Chapter 6. The law of conservation of energy (6-28)

Review

Equation 6-28 suggests that we broaden our definition of energy to include both total mechanical energy \((E = K + U)\) and internal energy \(E_{\mathrm{other}}\). In this case, we have to expand the system to include not only the object and the sources of the conservative forces that produce \(\Delta{U}\), but also the sources of the nonconservative forces that result in \(\Delta{E}_{\mathrm{other}}\) (like your hand in the case of the thrown pencil). As the object moves, \(K\), \(U\), and \(E_{\mathrm{other}}\) can all change values, but the sum of these changes is zero: One kind of energy can transform into another, but the total amount of energy of all forms remains the same. This is the most general statement of the \(\textbf{law of conservation of energy}\).