question_answer

               Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to it eventually? Is it a violation of the law of conservation of energy? 

Answer:

                  A simple pendulum is simply a heavy mass (often called bob) suspended by an inextensible string whose other end is tied to a rigid support  S. When bob of the pendulum is at extreme position A, its height is H above the mean position O; so it has potential energy equal to mgH(with no kinetic energy) so its total energy is also mgH. As the bob of pendulum swings from A to O, its height decreases and so its potential energy is converted into kinetic energy. At point O, its potential energy is zero and kinetic energy is maximum. At equilibrium position O, its total energy is in the form of kinetic energy. If is the speed of bob at O, then its kinetic energy at . At O bob has velocity towards end B, so due to inertia it swings towards B; in this duration its height again increases and its kinetic energy is converted into potential energy. At extreme position B, its kinetic energy becomes zero and its potential energy is maximum again equal to mgH which is also equal to total energy. At B, the particle is momentarily at rest and due to restoring force directed towards O, it again swings from B to A; its potential energy decreases and kinetic energy increases. At O, potential energy is again zero and kinetic energy is maximum; thus, again at O, its total energy is in the form of kinetic energy. Now at O its velocity is towards end A and due to inertia it moves towards A. During this period, its kinetic energy is again converted into potential energy, which becomes maximum equal to height at A. Thus, at A it has total energy in the form of potential energy. This completes one oscillation of pendulum. At A, it is momentarily at rest and due to restoring force now directed towards O, it again swings towards O and the process is repeated. Thus, in simple pendulum, the potential energy is converted into kinetic energy and vice versa, so that total energy is constant at every position of bob. Total energy of swinging bob = Potential energy at extreme position (A or B) = mgH = Kinetic energy at mean position At any intermediate position such as P or Q, it has partly kinetic energy and partly potential energy, but sum of both energies remains constant equal to When the bob of a simple pendulum oscillates in air, the air friction opposes its motion. As the bob of pendulum strikes the air molecules, the kinetic energy of the bob is converted into heat energy. The amplitude of pendulum decreases and finally it stops. Here, one form of energy is converted into another form of energy, so the law of conservation of energy is not violated.