Physics 218 Lecture 12

1. Physics 218Lecture 12 Dr. David Toback Physics 218, Lecture XII

2. Checklist for Today • Things due for Last Thursday: • Read Chapters 7, 8 & 9 • Things that were due Yesterday: • Chap 5&6 turned in on WebCT • Things due for Wednesday’s Recitation: • Problems from Chap 7 • Things due for this coming Monday: • Problems from Chap 7 on WebCT Physics 218, Lecture XII

3. The Schedule This week: (2/25) • HW on Chaps 5&6 on WebCT • 3rd and 4th lectures (of six) on Chapters 7, 8 & 9 • Chapter 7 in recitation Next week: (3/3) • Chapter 7 due in WebCT • 5th and 6th lectures (of six) on Chapters 7, 8 & 9 • Chapter 8 in recitation • Following Wee Following week: (3/10) Spring Break!!! Following Week: (3/17) • Chapter 8 due in WebCT • Reading for Chapters 10 & 11 • Lecture on Chapters 10 & 11 • Chapter 9 and Exam 2 Review in recitation Following Week: (3/24) • Chapter 9 due in WebCT • Exam 2 on Tuesday • Reading for Chapters 12 & 13 for Thursday • Lecture 12 & 13 on Thursday Physics 218, Lecture XII

4. Chapters 7, 8 & 9 Cont Last time: • More on Work This time • Work and Energy • The Work-Energy relationship • Potential Energy • Conservation of Mechanical Energy • Conservation of Energy Physics 218, Lecture XII

5. Physics 218, Lecture XII

6. Different Style Than the Textbook I like teaching this material using a different style than the textbook • Teach you the concepts • Give you the important equations • Then we’ll do lots of problems Physics 218, Lecture XII

7. Kinetic Energy and Work-Energy • Energy is another big concept in physics • If I do work, I’ve expended energy • It takes energy to do work (I get tired) • If net work is done on a stationary box it speeds up. It now has energy • We say this box has “kinetic” energy! Think of it as Mechanical Energy or the Energy of Motion Kinetic Energy = ½mV2 Physics 218, Lecture XII

8. Work-Energy Relationship • If net work has been done on an object, then it has a change in its kinetic energy (usually this means that the speed changes) • Equivalent statement: If there is a change in kinetic energy then there has been net work on an object Can use the change in energy to calculate the work Physics 218, Lecture XII

9. Summary of equations Kinetic Energy = ½mV2 W= DKE Can use change in speed to calculate the work, or the work to calculate the speed Physics 218, Lecture XII

10. Multiple ways to calculate the work done Multiple ways to calculate the velocity Physics 218, Lecture XII

11. Multiple ways to calculate work • If the force and direction is constant • F.d • If the force isn’t constant, or the angles change • Integrate • If we don’t know much about the forces • Use the change in kinetic energy Physics 218, Lecture XII

12. Multiple ways to calculate velocity If we know the forces: • If the force is constant F=ma →V=V0+at, or V2-V02 = 2ad • If the force isn’t constant • Integrate the work, and look at the change in kinetic energy W= DKE = KEf-KEi = ½mVf2 -½mVi2 Physics 218, Lecture XII

13. Quick Problem I can do work on an object and it doesn’t change the kinetic energy. How? Example? Physics 218, Lecture XII

14. Problem Solving How do you solve Work and Energy problems? BEFORE and AFTER Diagrams Physics 218, Lecture XII

15. Problem Solving Before and After diagrams • What’s going on before work is done • What’s going on afterwork is done Look at the energy before and the energy after Physics 218, Lecture XII

16. Before… Physics 218, Lecture XII

17. After… Physics 218, Lecture XII

18. Compressing a Spring A horizontal spring has spring constant k • How much work must you do to compress it from its uncompressed length (x=0) to a distance x=-D with no acceleration? You then place a block of mass m against the compressed spring. Then you let go. • How much work will be done by the spring? • Assuming no friction, what will be the speed of the block when it separates at x=0? Physics 218, Lecture XII

19. Potential Energy • Things with potential: COULD do work • “This woman has great potential as an engineer!” • Here we kinda mean the same thing • E.g. Gravitation potential energy: • If you lift up a brick it has the potential to do damage Physics 218, Lecture XII

20. Example: Gravity & Potential Energy You lift up a brick (at rest) from the ground and then hold it at a height Z • How much work has been done on the brick? • How much work did you do? • If you let it go, how much work will be done by gravity by the time it hits the ground? We say it has potential energy: U=mgZ • Gravitational potential energy Physics 218, Lecture XII

21. Mechanical Energy • We define the total mechanical energy in a system to be the kinetic energy plus the potential energy • Define E≡K+U Physics 218, Lecture XII

22. Conservation of Mechanical Energy • For some types of problems, Mechanical Energy is conserved (more on this next week) • E.g. Mechanical energy before you drop a brick is equal to the mechanical energy after you drop the brick K2+U2 = K1+U1 Conservation of Mechanical Energy E2=E1 Physics 218, Lecture XII

23. Problem Solving • What are the types of examples we’ll encounter? • Gravity • Things falling • Springs • Converting their potential energy into kinetic energy and back again E = K + U = ½mv2 + mgy Physics 218, Lecture XII

24. Problem Solving For Conservation of Energy problems: BEFORE and AFTER diagrams Physics 218, Lecture XII

25. Quick Problem We drop a ball from a height D above the ground Using Conservation of Energy, what is the speed just before it hits the ground? Physics 218, Lecture XII

26. Potential Energy A brick held 6 feet in the air has potential energy • Subtlety: Gravitational potential energy is relative to somewhere! Example: What is the potential energy of a book 6 feet above a 4 foot high table? 10 feet above the floor? • DU = U2-U1 = Wext = mg (h2-h1) • Write U = mgh • U=mgh + Const Only change in potential energy is really meaningful Physics 218, Lecture XII

27. Other Potential Energies: Springs Last week we calculated that it took ½kx2of work to compress a spring by a distance x How much potential energy does it now how have? U(x) = ½kx2 Physics 218, Lecture XII

28. Problem Solving For Conservation of Energy problems: BEFORE and AFTER diagrams Physics 218, Lecture XII

29. Conservation of Energy Problems Before… Physics 218, Lecture XII

30. After Physics 218, Lecture XII

31. Falling onto a Spring BeforeAfter Z Z C We want to measure the spring constant of a certain spring. We drop a ball of known mass m from a known height Z above the uncompressed spring. Observe it compresses a distance C. What is the spring constant? Physics 218, Lecture XII

32. Roller Coaster • You are in a roller coaster car of mass M that starts at the top, height Z, with an initial speed V0=0. Assume no friction. • What is the speed at the bottom? • How high will it go again? • Would it go as high if there were friction? Z Physics 218, Lecture XII

33. Non-Conservative Forces • In this problem there are three different types of forces acting: • Gravity: Conserves mechanical energy • Normal Force: Conserves mechanical energy • Friction:Doesn’t conserve mechanical energy • Since Friction causes us to lose mechanical energy (doesn’t conserve mechanical energy) it is a Non-Conservative force! Physics 218, Lecture XII

34. Law of Conservation of Energy • Mechanical Energy NOT always conserved • If you’ve ever watched a roller coaster, you see that the friction turns the energy into heating the rails, sparks, noise, wind etc. • Energy = Kinetic Energy + Potential Energy + Heat + Others… • Total Energy is what is conserved! Physics 218, Lecture XII

35. Conservative Forces If there are only conservative forces in the problem, then there is conservation of mechanical energy • Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another • Good examples: Gravity and Springs • Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc… Mechanical energy is lost. • Good example: Friction (like on Roller Coasters) Physics 218, Lecture XII

36. Law of Conservation of Energy • Even if there is friction, Energy is conserved • Friction does work • Can turn the energy into heat • Changes the kinetic energy • Total Energy = Kinetic Energy + Potential Energy + Heat + Others… • This is what is conserved • Can use “lost” mechanical energy to estimate things about friction Physics 218, Lecture XII

37. Roller Coaster with Friction A roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Physics 218, Lecture XII

38. Energy Summary If there is net work on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up  Work done.) Wnet = DK If there is a change in the potential energy, some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball) DUTotal = WPerson =-WGravity Physics 218, Lecture XII

39. Energy Summary If work is done by a non-conservative force it does negative work (slows something down), and we get heat, light, sound etc. EHeat+Light+Sound.. = -WNC If work is done by a non-conservative force, take this into account in the total energy. (Friction causes mechanical energy to be lost) K1+U1 = K2+U2+EHeat… K1+U1 = K2+U2-WNC Physics 218, Lecture XII

40. Next time… • More problems on Chapters 7, 8 & 9 • Recitation tomorrow on Chapter 7 problems Physics 218, Lecture XII

41. End of Lecture Notes Physics 218, Lecture XII

42. Next Week • Reading for Next Time: • Finish Chapters 7, 8 and 9 if you haven’t already • Non-conservative forces & Energy • Chapter 5&6 Due Monday on WebCT • Start working on Chapter 7 for recitation next week Physics 218, Lecture XII

43. Energy • Conservation of Mechanical Energy problems • Conservative Forces • Conservation of Energy Physics 218, Lecture XII

44. Roller Coaster with Friction A roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2). An odometer tells us that the total scalar distance traveled is d. Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Physics 218, Lecture XII

45. What if the Roller Coaster had Friction? • If there were no friction, the roller coaster would go back up to height Z and come to a stop (then come back down again) Physics 218, Lecture XII

46. Roller Coaster • You are in a roller coaster car of mass M that starts at the top, height Z, with an initial speed V0=0. Assume no friction. • What is the energy at the top? • What is the speed at the bottom? • How much work is done by gravity in going from the top to the bottom? Z Physics 218, Lecture XII

47. Friction and Springs A block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed vo and compresses it by an amount D. Determine m Physics 218, Lecture XII

48. Bungee Jump A jumper of mass m sits on a platform attached to a bungee cord with spring constant k. The cord has length l (it doesn’t stretch until it has reached this length). How far does the cord stretch Dy? l Physics 218, Lecture XII