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Speed, velocity, acceleration & Newton

Speed, velocity, acceleration & Newton. Micro-World Macro-World Lecture 2. speed. distance traveled elapsed time. speed = v =. Hawaii Kai  Haleiwa In one hour. 50km 1 hr. v =. = 50 km/hr. This is the average speed over 1 hour. For shorter time intervals it can be

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Speed, velocity, acceleration & Newton

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

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

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

  4. Earth’s motion around the Sun r=1.5x1011m distance elapsed time 2 p r 2 x 3.14 x 1.5 x 1011m 365 days x 24 hr/day = V = = 1year 9.4 x 1011 m 8.76 x103 hr 9.4 8.7 9.4 x 1011 m 8760 hr = x 1011-3 m/hr = = =10-3km = 1.1x105 km/hr  110,000 km/hr = 1.1x108 m/hr

  5. Tip of a watch’s minute hand (HW!!) r=1 cm distance elapsed time 2 p r 2 x 3.14 x 1cm 60 min x 60 s/min = V = = 1hr 6.28 cm 3. 6 x103s 6.28 cm 3600 s = 1.7x10-3 cm/s = = =10-2m = 1.7x10-5 m/s

  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 6 months later speed = same different direction v r=1.5x1011m 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) change in velocity elapsed time acceleration = change in v elapsed time a =

  9. Change in V = 100km/hr Elapsed time = 3 sec change in v elapsed time a = 103 m 100km/hr 3 s = 33 km/hr s = 3600s =3.6x103s 33x103m 3.6x103 sxs = 9.1 m/s2 = “This baby goes from 0 to 100km/hr in only 3 seconds”

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

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

  12. a & v on a hot wheels track

  13. Free Fall

  14. t=0 v0=0 4.9m 1 s dist time vavg = = = 4.9m/s 0 + v1 2 v0 + v1 2 v1 2 vavg = = = 4.9m v1 = 2vavg = 9.8 m/s t=1s v1=? V1 = 9.8 m/s

  15. Free-fall acceleration 9.8m/s change in velocity elapsed time acceleration = 1s 9.8m/s 1s g a = = 9.8 m/s2 This is called the “acceleration due to gravity” and given the special symbol: g=9.8m/s2 In this class g10 m/s2 will be close enough for us.

  16. Free fall from greater heights t = 0s Total distance V0 = 0 5m 5m t = 1s V1 = 10m/s 15m 20m t = 2s 1 2 gt2 V2 = 20m/s 25m t = 3s 45m V3 = 30m/s 35m t = 4s 80m V4 = 40m/s

  17. Upward toss Total height t = 4s V4 = 0 80m 5m V3 = 10m/s t = 3s 75m 15m 60m V2 = 20m/s t = 2s 1 2 v0t - gt2 25m V1 = 30m/s 35m t = 1s 35m t = 0 V0 = 40m/s 0m

  18. Simple rule for free fallaka: projectile motion When Earth’s gravity is the only force involved: actual height = height for no gravity – ½gt2

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

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

  21. dead white European male Shoot the monkey communist

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

  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. 1st 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. 2nd Law: F=ma The acceleration of a body is directly proportional to the netforce 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 a Small force Small acceleration Large force Largeacceleration

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

  35. “Inertial” mass “Inertial” mass, mi, is the resistance to changes in the state of motion Objects with large mi are hard to get moving (& once started, hard to stop), Objects with small mi 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 10cm This much water! 10cm 10cm

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

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

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

  40. Weight = Force of gravity Free-fall acceleration of a beach ball & a bowling ball are the same: a=g m M Beach ball Bowling ball F2 = Ma a = g F1 = ma 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 2nd law: F=ma If gravity is the only force: F = W a = g W = mg acceleration due to gravity weight “gravitational” mass

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

  43. Units of Force F=ma m s2 kg Unit of force: 1 Newton = 1N = 1 kg m/s2 1 pound =1lb = 4.5 N

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

  45. !!!!! Mass & weight “weight” = 85 kg kg is a unit of mass, not force “my weight” Convert to Newtons: W = 85 kg x 9.8m/s2 = 833 N = Units of N kg m/s2 Kgf =“kilogram force” = 9.8 N

  46. Newton’3rd 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. reaction: the canoe pushes me forward action: I push on the canoe

  47. Action Reaction

  48. I push on the bus v= 0 F

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

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

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