Physics 111: Elementary Mechanics – Lecture 7 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

October 17, 2006Center for Solar-Terrestrial Research Introduction  Potential Energy and Conservation of Energy  Conservative Forces  Gravitational and Elastic Potential Energy  Conservation of (Mechanical) Energy  Potential Energy Curve  External Forces

October 17, 2006Center for Solar-Terrestrial Research Work and Potential Energy Potential Energy General Form Gravitational Potential Energy Elastic Potential Energy

October 17, 2006Center for Solar-Terrestrial Research (Non-)Conservative Forces  The system consists of two or more objects.  A force acts between a particle–like object in the system and the rest of the system.  When the system configuration changes, the force does work W 1 on the particle–like object, transferring energy between the kinetic energy K of the object and some other form of energy of the system.  When the configuration change is reversed, the force reverses the energy transfer, doing work W 2 in the process.  W 1 = –W 2  conservative force

October 17, 2006Center for Solar-Terrestrial Research Path Independence of Conservative Forces  The net work done by a conservative force on a particle moving around every closed path is zero.  The work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle.

October 17, 2006Center for Solar-Terrestrial Research Conservation of Mechanical Energy Mechanical Energy Conservation of Mechanical Energy In an isolated system where only conservative forces cause energy changes, the kinetic and potential energy can change, but their sum, the mechanical energy E mec of the system, cannot change.

October 17, 2006Center for Solar-Terrestrial Research Potential Energy Curve  Turning Points  Equilibrium Points Neutral Equilibrium Unstable Equilibrium Stable Equilibrium A plot of U(x), the potential energy function of a system containing a particle confined to move along the x axis. There is no friction, so mechanical energy is conserved. 1D Motion

October 17, 2006Center for Solar-Terrestrial Research Conservation of Energy  The total energy of a system can change only by amounts of energy that are transferred to or from the system.  The total energy E of an isolated system cannot change. Thermal Energy/Friction