1. PH 201 Dr. Cecilia Vogel Lecture 14

2. REVIEW  Kinetic energy  Potential Energy  Energy Conservation OUTLINE  Friction and Energy  Power  Center of mass

3. Conservation of Energy  If we take into account dissipated energy,  energy of  if the system isn’t isolated,  W =  U +  K + E diss  isolated system   U +  K + E diss = 0

4. Friction and Energy  How much energy will be dissipated?  energy dissipated by kinetic friction:  This is not the work done by friction  friction is not taking the energy away from the object  it just turns it into thermal energy  The system still has the energy, it’s just not mechanical energy anymore

5. Power  Often it is important, not only how much work is done, how much energy is lost or gained,  but  Power is the rate of energy transfer

6. Power and Force  The amount of energy transferred by a force in a time  t depends on the  In the limit as  t goes to zero, we get

7. Power Example A 35-kg girl slides down a hill. The length of the hill is 3.0 m, the height of the hill is 1.1 m. She starts from rest. By the time she reaches the bottom, her speed is 0.75 m/s. What is the rate at which gravity is doing work on the girl: a)just as she starts? b)just as she gets to the bottom? mg v

8. Momentum  Define the momentum as p=mv  then the above equation says: p i =p f  the total momentum of a system is conserved (if no net external force)

9. Momentum  Two carts of equal mass begin at rest, then a spring between them releases, sending them in opposite directions. After this, do the carts have the same magnitude of momentum? __ Do they have the same speed?__ a)yes, yes b)yes, no c)no, yes d)no, no

10. Momentum  Two carts of UNequal mass begin at rest, then a spring between them releases, sending them in opposite directions. After this, which cart has larger magnitude of momentum? __ Which has larger speed?__ a)neither, neither b)neither, lighter c)heavier, neither d)heavier, lighter

11. Momentum  One cart begins at rest, the other cart is moving toward it with speed, v. They collide and stick together. What is the speed of the two (together) just after they stick together? a)0 b)v c)<v d)>v

12. Calculus  Are you planning to take Calc II next term (winter)? a)yes b)no c)maybe – leaning toward yes d)maybe – leaning toward no