1. PHYS 1110 Lecture 2 Professor Stephen Thornton August 30, 2012

2. An Issue Other classes are also using iClickers nearby. Therefore, we will need to change frequencies. iClicker 1 (old one): Press and hold the On/Off power button on the remote until the blue Power light begins flashing. Then press BB. A green Vote Status light on your remote will indicate that you have successfully reset the remote frequency. iClicker 2: Press and hold the On/Off power button on the remote until the BB on the LCD begins flashing.

3. Reading Quiz: What is the total displacement from start to finish? A) - 2 m B) +2 m C) +3 m D) +7 m E) +10 m

4. Reading Quiz: What is the total displacement from start to finish? A) - 2 m B) +2 m C) +3 m D) +7 m E) +10 m

5. How can we change things? Be more energy efficient. Could reduce electricity need by 15% by 2020, 30% by 2030. Develop more renewable energy. Energy policy like tax credits, policy changes. Carbon capture and storage in order to use fossil fuels. Revolutionary nuclear reactors that are simpler and safer. They probably are already imagined.

6. Hydraulic fracturing video: http://www.oerb.com/Default.a spx?tabid=242 - man talking http://www.oerb.com/Default.a spx?tabid=242 http://www.youtube.com/watch ?v=kv3cQngRPmwhttp://www.youtube.com/watch ?v=kv3cQngRPmw – watered down, woman talking

7. Solar and wind energy did not even show up in 2008, < 1% in US. By mid-2012 wind energy had grown to 50 GW (4.5%). Solar is still way behind (~0.2%), but growing by 30% a year. By some estimates it is as much as 30 GW or 3%. Wind and solar energy represent the greatest potential increase of renewable energy. There are 104 nuclear reactor power plants operating in the United States, 4 in Virginia, which generates 38% of its power.

8. Growth of Fuel Inputs to World Power Generation

9. Estimates of Levelized Cost of Electricity for New Baseload and Intermittent Sources for 2020. Dashed is actual 2007 price; shaded is range in 2007.

10. And then there is the transportation energy problem. The United States is committed to ethanol. It has been growing for 25 years and is now a political issue. US law requires us to use 10% ethanol in our gas – 15% in some places. Ethanol use is required to increase every year. Biofuel generation has not worked, but there is progress.

11. The electrical distribution system is a huge problem. At least 10% of our electricity is lost. It is a patchwork and archaic system.

13. Quiz: Which of the following energies had the greatest increase in the last few years in the US? A) Concentrated solar power B) Wind C) Biomass D) Geothermal E) Hydropower

14. Quiz: Which of the following had the greatest increase in the last few years in the US? A) Concentrated solar power B) Wind C) Biomass D) Geothermal E) Hydropower

15. One-Dimensional Coordinate System

16. Distance = total length traveled Example: You can run 2 m/s. How far can you run in 4 s? Answer: 2 m/s x 4 s = 8 m

17. Displacement Definition: displacement = change in position = final position – initial position Δx = x f - x i

18. One-Dimensional Motion Along the x-axis – do quiz What is the total distance traveled (0-4s)? What is the displacement? – Reading Quiz

19. What is the total distance traveled from start to finish? A) - 4 m B) +4 m C) +3 m D) +8 m E( +10 m

20. What is the total distance traveled from start to finish? A) - 4 m B) +4 m C) +3 m D) +8 m E( +10 m

21. Average Speed Note that this is always a positive number.

22. Average Velocity Velocity is different than speed, because velocity is a vector.

23. One-Dimensional Motion Along the x Axis What is average velocity (0 – 4 s)?

24. Motion Along the x axis represented with an x-versus-t graph

25. Average Velocity on an x-Versus-t Graph trajectory

26. Instantaneous Velocity In this way we can find the velocity at any particular instant of time.

27. What is the instantaneous velocity at t = 1 s?

28. Graphical Interpretation of Average and Instantaneous Velocity

29. Acceleration Just like velocity is given by the rate of change of position with respect to time, the acceleration is given by the rate of change of velocity with respect to time. We are still dealing with one- dimensional motion, so vector direction is simple.

30. Average Acceleration We must be very careful with units. What are they? m/s 2

31. Instantaneous Acceleration Similarity between velocity and acceleration is clear.

32. Graphical Interpretation of Average and Instantaneous Acceleration If you don’t remember about tangents, please review!

33. We use signs to denote the directions of both velocity and acceleration along a particular axis. x  When v is +, motion is to right.  When v is -, motion is to left.  When motion is to the right, and a is +, then object speeds up (accelerates) to the right.  When motion is to the left, and a is +, then object is slowing down and will eventually turn to the right. (not shown here)

34. Cars Accelerating or Decelerating speeding up slowing down Much easier to see what is happening, when we draw a picture.

35. Conceptual Quiz: The graph shows position as a function of time for two trains running on parallel tracks. Which of the following is true? A) At time t B, both trains have the same velocity. B) Both trains speed up all the time. C) Both trains have the same velocity at some time before t B. D) Somewhere on the graph, both trains have the same acceleration. time

36. Conceptual Quiz: The graph shows position as a function of time for two trains running on parallel tracks. Which of the following is true? A) At time t B, both trains have the same velocity. B) Both trains speed up all the time. C) Both trains have the same velocity at some time before t B. D) Somewhere on the graph, both trains have the same acceleration. time

37. Motion with Constant Acceleration If the acceleration is constant, then we have where v = v 0 at t = 0. This result is easy to show from our definition of a.

38. The Average Velocity constant acceleration

39. The Average Velocity nonconstant acceleration

40. Constant acceleration Another important result: Note that I have used v i and v f, which is more general than using v 0 and v, because we may want to find the average between some initial and final position other than v 0 and a general v. Let’s determine some important equations.

41. Insert our previous result for v av Only for constant acceleration!!!!!

42. This is a very important equation. It relates the position x to the velocity v as a function of time t. But we also know the relationship between velocity v and acceleration a. It was

45. Four important equations

46. with initial time t 0

47. Freely falling objects Most important example of constant acceleration; a = ± g =  9.81 m/s 2 Do demo: Paper and racquetball Nickel and feather Galileo – father of physics

48. We let x be downward. Look at our previous equation: x Let’s release an object at x 0 = 0 at t = 0. We then also have v 0 = 0. a = g Note that g is always positive. Here x is down.

49. Our previous equations for v become These are useful equations. Drop from rest.

50. Now use acceleration of gravity, with. Note y is up. y

51. Free fall from rest  x = 14.7 m9   x=4.91 m  x = 24.5 m  x = 34.4 m  x = 4.9 m

52. So what would happen if we dropped a rope that had masses at equal intervals? Do demo. Free fall What would happen if we dropped a rope that had masses spaced out as t 2 ? Do demo. Free fall

53. What happens if we throw a ball up? We throw a ball up at x = 0 with speed v 0. What is its speed when it returns? v 0 How long does it take to return? 2v 0 /g How can we determine these numbers? The equations we have determined must tell us these answers! x = 0

54. Conceptual Quiz: Throw ball up. Initial speed = v 0. Round trip time is 2v 0 /g. What is minimum speed? A) 0 B) -v 0 C) v 0 D) -2v 0 E) 2v 0

55. Conceptual Quiz: Throw ball up. Initial speed = v 0. Round trip time is 2v 0 /g. What is minimum speed? A) 0 B) -v 0 C) v 0 D) -2v 0 E) 2v 0

56. Conceptual Quiz: Throw ball up. Initial speed = v 0. Round trip time is 2v 0 /g. What is time when minimum speed is reached? A) 0 B) v 0 /g C) 2v 0 /g D) Can not be determined

57. Conceptual Quiz: Throw ball up. Initial speed = v 0. Round trip time is 2v 0 /g. What is time when minimum speed is reached? A) 0 B) v 0 /g C) 2v 0 /g D) Can not be determined

58. Review of Vectors A scalar is a number with units. It can be positive, negative, or zero. A vector has both a magnitude and direction. We will put an arrow over a quantity that is a vector. Sometimes a vector is in boldface.

59. Directions to the library 3 blocks west, 3 blocks north.

61. The Sum of Two Vectors We can add vectors.

62. Component Addition of Vectors

63. Unit Vectors

64. Multiplying a Vector by a Scalar We can multiply a vector by a scalar.

65. Vector Component Use Unit vectors make vector addition and subtraction reasonably easy.

66. Good review of vector use: http://www.physics.uoguelph.ca/tutorials/ vectors/vectors.html