Physics 40 1-D Kinematics

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1 Physics 40 1-D Kinematics

2 Physics 40 IS Classical Mechanics! Study of the motion of objects and mechanical systems that are large relative to atoms and move at speeds much slower than the speed of light.

3 Isaac Newton ( ) In Principia (1687 ) Newton Invented Calculus 3 Laws of Motion Universal Law of Gravity The force of gravity is Universal: The same force that makes an apple fall to Earth, causes the moon to fall around the Earth and the planets to orbit the Sun.

4 Our Goal. Celestial Mechanics!

5

6 Let no one unversed in geometry enter here. The Universe is made of pure mathematical ideas the Platonic Solids. Plato believed that the stars, planets, Sun and Moon move round the Earth in crystalline spheres.

7 Earth and the universe were seen as constructed out of five basic elements: earth, water, air, fire, and ether. The natural place of the motionless Earth was at the center of that universe. The stars in the heavens were made up of an indestructible substance called ether (aether) and were considered as eternal and unchanging. The laws of nature of the Earth were different from those of the Heavens.

8 Naïve Science: From our perspective, the sun and stars appear to orbit us!

9 Ptolemy's Geocentric Model of the Universe 150 AD

10 Problem with the Theory: Apparent Retrograde Motion of Planets In a Geocentric Model there shouldn t be Retrograde motion.

11 Ptolemy AD Saving the Appearances The Sun and the planets would revolve in small circles whose centers revolve in large circles about the Earth ("epicycles"). 150 AD

12 As Christianity started taking over the Roman Empire, Paganism was illegal including astronomy. The Burning of the Library at Alexandria in 391 AD destroyed scientific texts. The murder of Hypatia marks the end of the Golden Age of the Greeks and the dawn of the European Dark Ages..

13 An avowed paganist in a time of religious strife, Hypatia was also one of the first women to study math, astronomy and philosophy. ne day on the streets of Alexandria, Egypt, in the year 415 or 416, a mob of Christian zealots led by Peter the Lector accosted a woman s carriage and dragged her from it and into a church, where they stripped her and beat her to death with roofing tiles. They then tore her body apart and burned it

14 5 th -15 th Centuries

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18 Developed science & medicine based on observation and experiment, rather than on conjecture creating the basis of what would later be called The Scientific Method.

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24 Recovery of Aristotle spanned about 100 years, from the middle 12th century into the 13th century, and copied or translated over 42 books from Arabic texts into latin. Aristotle's newly translated views discounted the notions of a personal God, immortal soul, or creation which was counter to church dogma. His books included physics and astronomy. Galileo read Aristotle and then challenged his ideas, using the scientific method of experimentation invented by Islamic scientists. Hence began the start of modern physics & the Renaissance. Without Islamic scientists keeping science alive during the dark ages, Europe might still be in the dark ages!

25 European Enlightenment Renaissance 14 th & 15 th Century The Vitruvian Man 1490

26 De revolutionibus orbium coelestium On the Revolutions of the Heavenly Spheres, 1543 If the Sun is at the Center of the Solar System you don t need epicycles.

27 REVOLUTION!

28 The Catholic Congregation for the Doctrine of the Faith, ruled that the propositions that the Sun is immobile and at the center of the universe and that the Earth moves around it, are both "foolish and absurd in philosophy," and the first to be "formally heretical" and the second "at least erroneous in faith" in theology. Catholic Inquisition

29 The Rejection of the Copernican Heliocentric Model: No Stellar Parallax

30 I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it.

31 Heliocentric Heretics

32 Rome, Campo de'fiori: The monument to Giordano Bruno, burnt at the stake here.

33 The Trial of Galileo June 22, 1633: Galileo was convicted and sentenced to life imprisonment by the Catholic Inquisition. In 1992, the church finally lifted its edict of Inquisition against Galileo, who went to his grave a devout Catholic, despite the church s treatment of him.

34 Tycho Brahe and Johanes Kepler Tycho was a great observational astronomer and took detailed data of planetary motion. Kepler worked for Tycho as his mathematician. Kepler introduced physics into astronomy for the first time and derived his laws of planetary motion from Tycho s observational data. Kepler s Laws are thus empirical - based on observation and not theory.

35 Based on observational data he derived three laws of planetary motion that put the sun at he center of the universe with elliptical orbits.

36 "The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit. As you will see, the answer is not very far from the truth. The only difference is that the angels sit in a different direction and their wings push inward." -Richard Feynman

37 Isaac Newton ( ) Using his Calculus, Newton derives Kepler s three laws of planetary motion from his own three laws of motion and his Universal Law of Gravity. Newton is the man of the millennium. In Principia (1687 ) Newton Invented Calculus 3 Laws of Motion Universal Law of Gravity

38 325 years later we know..

39 NOT ONLY is the Earth not immobile! The Earth Moves through Solar System at 30Km/sec!!!

40 464m/s

41 Precession causes the position of the North Pole to change over a period of 26,000 years.

42 Orbital Speed of Earth: ~ 30 km/s

43 Milky Way Galaxy Orbital Speed of Solar System: 220 km/s Orbital Period: 225 Million Years

44 Universe expands with Hubble Flow.

45 Types of Motion Translational Motion Circular Motion Projectile Motion Rotational Motion

46 Natural Motion Objects have a proper place Objects seek their natural place External forces must be constantly applied to moving objects in order to keep them going. The heavier the object, the faster it falls. Did not experiment to test theories.

47 Galileo Challenged The Dogma Of Natural Motion with Experiments

48 Galileo Challenged The Dogma Of Natural Motion The natural motion of a body is to remain in whatever state of motion it is in unless acted upon by net external forces.

49 Galileo Challenged Aristotle Physics In a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s 2, independent of their weight.

50 Galileo s Motion Studies gave us Definitions: x v = t v0 + v v = 2 v a = t f

51 Distance and Displacement The total distance traveled relative to an origin. Distance is a scalar. Displacement is a vector. The unit is the meter. x= x x f 0 (delta) means "change in" = 'final - initial'

52 Average Speed &Velocity Speed is how fast something moves. The average speed is the total distance per time. The average velocity is the the total displacement per time. Velocity is a vector. The unit is m/s. v total displacement x = = total time t

53 Acceleration How fast How fast is changing. The rate at which the speed is changing. a change in velocity v = = change in time t Speeding up Slowing down Constant speed, changing direction.

54 Acceleration is in the direction of the net Force but not necessarily in the direction of velocity. Velocity is always in the direction of the motion!

55 Galileo s Motion Studies gave us Kinematic Equations x v0 + v v =, v = f, a = t 2 v t With a little al-jbr.

56 Start: x v0 + v v =, v = f, a = t 2 v t Assume constant acceleration! v a = t v v = a t f 0 v = v + a t f 0

57 Start: x v0 + v v =, v = f, a = t 2 v t Assume constant acceleration! v a = t v v = a t f 0 v = v + a t f 0

58 Start: x v0 + v f v =, v =, a = t 2 v t x = t v + v f 0 2 xf x0 v0 + ( v0 + a t) = t 2 Assume t 0 = 0s 1 x() t = x0 + v0t + at 2 2

59 Start: x v0 + v f v =, v =, a = t 2 v t x = t v0 + v f 0 a 2 v = t t = t v v = f 2 + v a v f 0 x Combine & Eliminate t: v v 2 f 0 t = x = v + v a 0 f Algebra: 2 2 f 0 2 v = v + a x

60 Galileo s Motion Studies gave us Kinematic Equations x v0 + vf v =, v =, a = t 2 v t v = v + at f x = v0t + at 2 v = v + 2a x 2 2 f 0

61 Quicky Question An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. a) What is the automobile s average velocity? Which equation? v ave = v v f 15 m/ s+ 25 m/ s = = 2 20 m/ s

62 Quicky Question An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. b) What is the automobile s average acceleration? Which equation? a v = = t v f t v i 25 m/ s 15 m/ s = = 1 m/ s 10s 2

63 Quicky Question An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. 2 c) What is the distance traveled in this amount of time? Which equation? 0 1 x = v t + at m 15 / (10 ) 1 (10 ) = + x= m s s s 2 2 s 200m a = 1 m/ s (you could also use v ave equation.) 2

64 Motion Diagrams

65 Skiing through the woods

66 Draw the Motion Diagram An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s.

67 Problem Solving Strategy

68 Acceleration: Changing Velocity From t = 0, how long does it take the car to come to a full stop? How far does the car travel before it comes to a stop? Draw the Motion Graph +x

69 Acceleration: Changing Velocity Knowns a v v i f = 5 m/ s = 28 m/ s = 0 t =? 2 Which equation to use? f Solve for t: v = v + at i v t = f a v 0 28 m/ s = = 5.6s 2 5 m/ s i t = 5.6s

70 Acceleration: Changing Velocity From t = 0, to t = 5.6s, how far does the car travel before it comes to a stop? Knowns Which equation? a= 5 m/ s x = v t + at v v i f = 28 m/ s = 0 t = 5.6s 2 m x= s+ ( 5 m/ s )(5.6 s) = 78.4m s 2 0 YOU TRY IT! x= 78.4m +x

71 Motion Graphs What kind of motion is this?

72 What kind of motion is this?

73 What is the velocity during each segment? v2 = 0 m/ s v 3 x v = t 400m = = 1 m/ s 400s v 1 400m = = 200s 2 m/ s

74 Which position-versus-time graph represents the motion shown in the motion diagram?

75 Which position-versus-time graph represents the motion shown in the motion diagram?

76 The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

77 The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

78 Motion Graphs What is the average velocity between A and B? v x x = t x(1 s) x(0 s) = (1s 0 s) = 2m 0 1s = 2 m s

79 Motion Graphs What is the average velocity between B and D? v x x = t = x(3 s) x(1 s) (3s 1 s) 6 ( 2 ) = m m 2s = 4 m s

80 Motion Graphs What kind of motion does this graph represent? What is the NARRATIVE? (story) A-B: Object moves backwards with average speed of 2m/s, slows down and stops. B-C: C-D: Object moves forward with average speed of 2m/s, speeding up until it comes back to where it started. Object continues to move forward and increasing speed. Is the acceleration constant or changing during the motion? Find the equation for the displacement. xt () = 4t+ 2t 2

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