1. Classical Mechanics Lecture 9 Today's Concepts and Examples: a) Energy and Friction b) Potential energy & force Mechanics Lecture 9, Slide 1 Midterm 2 will be held on March 13. Covers units 4-9 Unit 9 Homework Due Thursday March 12 11:30 PM. No extension!

2. Homework 8. Awesome Job! Mechanics Lecture 8, Slide 2 Average = 92%

3. Practice Exams Mechanics Lecture 8, Slide 3 Phys 1500 Exams https://utah.instructure.com/courses/320947/files - Spring 2013: http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2.pdf http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2.pdf - Solutions: http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2Soln.pdf http://www.physics.utah.edu/~springer/phys1500/exams/MidtermExam2Soln.pdf - Long Sample: https://utah.instructure.com/courses/320947/files/45779670/download?wrap=1https://utah.instructure.com/courses/320947/files/45779670/download?wrap=1 Phys 2210 Exams - Practice : http://www.physics.utah.edu/~woolf/2210_Jui/rev2.pdfhttp://www.physics.utah.edu/~woolf/2210_Jui/rev2.pdf - Spring 2015: http://www.physics.utah.edu/~woolf/2210_Jui/ex2.pdfhttp://www.physics.utah.edu/~woolf/2210_Jui/ex2.pdf

4. Main Points Mechanics Lecture 8, Slide 4

5. Main Points Mechanics Lecture 8, Slide 5

6. Incline with Friction: Work-Kinetic Energy Mechanics Lecture 8, Slide 6 Using Work-Kinetic Energy Theorem Same result as using Newton’s Law

7. H N1N1 mg N2N2   mg must be negative m Work by Friction :W friction <0 Mechanics Lecture 9, Slide 7 What is the macroscopic work done on the block by friction during this process? A) mgH B) –mgH C)  k mgD D) 0

8. Checkpoint Mechanics Lecture 8, Slide 8 What is the total macroscopic work done on the block by all forces during this process? A) mgH B) –mgH C)  k mgD D) 0 Mechanics Lecture 9, Slide 8 D m H

9. Mechanics Lecture 8, Slide 9

10. Force from Potential Energy:1D Mechanics Lecture 8, Slide 10

11. Force from Potential Energy in 3-d Mechanics Lecture 8, Slide 11 Gradient operator

12. Potential Energy vs. Force Mechanics Lecture 9, Slide 12

13. Potential Energy vs. Force Mechanics Lecture 9, Slide 13

14. Potential Energy vs. Force Mechanics Lecture 9, Slide 14

15. Potential Energy vs. Force Mechanics Lecture 9, Slide 15

16. Demo Potential Energy vs. Force Mechanics Lecture 9, Slide 16

17. Equilibrium Mechanics Lecture 8, Slide 17

18. Equilibrium points Mechanics Lecture 8, Slide 18

19. Equilibrium points Mechanics Lecture 8, Slide 19

20. Equilibrium points Mechanics Lecture 8, Slide 20

21. Block on Incline Mechanics Lecture 8, Slide 21

22. Block on Incline Mechanics Lecture 8, Slide 22

23. Block on Incline Mechanics Lecture 8, Slide 23

24. Block on Incline Mechanics Lecture 8, Slide 24

25. Energy Conservation Problems in general Mechanics Lecture 8, Slide 25 For systems with only conservative forces acting E mechanical is a constant

26. Gravitational Potential Energy Mechanics Lecture 8, Slide 26

27. Gravitational Potential Problems Mechanics Lecture 8, Slide 27  conservation of mechanical energy can be used to “easily” solve problems.  Define coordinates: where is U=0? as  Add potential energy from each source.

28. Trip to the moon Mechanics Lecture 8, Slide 28

29. Trip to the moon Mechanics Lecture 8, Slide 29 Can ignore effect of moon for this problem at level of precision for SmartPhysics

30. Trip to the moon Mechanics Lecture 8, Slide 30 …or you can practice solving the quadratic equation with many terms!!!

31. Trip to the moon Mechanics Lecture 8, Slide 31 Can NOT ignore effect of moon for this problem since the rocket is AT the moon in the end !!!!

32. Trip to the moon Mechanics Lecture 8, Slide 32

33. Trip to the moon Mechanics Lecture 8, Slide 33

34. Trip to the moon Mechanics Lecture 8, Slide 34 x x

35. Block on Incline 2 Mechanics Lecture 8, Slide 35

36. Block on Incline 2 Mechanics Lecture 8, Slide 36

37. Block on Incline 2 Mechanics Lecture 8, Slide 37

38. Block on Incline 2 Mechanics Lecture 8, Slide 38

39. Clicker Question A. B. C. D. Mechanics Lecture 8, Slide 39 Suppose the potential energy of some object U as a function of x looks like the plot shown below. Where is the force on the object zero? A) (a) B) (b) C) (c)D) (d) U(x)U(x) x (a)(b) (c)(d)

40. Clicker Question A. B. C. D. Mechanics Lecture 8, Slide 40 Suppose the potential energy of some object U as a function of x looks like the plot shown below. Where is the force on the object in the +x direction? A) To the left of (b) B) To the right of (b) C) Nowhere U(x)U(x) x (a)(b) (c)(d)

41. Clicker Question A. B. C. D. Mechanics Lecture 8, Slide 41 Suppose the potential energy of some object U as a function of x looks like the plot shown below. Where is the force on the object biggest in the –x direction? A) (a) B) (b) C) (c)D) (d) U(x)U(x) x (a)(b) (c)(d)