1. Speed, velocity, acceleration & Newton Micro-World Macro-World Lecture 2

2. speed speed = v = distance traveled elapsed time 50km v = 50km 1 hr = 50 km/hr Hawaii Kai  Haleiwa In one hour This is the average speed over 1 hour. For shorter time intervals it can be higher or lower.

3. instantaneous speed Instantaneous speed = 0 here & here Speed determined for very short time intervals v istantaneous = distance traveled “very short” time km

4. Earth’s motion around the Sun r=1.5x10 11 m V = distance elapsed time = 2  r 2 x 3.14 x 1.5 x 10 11 m 365 days x 24 hr/day = 1year = 9.4 x 10 11 m 8760 hr = 9.4 x 10 11 m 8.76 x10 3 hr = 1.1x10 8 m/hr = 1.1x10 5 km/hr  110,000 km/hr 9.4 8.7 = x 10 11-3 m/hr =10 -3 km

5. Tip of a watch’s minute hand (HW!!) V = distance elapsed time = 2  r 2 x 3.14 x 1cm 60 min x 60 s/min = 1hr = 6.28 cm 3600 s = 6.28 cm 3. 6 x10 3 s = 1.7x10 -3 cm/s = 1.7x10 -5 m/s r=1 cm =10 -2 m

6. Scalars and Vectors Simple numbers: Speed v Temperature T Number + direction Velocity v relative positions r Force F Acceleration a Library r Campus Center

7. Velocity = speed + direction r=1.5x10 11 m 6 months later speed = same different direction v velocity is a “vector”: a quantity that has both magnitude and direction Length of the arrow = speed Direction of arrow same as direction of the motion

8. Acceleration (  changes in v) acceleration = change in velocity elapsed time a = change in v elapsed time

9. Change in V = 100km/hr Elapsed time = 3 sec “This baby goes from 0 to 100km/hr in only 3 seconds” a = change in v elapsed time = 100 km/hr 3 s = 33 km/hr s 10 3 m 3600 s =3.6x10 3 s = 33x10 3 m 3.6x10 3 s x s = 9.1 m/s 2

10. Different ways to change V v v Car speeds up v Car slows up v screech! a a

11. Accelerations (continued) v Car turns v In all three cases, v changes. Therefore these are all examples of accelerations a

12. a & v on a hot wheels track

13. Free Fall

14. 4.9m t=0 v 0 =0 t=1s v 1 =? v avg = dist time 4.9m 1 s == 4.9m/s v avg = v 0 + v 1 2 0 + v 1 2 = v12v12 = v 1 = 2v avg = 9.8 m/s V 1 = 9.8 m/s

15. Free-fall acceleration acceleration = change in velocity elapsed time a = 9.8m/s 1s = 9.8 m/s 2 9.8m/s 1s This is called the “acceleration due to gravity” and given the special symbol: g=9.8m/s 2 In this class g  10 m/s 2 will be close enough for us. g

16. Free fall from greater heights V 0 = 0 t = 0s V 1 = 10m/s t = 1s 5m V 2 = 20m/s t = 2s V 3 = 30m/s t = 3s V 4 = 40m/s t = 4s 15m 25m 35m 5m 20m 45m 80m Total distance 1212 gt 2

17. Upward toss V 4 = 0 t = 4s V 3 = 10m/s t = 3s 5m V 2 = 20m/s t = 2s V 1 = 30m/s t = 1s V 0 = 40m/st = 0 15m 25m 35m 75m 60m 35m 0m Total height 80m gt 2 1212 v 0 t 

18. Simple rule for free fall aka: projectile motion When Earth’s gravity is the only force involved: actual height = height for no gravity – ½gt 2

19. Horizontal toss t = 0s t = 1s 5m t = 2s t = 3st = 4s 20m 45m 80m

20. upward toss t = 0s t = 1s 5m t = 2s t = 3s t = 4s 20m 45m 80m

21. Shoot the monkey communist dead white European male

22. Very fast horizontal toss t = 0s t = 1s x= 8km 5m t = 2s x=16km t = 3s x=24km 20m 45m V=8km/s

23. Orbital motion is free fall

24. Artificial satellite a = g v = 8 km/s

25. Turning car An object free to slide on the dashboard, tries to follow a straight line path

26. Newton’s 3 laws of motion Isaac Newton 1642 --- 1727

27. Alexander Pope: Nature and nature’s laws lay hid in the night God said, “Let Newton be,” and all was light.

28. 1 st Law: Law of Inertia A body at rest tends to stay at rest, a body in motion tends to keep moving along at a constant speed and in a straight-line path unless interfered with by some external forces.

29. example

30. Motorcycle crash dummy

31. Another example (watch the ladder)

32. 2 nd Law: F=ma T he acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.The direction of the acceleration is in the direction of the applied force.

33. Directly proportional to Force a Small force Small acceleration a Large force Large acceleration

34. inversely proportional to mass a a Large mass Small acceleration small mass Large acceleration Bowling ball Beach ball

35. “Inertial” mass “Inertial” mass, m i, is the resistance to changes in the state of motion Objects with large m i are hard to get moving (& once started, hard to stop), Objects with small m i easier to get moving (& easier to stop),

36. Units again! (we cant avoid them!) Mass: basic unit = 1kilogram = 1kg mass of 1 liter (1.1 quarts) of water This much water! 10cm

37. Net force Tip-to-tail method for adding vector Slide tail of one to tip of the other (keep directions fixed) Net force is the vector from the tail of the 1 st to the tip of the 2nd. (0 in this case).

38. Tip-to-tail method Slide tail of one to tip of the other (keep directions fixed) Net force points down the hill

39. Newton’s 2 nd law  F=ma a  F a  1/m a is proportional to F: direction of a = direction of F: a  F a is inversely proportional to m: a  F/m combine: set proportionality constant = 1: a = F/m  multiply both sides by m

40. Weight = Force of gravity a = g M Bowling ball m Beach ball a = gF 1 = ma F 2 = M a Free-fall acceleration of a beach ball & a bowling ball are the same: a=g Bowling ball has more inertia: M > m Force of gravity must be larger on the bowling ball by a factor that is proportional to mass

41. Weight is proportional to mass Newton’s 2 nd law: F=ma If gravity is the only force: F = W a = g W = mg weight “gravitational” mass acceleration due to gravity

42. Two different aspects of mass Weight: W = m g Force of gravity is proportional to “gravitational” mass a = FmFm Inertia; resistance to changes in state is proportional to “inertial” mass mimi mggmgg Newton’s 2 nd law: Experiment shows: m g = m i

43. Units of Force F=ma kg ms2ms2 Unit of force: 1 Newton = 1N = 1 kg m/s 2 1 pound =1lb = 4.5 N

44. What is your mass? Weight = force of Earth’s gravity on you W=mg W a=g F=ma m= WgWg Suppose I jump off a tqble

45. Mass & weight !!!!! Convert to Newtons: W = 85 kg x 9.8m/s 2 = 833 N kg m/s 2 Units of N = Kgf =“kilogram force” = 9.8 N “weight” = 85 kg kg is a unit of mass, not force “my weight”

46. Newton’3 rd Law: action-reaction Whenever one object exerts a force on a second object, the second object exerts an equal in magnitude but opposite in direction force on the first. action: I push on the canoe reaction: the canoe pushes me forward

47. Action  Reaction

48. I push on the bus F v= 0

49. But I accelerate Newton: The bus exerted an “equal but opposite” force on me. v

50. Look again F -F All forces come in pairs! This force causes me to accelerate backwards This force tries to accel. the bus forward

51. Air-filled balloon action: balloon pushes on air reaction: air pushes on balloon

52. recoil action: gun exerts force F 2 on bullet making it accelerate reaction: equal but opposite force on the gun F 1 Produces a recoil

53. Rocket propulsion action: rocket engine pushes exhaust gasses out the rear reaction: rocket gets pushed in the opposite direction