1. Nonconservative Forces

2. Conservation Law  In the work-energy principle, the work is divided into conservative and non-conservative forces. Kinetic energy  K = W con + W nonKinetic energy  K = W con + W non  The conservative forces have a related potential energy. Kinetic energy  K =  U + W nonKinetic energy  K =  U + W non  K +  U = W non

3. Other Forms of Energy  The conservation of energy includes nonconservative forces.  These are also called dissipative forces. The work done is always negative. The work dissipates energy. F =  F N d dd F =  F N

4. Conservation of Energy  Nonconservative forces do not violate the conservation of energy.  The energy has taken another form. Molecules vibrate moreMolecules vibrate more This becomes internal energy or heatThis becomes internal energy or heat

5. Using Friction and Energy  The hill is 2.5 km long with a drop of 800 m.  The skier is 75 kg.  The speed at the finish is 120 km/h.  How much energy was dissipated by friction? 

6. Friction and Height  Find the total change in kinetic energy.  Find the total change in potential energy.  The difference is due to friction and drag.   K = ½ mv 2 - 0  = ½(75 kg)(130 m/s) 2  = 5.4 x 10 5 J   U = mgh  = (75 kg)(9.8 m/s 2 )(-800 m)  = -5.9 x 10 5 J  W non =  K +  U  = -0.5 x 10 5 J

7. Friction and Springs  The dissipation of energy due to friction also affects the mechanical energy in a spring.  If the car stopped, the bumper dissipated the energy. next v x 980 kJ initial kinetic energy 980 kJ dissipated energy