III. Motion. 1. Motion in Time. A. Speed and Acceleration. b. Motion in Time. a. Descarte s Graph. A. Speed and Acceleration. B.

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Physics Part 1 MECHANICS III. Motion A. Speed and Acceleration Topic III. Motion B. Falling Motion W. Pezzaglia Updated: 01Jun9 C. Projectile Motion (D) A.

. Average Speed vs Velocity Why does time only flow forward? 3. Acceleration Are all measurements of time indirect? (i.e. involve motion) a.

Motion in Time 6 Cogito ergo sum (I think, therefore I am) 1637 Cartesian Coordinates Geometry could be represented by algebraic equations Hence path of

1 Physics Part 1 MECHANICS III. Motion A. Speed and Acceleration Topic III. Motion B. Falling Motion W. Pezzaglia Updated: 01Jun9 C. Projectile Motion (D) A. Speed and Acceleration 3 1. Motion in Time 4 1. Motion in Time What IS time? Time is what happens when nothing else does.. Average Speed vs Velocity Why does time only flow forward? 3. Acceleration Are all measurements of time indirect? (i.e. involve motion) a. Descarte s Graph 5 b. Motion in Time 6 Cogito ergo sum (I think, therefore I am) 1637 Cartesian Coordinates Geometry could be represented by algebraic equations Hence path of motion (e.g. orbit of moon) could be described by an equation and plotted on a graph. Rene Descartes Galileo is the first (I think) to represent motion by a graph of position with respect to time An Event is a point in spacetime (x,t), saying the object is at position x at time t Worldline of an object is a sequence of events 1

2 c. Velocity 7. Average Speed vs Velocity 8 Slope of worldline is velocity x v SI Units: meters/second (a) Average Speed Avg Speed Total Distance Total Time Equation of uniform motion (initial position x 0 at time zero) x( t) 0 x vt Total distance 10 m Total time: 15 seconds Avg Speed=10/15= 8 m/s What is the average speed here? b. Displacement 9 c. (Average) Velocity 10 Displacement is the change in position Velocity is speed with a direction Avg Velocity Total Displacement Total Time 0 to 5 s x=+60 m Time Interval 0 to 5 s Average Velocity v= 1 m/s 0 to 10 s x=+60 m 0 to 10 s v= 6 m/s 10 to 15 s 0 to 15 s x=-60 m x=+0 m Note minus displacement means movement backwards! 10 to 15 s 0 to 15 s v= -1 m/s v= 0 m/s The average velocity is zero because you end up where you started (but the average speed is NOT zero) 3. Acceleration 11 B. Falling Motion 1 Definition Acceleration is the rate of change of velocity (i.e. change in velocity with respect to a change in time) Δv a Δt v Change in velocity Change in time In first 30 seconds the velocity has gone from zero to 10 m/s. What is the acceleration? What is the acceleration from 30 to 45 sec? m Δv 10 s a 0.33 Δt 30 s Zero! (no change in velocity) m s 1. Galileo s Law of falling bodies. Inclined Plane Experiments 3. The Kinematic Equations

peripatetics (followers of Aristotle) postulated that the speed was proportional to the distance fallen.

must be wrong, for an object starting at zero speed would never acquire any speed!

The Einstein Equivalence Principle Reference at rest with Gravity is indistinguishable to a reference frame which is accelerating upward in

3 1a. Law of Falling 13 1b. Aristotle and Falling Motion 14 the rate of falling is proportional to the weight and inversely proportional to the density of the medium the peripatetics (followers of Aristotle) postulated that the speed was proportional to the distance fallen. x v x Aristotle: 384 BC-3 BC Aristotle: Heavier balls will fall faster Galileo: They fall at the same acceleration Galileo shows that this must be wrong, for an object starting at zero speed would never acquire any speed! (b) Galileo s Experiment at Pisa 1590 Galileo s Principle: all bodies fall at the same rate, regardless of mass 15 1c. The Einstein Equivalence Principle Reference at rest with Gravity is indistinguishable to a reference frame which is accelerating upward in gravity free environment Strong EEP (Einstein Equivalence Principle) same result, but Einstein argued from a different way. Einstein proposed that falling bodies in gravity are equivalent to being in an accelerated frame (e.g. in an accelerating elevator) The apple accelerating downward due to gravity looks the same as an apple at rest in space, with the floor accelerating upward towards it. 17. Inclined Plane Experiments b. Galileo s Law of Squares 18 Falling motion is too fast to measure Galileo shows rolling balls down inclined plane is same type of motion, but easier to measure because slower Discovers falling motion has constant acceleration 3

c. Results 19 3. Kinematic Equations 0 Total distance d traveled is proportional to square of time Equation: d 1 at Where a is the acceleration For gravity, a=g= 9.

Hence distance is related to velocity: v at d 1 at v ad C. Projectile Motion 1.

Galileo shows the natural path is a parabola (which is a combination of constant speed in the horizontal motion with constant acceleration in the vertical) 3.

4 c. Results Kinematic Equations 0 Total distance d traveled is proportional to square of time Equation: d 1 at Where a is the acceleration For gravity, a=g= 9.8 m/s For constant acceleration (falling motion, or ball rolling down inclined plane): Velocity increases linearly with time: Distance increases with square of time: Hence distance is related to velocity: v at d 1 at v ad C. Projectile Motion 1. Projectile Motion 1. Path of a projectile Old view was that projectile travelled in an arc until it ran out of impetus and then it fell straight down. Galileo shows the natural path is a parabola (which is a combination of constant speed in the horizontal motion with constant acceleration in the vertical) 3. Simultaneous Fall Simultaneous Fall: Galileo shows a bullet fired horizontal will hit ground at same time as bullet dropped. 3 3b Simultaneous Fall Both balls fall in the vertical direction at the same acceleration. Their paths only differ because of the constant horizontal velocity 4 (why?) 4

5 References & Links Descartes, R. La Géométrie. Livre Premier: Des problèmes qu'on peut construire sans y employer que des cercles et des lignes droites (Book one: Problems whose construction requires only circles and straight lines). (French) Galileo, Two New Sciences (1638). Chapter Third Day discusses motion and acceleration. Origin of terms abscissa and ordinate, see Inclined Plane short video: Video: Mechanical Universe #: Law of Falling bodies: PHET: Projectile Motion: Demo PhET: Energy State Park: SAT Physics: Good Java Demo: Galileo interview: Galileo: 5

II. Motion in 1D. Physics Part 1 MECHANICS Draft (part C incomplete) 1. Aristotle s Physics. A. Principle of Inertia. 2. Inertia

II. Motion in 1D. Physics Part 1 MECHANICS Draft (part C incomplete) 1. Aristotle s Physics. A. Principle of Inertia. 2. Inertia Physics Part 1 MECHANICS Draft (part C incomplete) Topic II. Motion in one Dimension (Kinematics) W. Pezzaglia Updated: 01Aug3 II. Motion in 1D A. Principle of Inertia B. Uniform Motion C. Acceleration