Potential Energy and Conservation of Energy

1. Potential Energy and Conservation of Energy Work and Potential Energy Path Independence of Conservative Forces Determining Potential Energy Conservation of Mechanical Energy Work Done by External Forces Isolated Systems pps by C Gliniewicz

2. Potential energy is due to the arrangement or position of a system of objects. The potential energy can be gravitational or elastic. Potential energy is typically designated by the letter, U. The change in gravitational potential energy of an object is the negative of the work done on the object in the earth-object system. A system is a group of two or more objects. A force exists between one object and the remainder of the system. When the configuration of the system is changed the force does work and kinetic energy is exchanged with some other form of energy. If the configuration is reversed, the energy transfer is reversed. When this occurs the force is said to be conservative. A nonconservative force is one where energy is lost to heat, the random motion of molecules. pps by C Gliniewicz

3. The net work done by a conservative force around any closed path is zero. The work done by a conservative force between any two points is independent of the path taken. It requires the same amount of work to get from A to B no matter what path is taken. The mechanical energy of a system is the sum of the kinetic and potential 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 cannot change. Since one knows that potential energy is the integral of the force with respect to distance, the equation can be reversed to find the force. A graph of energy vs. displacement can display information about the potential energy at any given position. From the equation above, one can determine that when the energy reaches the total mechanical energy, there is no kinetic energy and the direction of motion changes. pps by C Gliniewicz

4. An object is in neutral equilibrium when the graph is flat. There is no change in the potential energy. This is equivalent to a ball on a horizontal surface. An object in unstable equilibrium exists when the object is at a local maximum of potential energy. Any small displacement from that position reduces the potential energy and increases the kinetic energy (movement). An object in stable equilibrium is at a local minimum. Any small displacement from that position would bring it back to same position. Work is energy transferred to or from a system by means of an external force which acts on that system. If there is no friction involved, If there is friction involved, the formula must account for the thermal energy which is formed by friction. The total energy of a system can change only by the amount of energy transferred to or from the system. In an isolated system, the total energy cannot change. Power is the rate at which a force does work on a system. pps by C Gliniewicz