PHY 113 C General Physics I 11 AM-12:15 P M MWF Olin 101 Plan for Lecture 8:

1. PHY 113 C General Physics I • 11 AM-12:15 PM MWF Olin 101 • Plan for Lecture 8: • Chapter 8 -- Conservation of energy • Potential and kinetic energy for conservative forces • Energy and non-conservative forces • Power PHY 113 C Fall 2013-- Lecture 8

2. PHY 113 C Fall 2013-- Lecture 8

3. Comments on preparation for next Thursday’s exam PHY 113 C Fall 2013-- Lecture 8

4. Comments on preparation for next Thursday’s exam -- continued PHY 113 C Fall 2013-- Lecture 8

5. Comments on preparation for next Thursday’s exam – continued • What you should bring to the exam (in addition to your well-rested brain): • A pencil or pen • Your calculator • An 8.5”x11” sheet of paper with your favorite equations (to be turned in together with the exam) • What you should NOT use during the exam • Electronic devices (cell phone, laptop, etc.) • Your textbook PHY 113 C Fall 2013-- Lecture 8

6. Problem solving skills Equation Sheet Math skills • Advice: • Keep basic concepts and equations at the top of your head. • Practice problem solving and math skills • Develop an equation sheet that you can consult. PHY 113 A Fall 2013 -- Lecture 1

7. iclicker question Which of the following best describes your opinion about the equation sheet: I have not prepared my equation sheet yet but hope to do so soon I have a preliminary equation sheet but have not used it for doing homework I have a preliminary equation sheet and have used it for doing homework I am dreaming about preparing the equation sheet, but have not done it yet In my opinion, the equation sheet is not really necessary PHY 113 C Fall 2013-- Lecture 8

8. Review of energy concepts: PHY 113 C Fall 2013-- Lecture 8

9. Some questions from webassign Assignment #7 • In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth. • (a) How much work was done on the object by Arfeuillein this lift, assuming the object was lifted at constant velocity? T T yf yi mg mg PHY 113 C Fall 2013-- Lecture 8

10. Some questions from webassign Assignment #7 • In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth. • How much work was done on the object by gravity? T T yf yi mg mg PHY 113 C Fall 2013-- Lecture 8

11. Some questions from webassign Assignment #7 What is the work done as the particle moves from x=0 to x=3m? PHY 113 C Fall 2013-- Lecture 8

12. Some questions from webassign Assignment #7 -- continued What is the work done as the particle moves from x=8 to x=10m? PHY 113 C Fall 2013-- Lecture 8

13. Some questions from webassign Assignment #7 A 4.34-kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. What is its speed at x = 5.00 m? PHY 113 C Fall 2013-- Lecture 8

14. Work and potential energy Note: It is assumed that F is conservative PHY 113 C Fall 2013-- Lecture 8

15. Work and potential energy -- continued Example – gravity near the surface of the Earth: y yref mg mg PHY 113 C Fall 2013-- Lecture 8

16. Work and potential energy for gravity (near Earth’s surface) yref yf yi mg mg PHY 113 C Fall 2013-- Lecture 8

17. Work and potential energy continued • iclicker question • Why is there a strange “-” sign in the definition of potential energy? • Physicists like to be annoying • No reason at all • There is a somewhat good reason PHY 113 C Fall 2013-- Lecture 8

18. Work and potential energy continued For the case that the total force acting on the system is conservative, we can use the definition of potential energy with the work-kinetic energy theorem PHY 113 C Fall 2013-- Lecture 8

19. Summary of work, potential energy, kinetic energy relationships PHY 113 C Fall 2013-- Lecture 8

20. A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity? Example i h=0.5m h f PHY 113 C Fall 2013-- Lecture 8

21. Energy diagram U, K, E (J) E K U m yf yi PHY 113 C Fall 2013-- Lecture 8

22. k PHY 113 C Fall 2013-- Lecture 8

23. Energy diagrams PHY 113 C Fall 2013-- Lecture 8

24. Example: Model potential energy function U(x) representing the attraction of two atoms PHY 113 C Fall 2013-- Lecture 8

25. Comment on relationship between potential energy and (conservative) force: PHY 113 C Fall 2013-- Lecture 8

26. Example: Mass sliding on frictionless looping track • iclicker exercise: • In order for the ball completes the loop at A, what must the value of h? • h=R • h=2R • h>2R • Not enough information. i PHY 113 C Fall 2013-- Lecture 8

27. Example: Mass sliding on frictionless looping track i 0 0 PHY 113 C Fall 2013-- Lecture 8

28. Another example; first without friction Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)? • iclicker exercise: • What is the relationship of the final velocity of m1 and m2? • They are equal • m2 is faster than m1. • m1is faster than m2. PHY 113 C Fall 2013-- Lecture 8

29. Another example; first without friction T Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)? T m2 g PHY 113 C Fall 2013-- Lecture 8

30. Another example; now with friction T f Mass m1 (=0.2kg) slides horizontally on a table with kinetic friction and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)? T m2 g PHY 113 C Fall 2013-- Lecture 8

31. PHY 113 C Fall 2013-- Lecture 8

32. iclicker exercise: • Assume a mass m starts at rest at A and moves on the frictionless surface as shown. At what position is the speed the largest? • A • B • C • none of these. PHY 113 C Fall 2013-- Lecture 8

33. Power PHY 113 C Fall 2013-- Lecture 8

34. PHY 113 C Fall 2013-- Lecture 8