Work-Energy Balance & Conservation of Energy
Work-energy balance
The initial kinetic energy of the particle at state 1 plus the work done on the particle between state 1 and state 2 equals the final kinetic energy of the particle at state 2.
T1 + U1-2 = T2
Work (U1-2) may be broken up into conservative (V) and non-conservative work (U1-2,non). The energy transferred dut to conservative work is stored as potential energy.
T1 + V1 + U1-2,non = T2 + V2
Conservation of energy
When there are no non-conservative forces performing work on the particle, energy is conserved. For example, the figure shows a juggler. Once the ball leaves his hand, it possesses its maximum kinetic energy. That kinetic energy is converted into potential energy as it travels upward. Once the ball reaches its apex, it has no kinetic energy and possesses its maximum potential energy. As the ball falls, the potential energy is converted back into kinetic energy.
T1 + V1 = T2 + V2
