1. Today’s Plan – September 9 InspiredBike InspiredBike InspiredBike Introductions - me Introductions - me Class Expectations and Routines Class Expectations and Routines Resources Resources Web Web Who are you? Who are you? Start Unit 1 – Kinematics Start Unit 1 – Kinematics Lab 1 – velocity and speed Lab 1 – velocity and speed HOMEWORK HOMEWORK

2. What is Science? 3 things that shape our society: 3 things that shape our society:  Art  Religion  Science Science is the study of nature’s rules Science is the study of nature’s rules And physics… And physics…

3. Physics The science that explains all other sciences.

4. Physics It explains the large… It explains the large…  And the small

5. Examples of physics…

6. We start with Mechanics “Classical” or “Newtonian” physics “Classical” or “Newtonian” physics Galileo & Newton are the heroes Galileo & Newton are the heroes

7. Mechanics Objects pushing, pulling, and bumping into each other. Objects pushing, pulling, and bumping into each other. “The study of how forces change the motion of an object” “The study of how forces change the motion of an object”

8. Motion Key to understanding mechanics Key to understanding mechanics A change in motion is an indication that a force is being applied. A change in motion is an indication that a force is being applied. It is easy to recognize. It is easy to recognize.

9. When we describe motion it’s called KINEMATICS… (not the explanation of the motion) The “what” not the “why”.

10. What’s necessary to describe motion? Think about a moving object… Think about a moving object…  Like a race car… or the bikes… or…

11. To describe motion we need 5 things: 1. The object – What are we tracking? How do we describe the object? 1. The object – What are we tracking? How do we describe the object? 2. Position – Where is it? 2. Position – Where is it? 3. Time – When is it there? 3. Time – When is it there? 4. Velocity – How fast is it going? 5. Acceleration – Is the motion changing?

12. We’ll leave acceleration for later… Some finer points of speed and velocity.

13. Explain to me… Distance vs displacement? Distance vs displacement? Speed vs velocity? Speed vs velocity?

14. Instantaneous vs average What is the difference? What is the difference? Think of an example where we would use each? Think of an example where we would use each? Would we calculate them differently? Would we calculate them differently?

15. Average Speed = Total distance / total time Total distance / total time

16. Average Velocity = Total displacement / total time Total displacement / total time Displacement from start point to finish point in a straight line.

17. Velocity (& displacement) must always include a direction!!!

18. Simplifications and assumptions 1. Point Object 1. Point Object  An object is made of gazillions of specific points, but we look at the whole object as a single point. 2. Reference Point 2. Reference Point  Measure distance relative to something (most of the time we will measure in respect to Earth’s surface)

19. Today’s Lab READ THE LAB HANDOUT! READ THE LAB HANDOUT! Discuss how you are going to run the lab with your partners. Discuss how you are going to run the lab with your partners. Each person hands in a lab sheet. Each person hands in a lab sheet. And… And…

20. September 11! Today’s Plan: Homework Homework Lecture #2 – Acceleration Lecture #2 – Acceleration Lab #2 Lab #2

21. Homework and Lab Homework – answers please… Homework – answers please… Lab – what questions do you have? Lab – what questions do you have?

22. Quick Review - Describe Motion… Object Object Position Position Time Time Velocity Velocity Acceleration Acceleration

23. Simplifications and assumptions All measurements are relative to a reference frame. All measurements are relative to a reference frame. Point objects Point objects  We’re not concerned with odd shapes or spinning objects

24. Displacement = Measure from start point to finish point in a straight line. Measure from start point to finish point in a straight line.

25. Average speed = Total distance / total time Total distance / total time

26. Average Velocity = Total displacement / total time Total displacement / total time

27. Velocity always must include a direction!!!!

28. Acceleration

29. Instantaneous Velocity The rate of motion in one direction at a given instant in time (car’s speedometer). The rate of motion in one direction at a given instant in time (car’s speedometer).

30. Hmmm… An instant in time = 0 seconds An instant in time = 0 seconds Distance traveled in an instant = 0 meters Distance traveled in an instant = 0 meters Velocity = displacement / time Velocity = displacement / time 0/0 = undefined??!!! 0/0 = undefined??!!!

31. Solution… Pick smaller and smaller interval: Pick smaller and smaller interval: Eye in the sky Rubber tubes across the road Radar Smaller “average” – approaches instantaneous

32. Constant Velocity = (uniform motion) motion in a straight line at the same speed. (uniform motion) motion in a straight line at the same speed.

33. Can You Accelerate? 1 m/s/s means… 1 m/s/s means…  An object speeds up one meter per second  EVERY SECOND

34. Acceleration occurs When velocity changes When velocity changes This means: 1. Speed changes… 1. Speed changes…Or…

35. Accelerated motion – part 2 2. Direction changes 2. Direction changes

36. Acceleration… 3. Both Change 3. Both Change (speed and direction) (speed and direction)

37. Speed Changes: Speed up, increase, positive acceleration Speed up, increase, positive acceleration Slow down, decrease, decelerate (negative acceleration)

38. Direction Changes: Turns right, left Turns right, left Curves Curves Turns around Turns around

39. Acceleration Equation Acceleration = change in velocity / time Acceleration = change in velocity / time a = v/t a = v/t

40. Example You start from rest and accelerate to 27 m/s in 9 seconds… You start from rest and accelerate to 27 m/s in 9 seconds…

41. Or… Acceleration = Acceleration =  (Final Velocity – Initial Velocity) / Time a = (v f – v i ) / time a = (v f – v i ) / time

42. Example Starting at 2 m/s and speed up to 6 m/s over an 8 second period of time… Starting at 2 m/s and speed up to 6 m/s over an 8 second period of time…  What is the acceleration?

43. One more… You accelerate at a rate of 2 m/s 2. Starting at 1 m/s, how fast are you going after 5 seconds? You accelerate at a rate of 2 m/s 2. Starting at 1 m/s, how fast are you going after 5 seconds?

44. Acceleration can be large due to: 1. Large change in velocity 1. Large change in velocity

45. Acceleration can be large due to: 2. Change in velocity over a short period of time. 2. Change in velocity over a short period of time.

46. Homework Read Chap. 2.4 Read Chap. 2.4 Finish lab Finish lab Complete handout Complete handout

47. September 15:Today’s Plan: 1. Attendance 2. Grade Homework questions 3. Lecture #3 – Acceleration, freefall and graphical representation 4. Domino Lab – more velocity… 5. Homework – NOTE – no “Race Car WS”

48. A little review Three ways to change velocity? Three ways to change velocity? Change speed Change speed Change direction Change direction Change both Change both

49. Two ways to make acceleration large. Make the velocity change a lot. Make the velocity change a lot. a = v /t a = v /t  Make the time interval very small.  a = v/ t

50. Quick Review… Acceleration: Acceleration: in velocity / time

51. If a car that is moving at 24.5 meters per second (about 55 mph) hits a tree and comes to a complete stop in 2 seconds – what is the car’s acceleration?

52. Acceleration 5:30 of this video clip: “click on me” 5:30 of this video clip: “click on me”“click on me”“click on me”

53. Position, velocity and acceleration Velocity = rate of change of position Velocity = rate of change of position  Displacement / time  v = d/t Acceleration = rate of change of velocity Acceleration = rate of change of velocity  Velocity / time  a = v/t If acceleration is constant If acceleration is constant  Then the rate of change for velocity is constant

54. Let’s try somethingTime a (m/s/s) V (m/s) X (m) 0300 133?? 236?? 33????

55. Soooo????? If acceleration is constant… If acceleration is constant… Velocity = a t Velocity = a t Displacement: d = ½ (Δv) t Displacement: d = ½ (Δv) t  And d = ½ a t 2 And d = ½ a t 2 And d = ½ a t 2

56. Let’s fill in the table… And graph them! And graph them!

57. An example, please You are accelerating at 2 m/s/s You are accelerating at 2 m/s/s If you start from rest, how fast are you going after 1 second? If you start from rest, how fast are you going after 1 second? 2 seconds? 2 seconds? If you start from rest, how fast are you going after 7 seconds? If you start from rest, how fast are you going after 7 seconds? How far have you traveled in those 7 seconds? How far have you traveled in those 7 seconds?

58. One more factoid… When things fall to earth they accelerate at a constant rate When things fall to earth they accelerate at a constant rate 10 m/s/s 10 m/s/s This is HUGE!! This is HUGE!! From now on, as long as you have a meter stick… you can tell how much time has passed!!! From now on, as long as you have a meter stick… you can tell how much time has passed!!! d = ½ (10 m/s/s) t 2 d = ½ (10 m/s/s) t 2 d = 5 t 2 for falling things d = 5 t 2 for falling things

59. Another simplification We have been ignoring… We have been ignoring…  AIR RESISTANCE What happens when we factor this in? What happens when we factor this in?  For falling objects

60. Today’s Lab Purpose - More average velocity practice Purpose - More average velocity practice Goal: Determine optimum spacing for max velocity! Goal: Determine optimum spacing for max velocity! Toppling dominos Toppling dominos  Vary distance between the dominos  Measure space in between the dominos  Measure total distance!  Measure time to fall

61. Sept 17 th Today’s Plan: 1. Attendance 2. Go Over Homework 3. Turn in Domino lab 4. Free Falling Lecture 5. Reaction Time Lab Homework: Lab, book work and Freefall questions (handout)

62. Remember the human accelerator? Acceleration = 1 m/s 2 Acceleration = 1 m/s 2 Velocity increases by 1 m/s per second Velocity increases by 1 m/s per second Distance between second markers increases each time. Distance between second markers increases each time.

63. Free fall = when a falling object is only affected by gravity (no air resistance).

64. All objects free fall at the same speed (10 m/s)

65. Elapsed time versus Instantaneous Speed Time 1 secInst. Speed = 10 m/s Time 1 secInst. Speed = 10 m/s 2 sec = 20 m/s 2 sec = 20 m/s 3 sec = 30 m/s 3 sec = 30 m/s 4 sec = 40 m/s 4 sec = 40 m/s

66. Velocity (speed) of Falling Bodies: Velocity increases due to gravity as elapsed time increases (10 m/s for each second). Velocity increases due to gravity as elapsed time increases (10 m/s for each second). “little g” “little g”  g = 10 m/s/s v = g t v = g t

67. How do we calculate the distance traveled by free-falling objects… After 1 second, After 1 second,  Instantaneous speed = 10 m/s (not average velocity)

68. Speed? No, I want distance … To get average speed take initial velocity and final velocity and divide by 2. To get average speed take initial velocity and final velocity and divide by 2. V f + V i 2

69. Distance traveled of free-falling objects… After 1 second the average speed is 5 m/s. After 1 second the average speed is 5 m/s. Distance = average speed x time Distance = average speed x time  d = v avg t

70. After 2 seconds, how far has the object traveled? (20 + 0) = 10 m/s = avg velocity (20 + 0) = 10 m/s = avg velocity 2 distance = v t Time = 2 seconds

71. After 3 seconds? (30 + 0) (30 + 0) 2 d = v t

72. Ughhh – 3 equations… 1. v f = gt 2. V avg = (v f + v i )/2 3. d = v t Or…

73. Ahhh… easier equation: distance traveled = (1/2)gt 2 distance traveled = (1/2)gt 2

74. So how far will a freely falling object that is released from rest fall in 10 seconds?

75. In 3 seconds?

76. What happens to velocity when… The object is moving up to begin with? The object is moving up to begin with? It’s velocity slows down by 10 m/s/s It’s velocity slows down by 10 m/s/s Until… Until…  It stops and starts falling… And then its speed increases by 10 m/s/s And then its speed increases by 10 m/s/s

77. Initial upward speed of 20 m/s T = 1 second T = 1 second  V = v i - at  V = 20 – 10 m/s T = 2 seconds T = 2 seconds  V = 20 – 20 m/s T = 3 seconds ? T = 3 seconds ?

78. Lab! Trying to verify constant acceleration Trying to verify constant acceleration  Can we measure acceleration? We’ll need to approximate We’ll need to approximate  Take care in the lab!

79. September 21 Plan: 1. Review homework 2. Questions on lab? 1. Graph expectations 3. Accuracy vs. precision 4. Lab #4 5. Homework – Worksheet 1 st test on Friday!!!!

80. Free-fall Notes… Accelerates at constant rate Accelerates at constant rate g = 10 m/s/s g = 10 m/s/s Change in v = at Change in v = at d = ½ gt 2 d = ½ gt 2

81. Throwing an object straight up When an object is at its highest point – it has a speed of “0” When an object is at its highest point – it has a speed of “0” The change in speed (acceleration) each second is the same The change in speed (acceleration) each second is the same  whether it is going up or down.

82. Real Life… When you throw a ball straight up – the speed that it hits your hands when you catch it is the same as when you threw it. When you throw a ball straight up – the speed that it hits your hands when you catch it is the same as when you threw it.

83. Accuracy versus Precision

84. Accuracy = how close to “correct”

85. Precision = smallest unit used

87. Don’t sacrifice accuracy (care in taking measurements)

88. Don’t sacrifice precision by dropping a bunch of digits (no more digits than smallest measurement).

89. Graphing expectations Title Title Label axis Label axis  What it is and  what the units are Best fit line Best fit line

90. 1. Distance/Time Plots Time is typically on horizontal axis (x-axis). Time is typically on horizontal axis (x-axis). Distance is on vertical axis (y-axis). Distance is on vertical axis (y-axis). Time Distance

91. 2. Velocity/Time Plot If the line is horizontal and straight – the object is moving at a constant velocity. If the line is horizontal and straight – the object is moving at a constant velocity. Time Velocity

92. 3. Acceleration/Time Plot We will limit ourselves to constant acceleration We will limit ourselves to constant acceleration Time Acceleration

93. Lab Consider the accuracy and precision of your data Consider the accuracy and precision of your data Several steps – let’s set it up. Several steps – let’s set it up.

94. September 23 Review Homework Homework More graphical analysis More graphical analysis Review Review Lab 6 Lab 6

95. Graphical Representation of Motion

96. Graphs can give a quick picture of what happens…

97. Graphing Rule #1 Independent variable – Independent variable –  the variable that you change  goes on horizontal axis (x-axis). Dependent variable – Dependent variable –  the variable that you measure  goes on the vertical axis (y-axis).

98. 1. Distance/Time Plots Time is typically on horizontal axis (x-axis). Time is typically on horizontal axis (x-axis). Distance is on vertical axis (y-axis). Distance is on vertical axis (y-axis). Time Distance

99. 1. Distance/Time Plots If line is straight and horizontal – the object is at rest. If line is straight and horizontal – the object is at rest. Time Distance

100. 1. Distance/Time Plot If the line is at an angle, but is still straight – the object is moving at a constant velocity. If the line is at an angle, but is still straight – the object is moving at a constant velocity. Time Distance

101. 1. Distance/Time Plot If the line is curving up – the object is speeding up (accelerating). If the line is curving up – the object is speeding up (accelerating). Time Distance

102. 1. Distance/Time Plot If the line is “curving down” – the object is slowing down (decelerating). If the line is “curving down” – the object is slowing down (decelerating). Time Distance

103. 1. Distance/Time Plot If the line is a hill or a valley – the object is changing direction. If the line is a hill or a valley – the object is changing direction. Time Distance

104. 2. Velocity/Time Plot Time is on horizontal (x-axis) and Velocity is on vertical (y-axis). Time is on horizontal (x-axis) and Velocity is on vertical (y-axis). Time Velocity

105. 2. Velocity/Time Plot If the line is horizontal and straight – the object is moving at a constant velocity. If the line is horizontal and straight – the object is moving at a constant velocity. Time Velocity

106. 2. Velocity/Time Plot If the line is straight, but angled up – the object is speeding up. If the line is straight, but angled up – the object is speeding up. Time Velocity

107. 2. Velocity/Time Plot If the line is straight, but angled down – the object is slowing down. If the line is straight, but angled down – the object is slowing down. Time Velocity

108. 2. Velocity/Time Plot The steeper the line, the bigger the acceleration. The steeper the line, the bigger the acceleration. Time Velocity