Kinematics in One Dimension

1. Kinematics in One Dimension

2. Mechanics: The Study of Motion • Kinematics: How objects move • Dynamics: Forces and why objects move

3. Speed is Measured From a Frame of Reference

4. Frames of Reference • A car moving at 60 mph looks as if it is standing still if you are moving at 60 mph. • How fast does it seem to move if you are going 30 mph in the same direction as the car? • How fast does it seem to move if you are moving 60 mph in the opposite direction?

5. Frames of Reference • Any measurement of position, distance or speed must be made with respect to a frame of reference • The motion of an object is highly dependent on where you observe it from • Inside a pane flying at constant velocity, if there were no windows could you tell you were moving? How?

6. Measuring Motion • The displacement of an object is defined as the change of position of an object • Displacement is different from the distance an object travels? How? • Displacement is a vector quantity • It has magnitude and direction • Displacement over a unit of time is velocity

7. Displacement example 30 m west 70 m east Net displacement = 40 m east ∆x = x1 – x2

8. Graphical Interpretation Slope of the line is zero Velocity is zero Slope of the line is velocity Velocity is negative Distance Time Slope of the line is velocity Velocity is positive

9. Graphical Interpretation Slope of the line is zero Acceleration is zero Slope of the line is velocity Acceleration is negative Velocity Time Slope of the line is acceleration Acceleration is positive

10. Average Speed & Velocity • Average speed = distance traveled elapsed time • Average velocity = displacement elapsed time x2 –x1∆x t2 - t1 ∆t v = =

11. Constant Velocity (D vs T) What happens when the lines cross?

12. Constant Velocity (V vs T) Why don’t the lines cross?

13. Instantaneous Velocity ∆x ∆t v = If Then, the instantaneous velocity is: ∆x ∆t v = lim ∆ 0

14. Instantaneous Velocity As we let ∆t get smaller and smaller the line whose slope we use to get the velocity looks more and more like a tangent to the curve. In the limit of ∆ → 0 the line becomes the derivative of the curve. ∆x ∆t

15. Acceleration • Acceleration is the change in velocity of an object • Any change in velocity is the result of an acceleration Avg Accel = Final velocity – Original velocity Time

16. Calculating Acceleration • A car accelerates from a stop. After 6 seconds it is traveling at 28 m/s (about 60 mi/hr). What was its average acceleration? • Change in speed = 28 m/s • Time = 6 seconds • Acceleration = (28 m/s) / 6 s = 4.67 m/s/s = 4.67 m/s2

17. Motion to the Right with Constant Rightward Acceleration

18. Motion to the Right with Constant Leftward Acceleration

19. Equations of Constant Acceleration v = v0 + at x = x0 + v0t + ½ at2 v2 = v02 + 2a(x – x0) v = v + v0 2

20. Falling Objects • The most common example of constant acceleration is an object falling towards the earth • The acceleration due to gravity is 9.8 m/s2 • At the end of each second of fall the speed of the object will increase by 9.8 m/s • NOTE: on the AP test multiple choice problems assume that the gravitational acceleration is 10 m/s2

21. Questions • A ball is thrown upward • What is the magnitude and direction of its acceleration at A? • What is the magnitude and direction of its acceleration at B? • What is the direction of its velocity at A and B? B A

22. Multiple Choice • P. 44

23. Classwork/Homework • pp. 43, #21, 25, 27, 41, 47, 53, 57

24. Classwork • Go to http://cwx.prenhall.com/giancoli/ • Select Chapter 2, then push Begin • Select Practice Questions • Answer the 25 questions and then push Submit for Grading at that time you can enter your name and my email address: • jtimson@bpi.edu • It will save you time in the future if you set up an account in your name

25. Which Skier Gets There First? http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/RacingSkiers/RacingSkiers.html

26. Derivation of Equations of Linear Motion

27. Effects of Constant Acceleration

28. Practice: • Complete the multiple choice questions from yesterday. • Work with your group to brainstorm answers to the concept questions on pp. 45-46. Be prepared to discuss your thoughts!

29. Practice! • Work on your hw!!!

30. Do Now (9/3/13): (on a new sheet) An object is launched with initial velocity 20 m/s at an angle of 30°. Find the : • Initial vertical velocity • Initial horizontal velocity • Maximum height • Time of flight • How far away the object landed

31. 30 m/s 40 m Two-dimensional Motion • An object is dropped off a 40 meters cliff. How long does it take to reach the ground? • The same object is thrown horizontally with a velocity of 30 m/s. How long will it take to fall to ground? • Velocity is a vector. The horizontal velocity has no bearing on the time it takes to fall to the ground. All it does is change the trajectory

32. Vector Problems How long does it take to cross the river? 2 km/hr If the river is flowing at 2 km/hr, how long does it take to cross the river? 5 km/hr 10 km

33. Vector problems (cont’d) If the river is flowing at 2 km/hr, how far downstream will the boat be? 2 km/hr If the crew wanted to end up directly across the river, what path should they follow? How long will it take them to cross the river now? ? km 5 km/hr 10 km

34. Practice: • Work with your group to brainstorm answers to the conceptual questions 1-8 on p. 71 • 10 min!

35. Do Now (9/4/13): • In 1974 Nolan Ryan pitched a baseball at 100.8 mph. If a pitch were thrown horizontally with this velocity, how far would ball fall vertically by the time it reached home plate 60 ft away? • (*hint – conversions are in your textbook!!)

36. Practice: • Work with your group to brainstorm answers to the conceptual questions 9 and up on p. 71 • 10 min! • 14, 16, 20

37. Practice: • Complete problems 21 and 27 in Chapter 3. • Problem 60 is a bonus!

38. Do Now (9/5/13): • One baseball is dropped from a height, while another is launched horizontally from the same height. Draw a diagram to show their motion throughout their respective trips. • How far apart (timewise) will they land?

39. Agenda • Homework • Quiz info • Review: work on your homework, classwork (21, 27, and *60), conceptual questions, and/or your notecard

40. Do Now (9/6/13): • Come in quietly, pass in your Do Now’s, then clear your desk of everything except your quiz materials • No sharing notecards • No sharing calculators

41. Forces Are Vectors Also 200N 120N 53o cos 53o = 0.6 sin 53o = 0.8 150N x direction -120 N + 0.6 (200 N) = 0 y direction -150 N + 0.8 (200 N) = 10 N

42. Momentum

43. Momentum • Momentum depends on the mass of an object and the speed it is going. • Momentum = mass x velocity • Because velocity has direction then momentum does, also.

44. Momentum of Objects • Put the following in the order of most momentum to least: • Mosquito • Automobile • Space Shuttle • Bullet • Freight Train

45. Questions • Does a small object always have less momentum than a large one? • How can a rifle bullet knock over a person or an animal?

46. Conservation of Momentum • When two objects collide, the momentum after the collision must be equal to the momentum after the collision. • The total momentum of any group of objects remains the same unless outside forces act on the objects.

47. Conservation of Momentum The momentum of the two astronauts is equal to the momentum of the first astronaut before the collision

48. Conservation of Momentum—Inelastic Collisions Before the collision momentum = 1000 kg x 20 m/s = 20,000 kg m/s After the collision momentum = (1000 kg + 3000 kg) x 5 m/s = 20,000 kg m/s

49. Conservation of Momentum—Elastic Collisions After the collision the total momentum of the two vehicles is the same as the car’s before the collision.

50. Conservation of Momentum—Elastic Collisions