1. Motion Introduction Section 0 Lecture 1 Slide 1 Lecture 3 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion

2. Introduction Section 0 Lecture 1 Slide 2 Lecture 3 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Motion Introduction Section 0 Lecture 1 Slide 3 Lecture 3 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Units of Motion

4. Motion Introduction Section 0 Lecture 1 Slide 4 Lecture 3 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What Do We Need To Measure? What is the minimum about things we need to know? Where things are—a length, L When things are there—a time, T How thing interact with gravity—a mass, M How things interact with E&M—a charge, Q How thing inter act with weak nuclear force How things interact with strong nuclear force

5. Motion Introduction Section 0 Lecture 1 Slide 5 Lecture 3 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Describing Motion Position—where you are in space (L-meter) Speed—how fast position is changing with time (LT -1 or m/s) Acceleration—how fast speed is changing with time (LT -2 or m/s 2 )

6. Motion Introduction Section 0 Lecture 1 Slide 6 Lecture 3 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Units of Motion Need a distance unit: m, cm, mm, km ft, in, mi light years, furlongs Need a time unit: sec, min, hr, day, year ms, ns, fs fortnights Speed: A distance divided by time (DT -1 ) m/s, mi/hr, mm/yr, furlongs/fortnight Acceleration: A distance divided by time squared (DT -2 ) A speed divided by time (DT -2 ) m/s 2, mi/hr 2, mm/yr 2, furlongs/fortnight 2

7. Motion Introduction Section 0 Lecture 1 Slide 7 Lecture 3 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Examples of Distance Units Consider the lowly penny:

8. Motion Introduction Section 0 Lecture 1 Slide 8 Lecture 3 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Dimensions of Motion Distance: Dimensions; (L) Scalar Symbol: d Units: m, cm, km, in, ft, light years, furlongs Time: Dimensions; (T) Scalar Symbol: t Units: s (or sec), min, hr, day, year, ms, ns, fs, fortnights Speed: A distance divided by time Dimensions; (LT -1 ) Scalar Symbol: s Units: m/s, mi/hr, mm/yr, furlongs/fortnight Acceleration: A distance divided by time squared A speed divided by time Dimensions; (LT -2 ) Scalar Symbol: a Units: m/s 2, mi/hr 2, mm/yr 2, furlongs/fortnight 2

9. Motion Introduction Section 0 Lecture 1 Slide 9 Lecture 3 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Speed and Velocity

10. Motion Introduction Section 0 Lecture 1 Slide 10 Lecture 3 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What Is Speed? Speed is how fast something is moving. –Speed is always some distance divided by some time. –The units of speed may be miles per hour, or meters per second, or kilometers per hour, or inches per minute, etc. Rate is one quantity divided by another quantity. –For example: gallons per minute, pesos per dollar, points per game. –So average speed is the rate at which distance is covered over time.

11. Motion Introduction Section 0 Lecture 1 Slide 11 Lecture 3 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Average speed is total distance divided by total time. Instantaneous speed is the speed at that precise instant in time. –It is the rate at which distance is being covered at a given instant in time. –It is found by calculating the average speed, over a short enough time that the speed does not change much. What Is Speed?

12. Motion Introduction Section 0 Lecture 1 Slide 12 Lecture 3 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Average Speed Kingman to Flagstaff: 120 mi  2.4 hr = 50 mph Flagstaff to Phoenix: 140 mi  2.6 hr = 54 mph Total trip: 120 mi + 140 mi = 260 mi 2.4 hr + 2.6 hr = 5.0 hr 260 mi  5.0 hr = 52 mph

13. Motion Introduction Section 0 Lecture 1 Slide 13 Lecture 3 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Instantaneous Velocity Instantaneous velocity is a vector quantity having:  a size (magnitude) equal to the instantaneous speed at a given instant in time, and  a direction equal to the direction of motion at that instant.

14. Motion Introduction Section 0 Lecture 1 Slide 14 Lecture 3 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Instantaneous Speed: a car traveling on a local highway  A steep slope indicates a rapid change in velocity (or speed), and thus a large acceleration.  A horizontal line has zero slope and represents zero acceleration.

15. Motion Introduction Section 0 Lecture 1 Slide 15 Lecture 3 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What Does a Speedometer Measure? The speedometer tells us how fast we are going at a given instant in time. A speedometer measures instantaneous speed. (In a moment, we’ll see why a speedometer doesn’t measure velocity.)

16. Motion Introduction Section 0 Lecture 1 Slide 16 Lecture 3 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Average speed? Instantaneous speed? The speed limit indicates the maximum legal instantaneous speed. To estimate the time a trip may take, you want to use average speed. Which quantity is the highway patrol more interested in?

17. Motion Introduction Section 0 Lecture 1 Slide 17 Lecture 3 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Velocity Velocity involves direction of motion as well as how fast the object is going. –Velocity is a vector quantity. –Vectors have both magnitude and direction. –Velocity has a magnitude (the speed) and also a direction (which way the object is moving). A change in velocity can be a change in the object’s speed or direction of motion. A speedometer doesn’t indicate direction, so it indicates instantaneous speed but not velocity.

18. Motion Introduction Section 0 Lecture 1 Slide 18 Lecture 3 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Yes No At position A, the car has the velocity indicated by the arrow (vector) v 1. At position B, the car has the velocity indicated by the arrow (vector) v 2, with the same magnitude (speed) but a different direction. A car goes around a curve at constant speed. Is the car’s velocity changing?

19. Motion Introduction Section 0 Lecture 1 Slide 19 Lecture 3 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Changing Velocity  A force is required to produce a change in either the magnitude (speed) or direction of velocity.  For the car to round the curve, friction between the wheels and the road exerts a force to change the car’s direction.  For a ball bouncing from a wall, the wall exerts a force on the ball, causing the ball to change direction.

20. Motion Introduction Section 0 Lecture 1 Slide 20 Lecture 3 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Why Velocity Is So Useful Velocity is a vector and represents a bodies speed and direction. A force must act on a body to change its velocity (i.e. its speed, direction or both). The force causes the body to accelerate resulting in a change in its velocity. Acceleration is a vector and represents the rate of change of velocity with time.

21. Motion Introduction Section 0 Lecture 1 Slide 21 Lecture 3 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Acceleration

22. Motion Introduction Section 0 Lecture 1 Slide 22 Lecture 3 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Acceleration Acceleration is the rate at which velocity changes. –Our bodies don’t feel velocity, if the velocity is constant. –Our bodies feel acceleration. A car changing speed or direction. An elevator speeding up or slowing down. Acceleration can be either a change in the object’s speed or direction of motion. t 1 VV intervalTime velocityinChange accelerationAverage 2    2 sm t V a    

23. Motion Introduction Section 0 Lecture 1 Slide 23 Lecture 3 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Instantaneous Acceleration  Instantaneous acceleration is the acceleration at that precise instant in time. It is the rate at which velocity is changing at a given instant in time. It is found by calculating the average speed, over a short enough time that the speed does not change much.

24. Motion Introduction Section 0 Lecture 1 Slide 24 Lecture 3 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Acceleration: Vector Direction The direction of acceleration vector is given by the direction of the change in the velocity vector,. - Acceleration vector in same direction as velocity when velocity is increasing. -When the velocity is decreasing the change in is in the opposite direction to motion (ie. to slow car down) -Acceleration vector is opposite direction when velocity is decreasing. - Deceleration is negative acceleration. += a car accelerating V  + = car deceleratin g a V 

25. Motion Introduction Section 0 Lecture 1 Slide 25 Lecture 3 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example: Negative Acceleration Jet preparing to land Initial velocity V 1 =200 km/hr (=55.6 m/s) Final velocity V 2 =120 km/hr (=33.3 m/s) Time interval t=5 sec sm a 2 / 5 6.553.33   t VV t V a 1 2     In general: - Whenever the velocity is changing we say the object is accelerating (positive or negative). Acceleration: runway toward a46.4   sm 2 /

26. Motion Introduction Section 0 Lecture 1 Slide 26 Lecture 3 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Return to car on a bend Car moved at a constant speed but its direction continuously changed – thus its velocity was changing. But we now know that velocity changes are produced by an acceleration. Thus when the car rounds the bend at a constant speed it is accelerating!! Direction of acceleration is given bydirection. Question: what is ? Result: the vector acts towards the center of curvature of the bend! Acceleration Direction 1 V 2 V 2 V 1 V V  + = 1 V V  2 V V 

27. Motion Introduction Section 0 Lecture 1 Slide 27 Lecture 3 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 This is why the car does NOT change speed but you still feel a force on your body as you round the bend… (change in direction). Thus the acceleration is also directed towards the center of curvature. Force is due to friction of tires on road enabling the car to change direction. For a given speed the acceleration experienced (force) depends on the curvature of the bend. Skiing - sudden turns create large accelerations & large associated forces! Example: sharp shallow 2 V 2 V 2 V 1 V 1 V 1 V 1 V 2 V Large    t V a Small    t V a V  V 

28. Motion Introduction Section 0 Lecture 1 Slide 28 Lecture 3 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Graphing Motion

29. Motion Introduction Section 0 Lecture 1 Slide 29 Lecture 3 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Graphing Motion Time  Distance  Time  Speed  Time  Acceleration  Objectives: Understand what position, speed and acceleration are Learn to graph them versus time Develop some intuition for common situations Consider: Standing still Constant speed (different magnitudes) Constant acceleration (different magnitudes) Constant deceleration (different magnitudes) Arbitrary motion

30. Motion Introduction Section 0 Lecture 1 Slide 30 Lecture 3 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Standing Still Time  Distance  Time  Speed  Time  Acceleration 

31. Motion Introduction Section 0 Lecture 1 Slide 31 Lecture 3 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Constant Speed Time  Distance  Time  Speed  Time  Acceleration 

32. Motion Introduction Section 0 Lecture 1 Slide 32 Lecture 3 Slide 32 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Constant Speeds Time  Distance  Time  Speed  Time  Acceleration 

33. Motion Introduction Section 0 Lecture 1 Slide 33 Lecture 3 Slide 33 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Constant Acceleration Time  Distance  Time  Speed  Time  Acceleration 

34. Motion Introduction Section 0 Lecture 1 Slide 34 Lecture 3 Slide 34 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Graphs can help understand motion: D t D t D t D t Key: slope tells you about the instantaneous speed. - Stationary object -Constant velocity: Slope gives value of speed V=0 V=const d1d1 d2d2 Higher speed Lower speed t away toward Variable speed (d 2 > d 1 ) Distance vs. Time

35. Motion Introduction Section 0 Lecture 1 Slide 35 Lecture 3 Slide 35 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Velocity vs. Time Plots V t V t V t V t Key: - Slope of velocity-time plots gives information on the instantaneous acceleration. - Area under curve gives distance traveled. V= constant Constant velocity (no change with time) High constant acceleration Low const. acceleration a = constant Constant acceleration ( increases uniformly with time) Slope gives value of acceleration. V Variable acceleration away toward

36. Motion Introduction Section 0 Lecture 1 Slide 36 Lecture 3 Slide 36 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example: a t Car at rest accelerates uniformly up to a constant speed of 50 m/sec in 10 sec. - Constant acceleration produces a linear increase (decrease) in velocity with time. This is the simplest form of acceleration and occurs in nature whenever a CONSTANT FORCE is applied e.g. gravity! a= constant 10 s Acceleration does NOT change with time. Constant acceleration (speed increasing uniformly) Constant speed (zero acceleration)

37. Motion Introduction Section 0 Lecture 1 Slide 37 Lecture 3 Slide 37 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Equations of Motion for Uniform (Constant) Acceleration (a = constant) D t V t a = constant Produces a linear increase in velocity with time. V = a t Or if initial velocity (V 0 ) NOT zero: V = V 0 + a t Distance covered grows very rapidly with time. (as velocity is increasing with time). D = 1/2 a t 2 Or if initial velocity NOT zero: D = V 0 t +1/2 a t 2 Important formulas for calculating velocity and distance under constant (uniform) acceleration (i.e., constant force) Laws developed by Galileo (1638)!

38. Motion Introduction Section 0 Lecture 1 Slide 38 Lecture 3 Slide 38 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Summary: D t D t V t V t a t D t Constant acceleration “a” occurs in nature whenever the force is constant e.g. gravity. Stationary object Constant velocity Constant acceleration Distance increase uniformly with time Velocity increases uniformly with time Distance increases rapidly with time. (t 2 )

39. Motion Introduction Section 0 Lecture 1 Slide 39 Lecture 3 Slide 39 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Vectors: Velocity and Acceleration

40. Motion Introduction Section 0 Lecture 1 Slide 40 Lecture 3 Slide 40 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Scalars and Vectors Scalar: Measure of quantity or size Sometimes called “magnitude”. Examples: Length, volume, mass, temperature, speed… Vectors: Many measurements in physics require a knowledge of the magnitude and direction of quantity. These are termed vector quantities. Examples: Velocity, acceleration, force, electric field… Direction is an essential feature of a vector quantity. Example: Flying at 1000 km/hr due North is quite different to the same speed due East! Vectors require 2 pieces of information MAGNITUDE and DIRECTION.

41. Motion Introduction Section 0 Lecture 1 Slide 41 Lecture 3 Slide 41 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Resolving a Right Triangle into Components Resolving a right angle triangle into its horizontal (x) and vertical (y) components can be very helpful in solving problems of motion as well as static trigonometry. Example: Calculate the height of your house… high m 8.1684.0 x20 40tan. m20   tan.  Ayx  y x A

42. Motion Introduction Section 0 Lecture 1 Slide 42 Lecture 3 Slide 42 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 river 30 km launch N E55° balloon course 15 km/hr Question: How long before the balloon crosses the river? Example: Vectors Solution: V E = v cos(55°) V N = v sin(55°) 55° v =15 km/hr V E = v cos(55°) = 15 x 0.5736 = 8.6 km/hr As river is 30 km due E; the balloon will reach it in: (30 km)/(8.6 km/hr) = 3.49 hrs. Note: Can also use v N to get distance traveled Northwards.

43. Motion Introduction Section 0 Lecture 1 Slide 43 Lecture 3 Slide 43 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Example: Vector Velocities Boat crossing a river… 35° planned course actual course E N river flow Question: How fast is the river flowing? Solution: 35° v B = 7 km/hr actual course v R = v B tan(35°) Boat speed v B = 7 km/hr. = (7 km/hr) x 0.7002 = 4.9 km/hr Answer: The river is flowing at 4.9 km/hr Northwards. Note: To cross the river on planned course, the boat needs to aim upriver at an angle of 35°. Aircraft always need to take account of wind to get to the right place!

44. Motion Introduction Section 0 Lecture 1 Slide 44 Lecture 3 Slide 44 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Free Fall Tuesday 1:30-2:45 ESLC 53 Ch 2 Next Class: Wednesday 10:30-11:20 BUS 318 room Review Ch 3