PHY 113 C General Physics I 11 AM – 12:15 P M MWF Olin 101 Plan for Lecture 7: Chapter 7 -- The notion of work an

1. PHY 113 C General Physics I • 11 AM – 12:15 PM MWF Olin 101 • Plan for Lecture 7: • Chapter 7 -- The notion of work and energy • Definition of work • Examples of work • Kinetic energy; Work-kinetic energy theorem • Potential energy and work; conservative forces PHY 113 C Fall 2013 -- Lecture 7

2. 7.3,7.15,7.31,7.34 PHY 113 C Fall 2013 -- Lecture 7

3. Webassign questions for Assignment 6 -- #1 52. Consider a large truck carrying a heavy load, such as steel beams. … Assume that a 10,000-kg load sits on the flatbed of a 20,000-kg truck initially moving at vi=12 m/s. Assume that the load on the truck bed has a coefficient of static friction of mS=0.5. When the truck is braked at constant force, it comes to rest in a distance d. What is the minimum stopping distance d such that the load remains stationary relative to the truck bed throughout the breaking? m a vi f PHY 113 C Fall 2013 -- Lecture 7

4. Webassign questions for Assignment 6 -- #1 -- continued • iclicker exercise -- • Do we have enough information to calculate a? • Yes • No m a vi f PHY 113 C Fall 2013 -- Lecture 7

5. Webassign questions for Assignment 6 -- #1 -- continued m a vi f PHY 113 C Fall 2013 -- Lecture 7

6. Webassign questions for Assignment 6 -- #4 A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of q=50o with the horizontal. ms=0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary. f N f mg PHY 113 C Fall 2013 -- Lecture 7

7. f N f mg PHY 113 C Fall 2013 -- Lecture 7

8. Webassign questions for Assignment 6 -- #6 F PHY 113 C Fall 2013 -- Lecture 7

9. Preparation for the introduction of work: Digressionon the definition of vector “dot” product q PHY 113 C Fall 2013 -- Lecture 7

10. Digression: definition of vector “dot” product -- continued q PHY 113 C Fall 2013 -- Lecture 7

11. Digression: definition of vector “dot” product – component form q Note that the result of a vector dot product is a scalar. PHY 113 C Fall 2013 -- Lecture 7

12. Definition of work: F dr ri rj PHY 113 C Fall 2013 -- Lecture 7

13. Units of work: • work = force · displacement = (N · m) = (joule) • Only the component of force in the direction of the displacement contributes to work. • Work is a scalar quantity. • If the force is not constant, the integral form must be used. • Work can be defined for a specific force or for a combination of forces PHY 113 C Fall 2013 -- Lecture 7

14. iclicker question: A ball with a weight of 5 N follows the trajectory shown. What is the work done by gravity from the initial rito final displacement rf? 2.5m rf ri 1m 1m 10 m (A) 0 J (B) 7.5 J (C) 12.5 J (D) 50 J PHY 113 C Fall 2013 -- Lecture 7

15. Gravity does negative work: Gravity does positive work: ri rf mg mg ri rf W=-mg(rf-ri)>0 W=-mg(rf-ri)<0 PHY 113 C Fall 2013 -- Lecture 7

16. Work done by a variable force: PHY 113 C Fall 2013 -- Lecture 7

17. Example: PHY 113 C Fall 2013 -- Lecture 7

18. Example – spring force: Fx = - kx PHY 113 C Fall 2013 -- Lecture 7

19. Positive work Negative work F x PHY 113 C Fall 2013 -- Lecture 7

20. Detail: PHY 113 C Fall 2013 -- Lecture 7

21. More examples: Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward velocity of 4.9m/s. How much work is done by the rope? (A) 500 J (B) 750 J (C) 4900 J (D) None of these Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward acceleration of 4.9m/s2. How much work is done by the rope? (A) 500 J (B) 750 J (C) 4900 J (D) None of these PHY 113 C Fall 2013 -- Lecture 7

22. Another example FP n q fk mg xi xf Assume FP sinq<<mg Work of gravity? 0 FPcosq (xf-xi) Work of FP? -mkn(xf-xi)=-mk(mg- FP sin q) (xf-xi) Work of fk? PHY 113 C Fall 2013 -- Lecture 7

23. iclicker exercise: • Why should we define work? • Because professor like to torture students. • Because it is always good to do work • Because it will help us understand motion. • Because it will help us solve the energy crisis.  Work-Kinetic energy theorem. PHY 113 C Fall 2013 -- Lecture 7

24. Back to work: F dr ri rj PHY 113 C Fall 2013 -- Lecture 7

25. Why is work a useful concept? Consider Newton’s second law: Ftotal = m a  Ftotal · dr= m a ·dr Wtotal = ½ m vf2 -½ m vi2 Kinetic energy (joules) PHY 113 C Fall 2013 -- Lecture 7

26. Introduction of the notion of Kinetic energy Some more details: Consider Newton’s second law: Ftotal = m a  Ftotal · dr= m a ·dr Wtotal = ½ m vf2 -½ m vi2 Kinetic energy (joules) PHY 113 C Fall 2013 -- Lecture 7

27. Kinetic energy: K = ½ m v2 units: (kg) (m/s)2 = (kg m/s2) m N m = joules Work – kinetic energy relation: Wtotal = Kf – Ki PHY 113 C Fall 2013 -- Lecture 7

28. Kinetic Energy-Work theorem • iclicker exercise: • Does this remind you of something you’ve seen recently? • Yes • No PHY 113 C Fall 2013 -- Lecture 7

29. Kinetic Energy-Work theorem PHY 113 C Fall 2013 -- Lecture 7

30. Kinetic Energy-Work theorem Example: A ball of mass 10 kg, initially at rest falls a height of 5m. What is its final velocity? i 0 h f PHY 113 C Fall 2013 -- Lecture 7

31. A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity? Example h=0.5m h 0 PHY 113 C Fall 2013 -- Lecture 7

32. Example • A block of mass m slides on a horizontal surface with initial velocity vi, coming to rest in a distance d. vi vf=0 d Determine the work done during this process. Analyze the work in terms of the kinetic friction force. PHY 113 C Fall 2013 -- Lecture 7

33. Example -- continued f vi vf=0 d PHY 113 C Fall 2013 -- Lecture 7

34. Example A mass m initially at rest and attached to a spring compressed a distance x=-|xi|, slides on a frictionless surface. What is the velocity of the mass when x=0 ? k 0 PHY 113 C Fall 2013 -- Lecture 7

35. Special case of “conservative” forces conservative  non-dissipative PHY 113 C Fall 2013 -- Lecture 7

36. k PHY 113 C Fall 2013 -- Lecture 7

37. iclicker exercise: • Why would you want to write the work as the difference between two “potential” energies? • Normal people wouldn’t. • It shows a lack of imagination. • It shows that the work depends only on the initial and final displacements, not on the details of the path. PHY 113 C Fall 2013 -- Lecture 7

38. Work-Kinetic Energy Theorem for conservative forces: PHY 113 C Fall 2013 -- Lecture 7

39. Energy diagrams PHY 113 C Fall 2013 -- Lecture 7

40. Example: Model potential energy function U(x) representing the attraction of two atoms PHY 113 C Fall 2013 -- Lecture 7