2









                            Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
                            Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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