1. Group Work 1.A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall. a.What is the direction of the net force on the ball as it squishes into the wall? b.What is the direction of the net force on the ball as it pushes away from the wall? v

2. Group Work 1.A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall. c.What is the sign of the work done on the ball as it squishes into the wall? d.What is the sign of the work done on the ball as it pushes away from the wall?

3. Group Work 1.A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall. e.If the ball’s initial and final speeds are equal, what is the net work done on the ball?

4. Announcements Exam 2 Thursday –impulse, momentum, Newton’s third law, conservation of momentum, work, kinetic energy, gravitational potential energy –Standards 6–9 First re-do of Standards 2–5 Thursday too –If you do the practice problems before Wed

5. Work-Energy Theorem The work done on an object by the net force acting on it is its change in kinetic energy. ∑F·  r =  K

6. Objective Calculate the average power necessary to change an object’s energy by a given amount in a given time.

7. Power Rate of doing work  E = change in energy ( = work)  t = time interval Power = EE tt = w tt

8. Units of Power = J/s= W = watt Power = EE tt W = kg m 2 s 2 s kg m 2 s3s3 = Energy time

9. Group Work 2.The 2004 Tour de France’s Alpe d’Huez time trial stage was a steep climb with its finish 1200 m higher than the start. Lance Armstrong won with a time  t of 39:41 (2381 s). He and his gear had a combined mass of 84 kg. What was Lance’s average power  E/  t during the stage? Hint: Use change in gravitational potential energy for  E.

10. Power A different but equivalent formula Power = w tt = F·dF·d tt = F·v v = velocity  d = change in position

11. Example Problem Show that (force·velocity) gives the same units as (work/time). force units = velocity units = work units = time units =

12. Conservation of Energy

13. What’s the point? Nature keeps careful account of energy.

14. Objectives Track energy transfers in interactions.

15. Which is greater? A. The force F 1 exerted downward on the lever arm B. The force F 2 exerted upward on the rock C. They are the same magnitude Think Question

16. Which is greater? A. The distance d 1 traveled by the lever arm B. The distance d 2 traveled by the rock C. They are the same distance Think Question

17. Which is greater? A. The work done on the lever arm B. The work done on the rock C. They are the same Poll Question

18. Simple Machines Input and output forces can be different Trade-off is distance traveled Work is unchanged –work input = work output

19. Simple Machines

20. Conservation of Energy Energy can be transferred between objects or transformed into different forms, but the total amount of energy can never change.

21. Convert Potential  Kinetic Gravity exerts force mg as object drops distance h. work = mgh PE decreases mgh KE increases mgh Source: Griffith, The Physics of Everyday Phenomena

22. Conservation of Energy Source: Griffith, The Physics of Everyday Phenomena

23. Think Question The piglet has a choice of three frictionless slides to descend. Which slide’s path gives the piglet the greatest change in potential energy? ABC D.Same for all.

24. Think Question The piglet has a choice of three frictionless slides to descend. At the end of which slide will the piglet have the greatest kinetic energy? ABC D.Same for all.

25. Poll Question The piglet has a choice of three frictionless slides to descend. Down which slide will the piglet have the greatest speed at the end? ABC D.Same for all.

26. Poll Question If the slides have friction, with the same  against the piglet, along which is the force of friction the greatest? ABC D.Same for all.

27. Poll Question If the slides all have the same  > 0 against the piglet, along which will friction do the most (negative) work on the piglet? ABC D.Same for all.

28. Poll Question All three slides have the same  > 0 against the piglet. Down which slide will the piglet have the greatest speed at the end? ABC D.Same for all.

29. Rebound and Stop initial vfinal vinitial v final v = 0

30. Think Question Which changes its momentum the most? A.A moving object that stops when it hits a barrier. B.A moving object that bounces back from a barrier. Hint: Momentum is a vector.

31. Poll Question Which changes its kinetic energy the most? A.A moving object that stops when it hits a barrier. B.A moving object that bounces back from a barrier. Hint: kinetic energy depends on speed, not direction.

32. Inelastic Collisions Total kinetic energy decreases. Work done against friction and drag: –is not stored as potential energy –cannot be recovered as kinetic energy Thermal energy increases. Energy is conserved!

33. Reading for Next Time Uniform circular motion Big ideas: –Direction of motion changes but speed does not. –Acceleration and net force are well-defined, with a specific direction.