# Consider an example wherein we lift a heavy book from

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Consider an example wherein we lift a heavy book from the ground to a tabletop. We must use a force equal to the book’s weight, mg , in order to lift it without giving it an acceleration or final kinetic energy. If we apply this force from the ground to the final height, h , the work done is mg times change in height. Because there’s no kinetic energy at the top of the lift, the work you put into the book must have gone somewhere else. The energy was stored by the interaction with the gravitational field, and will expectedly come out as kinetic energy if we were to drop the book. Your study of kinematics tells you that the book accelerates with increasing speed until it strikes the ground. Up until impact, the book’s gravitational potential energy was completely converted to kinetic energy associated with its final speed. These two ideas are summarized in the following equations. 𝑃? = 𝑚𝑔Δℎ Eqn. 5-2: Gravitational Potential Energy 𝐾? = 1 2 𝑚𝑣 2 Eqn. 5-3: Kinetic Energy This convertibility of energy from one form to another is a universal constant called the Law of Conservation of Energy which states: energy cannot be created or destroyed, only converted from one form to another. This means that energy is never truly lost in an interaction, and that physics is basically glorified accounting. Follow the energies and balance the checkbooks.
5-2 “Conservation” is another word with different meanings in everyday speech and science. Whereas in English conservation is used to mean “saving for later,” in science conservation strictly means “not lost.” When we say “energy is conserved” we mean all of the energy before an event is accounted for after the event. Friction A second question comes up in our baseball example involving the catcher. The pitcher converted potential energy into kinetic; however, when the catcher did negative work to pull the kinetic energy out of the ball, the catcher did not convert it into stored potential energy. Where did the energy go? According to the Law of Conservation of Energy, the energy extracted from the baseball still exists. As the muscles contract and res ist the ball’s forward motion, the muscle fibers rub against one another and produce heat due to friction. Other forms of energy may have also come out (sound from slapping the mitt, deformations in the ball, etc.), and the total net sum of all their contributions must add up to the original kinetic energy of the baseball. Our bodies don’t have a mechanism for converting mechanical (or kinetic) energy into stored potential energy. A spring could have stored the ball’s energy as it compresses, but even th at amount would come up “a little short” due to some slight heating. Almost all energy conversions experience some inefficiency and appear not to be conserved. We tend to make a distinction between energy that can do “useful work” and energy that is “waste.” In the analogy between energy and accounting, think about an energy conversion as a purchase with some associated “tax.”