1 CONSERVATION LAWS IN PHYSICS 1. Up to this point we have dealt only with Newton’s laws of dynamics: a) Fma (First and second laws) b) FFAB BA (Third law). 2. We now turn to a discussion of the conservation laws of physics: a) conservation of energy b) conservation of linear momentum c) conservation of angular momentum 3. We will use Newton’s laws to derive these important conservation theorems (or laws). It is important to understand that we will not “prove” the conservation laws, but simply derive them as consequences of Newton’s laws. 4. A conservation law or theorem states that a certain defined quantity remains constant no matter what changes may occur. This quantity has the same numerical value before and after the changes occurred. For example, forces may act on an object between some initial and final time, or between some initial or final position, but certain quantities have the same value in the final state as it had in the initial state. 5. The application of these conservation laws allows us to reach certain conclusions about the state of an object without the need for a detailed analysis of all of the various forces acting on it in a given situation in the course of its motion. The quantities: kinetic energy, work, potential energy, linear momentum, and angular 2 momentum, will be defined, and Newton’s laws will be used to derive various conclusions about them. The use of the conservation laws will enable us to solve certain dynamical problems more easily than by the direct application of Newton’s laws. 6. The first conservation theorem that will be considered is the law of conservation of energy. As far as we know, this is an exact law that governs all natural phenomena; no exceptions to this principle have yet to be discovered. 7. We have such confidence in the conservation of energy principle, that it has been used as the basis for other discoveries. For example, there is a nuclear process called beta decay in which involves the decay of a neutron (zero charge) into a proton (+1 charge unit), an electron (1 change unit), and a uncharged particle called an anti- neutrino . In a typical beta decay carbon-14 is transformed into nitrogen-14: 14 14 67CNe . 8. When the energies involved in this reaction were considered, it appeared that there was less energy after the reaction than before the reaction. Enrico Fermi in 1931 suggested that another particle, the anti-neutrino, might be involved in beta decay and account for the missing energy. Because neutrinos have no charge and nearly zero mass (still disputed), they are extremely difficult to detect. Neutrinos were detected experimentally in 1956 by Cowan and Reines. 9. There is no complete understanding of what energy is. The energy concept was extended to include heat in the 18th century. It was later extended by Einstein to include mass in 1905. Nonetheless, we have formulas for calculating it, and find that no matter what happens, its numerical value is always the same. 3 WORK AND ENERGY 1. Work and energy are words that have certain common meanings, e.g., a) energy is the ability to do work, and b) the work done on an object can increase or decrease its energy 2. As physics concepts, these terms are given very specific definitions that may differ from our common understanding of the terms. For example, according to the physics definition, a person at rest holding a heavy object is actually doing no work. Someone employed to hold a heavy object for some period of time would certainly argue that this was work. Work is done, however, when a person lifts the object off of the ground. 3. In physics, work requires force and displacement in the direction of the force. Forces acting in a direction perpendicular to the displacement of an object do no work on it. For example, suppose a box is pushed across a frictionless horizontal surface by a horizontal force F. Work is performed only by the applied force F, and no work is done by gravity w or the normal force N. N F mg 4. The physics definition of energy also may be different from our everyday meaning. We might consider an object that is at rest to have no energy. However, according to physics definitions, objects can have a form of energy due to its position, even if it is not moving. The energy of a moving object is called kinetic 4 energy and the energy due to position is called potential energy. Potential energy is produced when an object is lifted up and converted back to kinetic energy when it is released and falls back. Work is one mechanism for transforming energy from one form to another. 5. The pile driver demonstration shown in the picture provides an excellent illustration of the connection between work and energy. A mass m is lifted and then released. It falls back down and crushes a pop can. In terms of work and energy, this involves the following processes: a) Work is done by some external agent to lift the mass b) The work done on the object is stored as potential energy m c) When the object is released, the potential energy is converted pop into kinetic energy because gravity does work on it d) The kinetic energy is used to do work to crush the pop can. .