CONSERVATION LAWS IN PHYSICS ∑, Lecture notes of Law

Download CONSERVATION LAWS IN PHYSICS ∑ and more Lecture notes Law in PDF only on Docsity! 1 CONSERVATION LAWS IN PHYSICS 1. Up to this point we have dealt only with Newton’s laws of dynamics: a)    F ma (First and second laws) b)     AB BAF F (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 6 7 .  C N e 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.