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Total Mechanical Energy • The total mechanical energy of a system is defined to be the sum of: • The total potential energy of the system • The total kinetic energy of the system • The symbol used for total mechanical energy is ME. The units of ME are joules. • The total mechanical energy of a system can be negative if and only if the total potential energy is negative and has a greater magnitude than the total kinetic energy. Law of Conservation of Energy Law of Conservation of Energy • When a ball flies through the air it does not lose energy even though it slows down and speeds up • The energy in the ball changes from kinetic to potential and then back to kinetic energy Example A 50.0 gram tennis ball is at rest on the ground. The tennis ball is then thrown upward… A 50.0 gram tennis ball is thrown upward – when it is at a height of 0.75 meters above the ground… The change in gravitational potential energy of the tennis ball is: PE PE f PEi 0.75 m PEg mgh f mghi PE (0.0500 kg)(9.80 m m )( 0 . 75 m) ( 0 . 0500 kg )( 9 . 80 )(0.00 m) 2 2 s s PE 0.37 J A 50.0 gram tennis ball is thrown upward – when it is at a height of 0.75 meters above the ground… When the ball reaches the height of 0.75 m, it is traveling at 1.35 m/s. The kinetic energy of the ball is: 1 2 KE mv 2 1 KE (0.050 kg)(1.35 m s) 2 2 KE 0.046 J 1.35 m/s 0.75 m A 50.0 gram tennis ball is lifted to a height of 0.75 meters above the ground. When the ball reaches the height of 0.75 m, it is traveling at 1.35 m/s. What is the total mechanical energy of the system? ME KE PE ME 0.046 J 0.37 J ME 0.42 J KE 0.046 J PE 0.37 J 1.35 m/s 0.75 m