Chapter 9.9 Efficiency The percentage of how much mechanical energy remains after some of it is transferred (dissipated) to non-useful energy

Efficiencies of Some Energy Systems Gasoline-Powered Automobile (35% efficient) Transmission of electricity from the electric power station across high-voltage lines (90-93% efficient)

9.7 Conservation of Energy Part of the PE of the wound spring changes into KE. The remaining PE goes into heating the machinery and the surroundings due to friction. No energy is lost. Energy output Energy input (elastic PE stored) Dissipated Energy What is the efficiency of the toy car? Energy output/energy input 8 J/10 J = 0.8 x 100 = 80%

Mechanical energy is not lost The roller coaster system begins with total mechanical energy stored when the roller coaster car is transported to the top of the first hill. TME = PE + KE Over the course of the ride, the TME is slowly reducing. It is not lost, it is just being transferred to dissipated energy (DE) because of friction, air resistance and vibrations as the roller coaster travels on the tracks. The increase in DE reduces the KE (and speed) of the roller coaster and the height at which the roller coaster will climb.

9.9 Efficiency In any machine, some energy is transformed into atomic or molecular kinetic energy by friction—making the machine warmer. This energy is referred to as internal energy or thermal energy, and represents non-useful energy that has been transferred away from the original total mechanical energy.

9.7 Conservation of Energy Same energy transformation applies 10 J of PE does 8 J useful work on the arrow and 2 J of non-useful work on the molecules that compose the bow and string and arrow. The arrow has 8 J of KE. The 2 J of heat can be called non-useful work (work that is not part of the object’s total mechanical energy).

9.7 Conservation of Energy Why does a tennis ball eventually stop bouncing? Eventually, all of the total mechanical energy is transformed into non-useful energy (heat, sound, movement of fibers) 50 J PE 50 J KE New height less than before means less PE stored 35 J PE 20 J PE 35 J KE 20 J KE Bounce! Bounce! (bounce and so on!)

9.7 Conservation of Energy Everywhere along the path of the pendulum bob, the sum of PE and KE is the same. Because of the work done against friction, this energy will eventually be transformed into heat. Non-useful work can also be called non-useful energy!

9.9 Efficiency If we put in 100 J of work on a lever and get out 98 J of work, the lever is 98% efficient. We lose 2 J of work input as heat. In a pulley system, a larger fraction of input energy is lost as heat. For example, if we do 100 J of work, the friction on the pulleys as they turn and rub on their axle can dissipate 40 J of heat energy. This pulley system has an efficiency of 60%.

9.9 Efficiency Transforming 100% of thermal energy into mechanical energy is not possible. Some heat must flow from the engine. Friction adds more to the energy loss. Even the best-designed gasoline-powered automobile engines are unlikely to be more than 35% efficient.