Welcome to

1. Physics B Welcome to Trina Merrick MCHS *Slides/material thanks to Dr. Peggy Bertrand of Oak Ridge High School, Oak Ridge,TN

2. Kinematics • Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion. • We will learn to describe motion in two ways. • Using graphs • Using equations

3. Particle • A particle is an object that has mass but no volume and occupies a position described by one point in space. • Physicists love to turn all objects into particles, because it makes the math a lot easier.

4. Position • How do we represent a point in space? • a) One dimension • b) Two dimensions • c) Three dimensions (x) (x,y) (x,y,z)

5. Distance (d) • The total length of the path traveled by a particle. • “How far have you walked?” is a typical distance question. • SI unit: meter (m)

6. Displacement (Dx) • The change in position of a particle. • “How far are you from home?” is a typical displacement question. • Calculated by… x = xfinal – xinitial • SI unit: meter (m)

7. Delta (  ) •  is a Greek letter used to represent the words “change in”. x therefore means “change in x”. It is always calculated by final value minus initial value.

8. Practice Problem Question: If x is the displacement of a particle, and d is the distance the particle traveled during that displacement, which of the following is always a true statement? • d = |Dx| • d < |Dx| • d > |Dx| • d > |Dx| • d < |Dx|

9. Practice Problem A particle moves from x = 1.0 meter to x = -1.0 meter. • What is the distance d traveled by the particle? • What is the displacement of the particle? 2.0 m -2.0 m

10. B 100 m displacement 50 m distance A Distance vs Displacement • A picture can help you distinquish between distance and displacement.

11. Practice Problem You get on a ferris wheel of radius 20 meters at the bottom. When you reach the top on the first rotation • what distance have you traveled? • what is your displacement from the bottom? • When you are on your way back down, does the distance increase, decrease, or stay the same? What about the displacement? • What is the distance traveled after you have completed the full ride of 10 rotations? What about the displacement?

12. Practice Problem answers You get on a ferris wheel of radius 20 meters at the bottom. When you reach the top on the first rotation • d = ½ (2  r) =  r = 20  m •  x = 20 + 20 = 40 m • distance increases, displacement decreases • d = 10 (2  r) = 400  m

13. Average Speed • How fast a particle is moving. • save = d t where: save = rate (speed) d = distance  t = elapsed time • SI unit: m/s Average speed is always a positive number.

14. Average Velocity • How fast the displacement of a particle is changing. • vave = ∆x ∆t where: vave = average velocity ∆x = displacement ∆t = change in time • SI unit: m/s Average velocity is + or – depending on direction.

15. Demonstration • You are a particle located at the origin. • Demonstrate how you can move from x = 0 to x = 10.0 with an average speed of 0.5 m/s. You may not leave the x-axis! • What was your average velocity in this case?

16. Demonstration • You are a particle located at the point x = 10.0 m. • Demonstrate how you can move from x = 10.0 to x = 0 with an average speed of 0.5 m/s. You may not leave the x-axis! • What is your average velocity in this case?

17. Demonstration • You are a particle located at the origin. • Demonstrate how you can move from x = 0 to x = 10.0 and back with an average speed of 0.5 m/s. You may not leave the x-axis! • What was your average velocity in this case?

18. 15.7 m/s 3.33 m/s Practice Problem A car makes a trip of 1½ laps around a circular track of diameter 100 meters in ½ minute. For this trip a) what is the average speed of the car? b) what is its average velocity?

19. Practice Problem How long will it take the sound of the starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s. Answer: 0.29 s

20. x t Practice Problem Describe the motion of this particle. It is stationary.

21. x t Practice Problem Describe the motion of this particle. It is moving at constant velocity in the + x direction.

22. B x A Dx Dt t Practice Problem What physical feature of the graph gives the constant velocity? The slope, because Dx/Dt is rise over run! vave = Dx/Dt

23. x (m) Practice Problem Determine the average velocity from the graph. Ans: 1/3 m/s

24. Force Concept Inventory No scratch paper or calculator is necessary. Use pencil on BLUE side of scantron sheet. Name: Write your NAME followed by your TEST NUMBER. Subject:FCI Date:8/17/05 Period:??? When you are done, bring your scantron sheet to the front of the room and quietly begin working on tonight’s homework.

25. Practice Q 7: Is it possible for a car to circle a race track with constant velocity? Can it do so with constant speed? Q 8: Friends tell you that on a recent trip their average velocity was +20 m/s. Is it possible that their instantaneous velocity was negative at any time during the trip? P 13: The human nervous system can propagate nerve impulses at about 102 m/s. Estimate the time it takes for a nerve impulse generated when your finger touches a hot object to travel the length of your arm. (HINT: How long is your arm, approximately?)

26. Average Velocity Lab • Purpose: Figure out a way to make your cart move with an average velocity of as close to 0.200 m/s as possible. Use only the equipment provided. Photogate must be in PULSE mode. • Tonight:Type your BRIEF and PARTIAL lab report. The sections I want you to do are: • Procedure • Data (include a tableof data for 5 trials, a sample calculations, and a diagram of your setup). Clearly indicate what you predicted your average velocity to be, and what it actually was during the demo. • Analysis (where did your errors come from?)

27. x t Practice Problem Does this graph represent motion at constant velocity? No, since there is not one constant slope for this graph.

28. A x B Dx Dt t Practice Problem Can you determine average velocity from the time at point A to the time at point B from this graph? Yes. Draw a line connecting A and B and determine the slope of this line. vave = Dx/Dt

29. Practice Problem Determine the average velocity between 1 and 4 seconds. Ans: 0.17 m/s

30. Practice Problem You drive in a straight line at 10 m/s for 1.0 hour, and then you drive in a straight line at 20 m/s for 1.0 hour. What is your average velocity? Answer: 15 m/s (this is probably what you expected!)

31. Practice Problem You drive in a straight line at 10 m/s for 1.0 km, and then you drive in a straight line at 20 m/s for another 1.0 km. What is your average velocity? Answer: 13.3 m/s (this is probably NOT what you expected!) Always use the formula for average velocity; don’t just take an “average” of the velocities!

32. Instantaneous Velocity • The velocity at a single instant in time. • Determined by the slope of a tangent line to the curve at a single point on a position-time graph.

33. x Dx Dt t Instantaneous Velocity vins = Dx/Dt Draw a tangent line to the curve at B. The slope of this line gives the instantaneous velocity at that specific time. B

34. Practice Problem Determine the instantaneous velocity at 1.0 second. Ans: 0.85 m/s

35. Practice Problem The position of a particle as a function of time is given by the equation x = (2.0 m/s) t + (-3.0 m/s2)t2. • Plot the x vs t graph for t = 0 until t = 1.0 s. • Find the average velocity of the particle from t = 0 until t = 0.50 s. • Find the instantaneous velocity of the particle at t = 0.50 s.

37. Practice Q 10: If the position of an object is zero, does its speed need to be zero? Q 11: For what kind of motion are the instantaneous and average velocities equal? P 27: The position of a particle as a function of time is given by x = (-2.0 m/s) t + (3.0 m/s2) t2. a) Plot x-vs-t for time from t = 0 to t = 1.0 s. b) Find the average velocity of the particle form t = 0.15 s to t = 0.25 s. c) Find the average velocity from t = 0.19 s to t = 0.21 s.

38. Acceleration (a) • Any change in velocity is called acceleration. • The sign (+ or -) of acceleration indicates its direction. • Acceleration can be… • speeding up • slowing down • turning

39. Uniform (Constant) Acceleration • In Physics B, we will generally assume that acceleration is constant. • With this assumption we are free to use this equation: a = ∆v ∆t • SI Unit: m/s2

40. Acceleration has a sign! • If the sign of the velocity and the sign of the acceleration is the same, the object speeds up. • If the sign of the velocity and the sign of the acceleration are different, the object slows down.

41. Practice Problem A 747 airliner reaches its takeoff speed of 180 mph in 30 seconds. What is its average acceleration?

42. Practice Problem A horse is running with an initial velocity of 11 m/s, and begins to accelerate at –1.81 m/s2. How long does it take the horse to stop?

43. v t Practice Problem Describe the motion of this particle. It is moving in the +x direction at constant velocity. It is not accelerating.

44. v t Practice Problem Describe the motion of this particle. It is stationary.

45. v t Practice Problem Describe the motion of this particle. It starts from rest and accelerates in the +x direction. The acceleration is constant.

46. B v A Dv Dt t Practice Problem What physical feature of the graph gives the acceleration? The slope, because Dv/Dt is rise over run! a = Dv/Dt

47. Practice Problem Determine the acceleration from the graph. Ans: 10 m/s2

48. Practice Problem Determine the displacement of the object from 0 to 4 seconds. Ans: 0 Describe the motion. The object is initially moving in the negative direction at –20 m/s, slows gradually and momentarily is stopped at 2.0 seconds, and then accelerates in the + direction. At 4.0 seconds, it is back at the origin, and continues to accelerate in the + direction.

49. Demonstration

50. Demonstration