Planning Ahead. Homework set 1 due W Save your chicken bones for lab on week 6 Level III: Motion graphs No class next Monday

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Planning Ahead Homework set 1 due W-9-12-18 Save your chicken

1 Planning Ahead Homework set 1 due W Save your chicken bones for lab on week 6 Level III: Motion graphs No class next Monday

2 Planning Ahead

3 Lecture Outline I. Physics Solution II. Visualization III. Motion Terminology IV. Particle Model Level II: Motion

4 Review: Study Guide The best way to learn Physics is to become a Physics tutor. Get into a study group. The act of explaining physics to someone is the best study and learning method.

5 Recall: Mass and Weight Mass Weight

6 Review Drill/Due Today We want to convert 9000 in. into km [1 in = 2.54 cm] 2.54cm 1m 9000in 1in 100cm 1km 1000m = 0.23 km

7 Review Drill/Due Today Energy E has the units m has the units kg a has the units kkkk mm2 ss 2 mm ss 2 A student writes the equation E = ma What is missing? Help the student fix the equation.

8 Preview Kinematics Equation If a = 0 then xx ff = vv ii tt + xx ii vv ff = vv ii

9 Graph Drill/Due Today Draw the position vs. time graph for the eq. x f x = v t + f i x i x i run rise rise v = slope = = run distanc time t

10 Problem Drill/Due Today

11 Preview Kinematics Equation If a = 0 then xx ff = vv ii tt + xx ii If a = constant then xx ff = 1 2 aa xxtt 2 + vv ii tt + xx ii vv ff = vv ii vv ff = aa xx tt + vv ii

12 v f (m / s) Graph Drill/Due Today Velocity t(s) v = a t + f x v i x f (m) t(s) Displacement 1 2 x f = a xt + vit + 2 x i

13 Problem Drill/Due Today

14 Preview Kinematics Equation If a = 0 then xx ff = vv ii tt + xx ii If a = constant then xx ff = 1 2 aa xxtt 2 + vv ii tt + xx ii vv ff = vv ii vv ff = aa xx tt + vv ii

15 Solving Problems Knight, College Physics

16 I. Physics Solution I. Visualization coordinate system, sketches, origin. II. Reasoning Model, Theory, First Principle, Assumptions, proper choice of values, etc. III. Solution algebraic, numeric, graphical, etc. IV. Assess Is the result believable, proper units, does it make sense, application of the result? Why do I need to solve the problem this way? Physics is not applied mathematics.

17 Problem Outline Student Reasoning Visualization Solution Assess

18 Recall: Physics Physics explains natural phenomena using fundamental laws and theories which can then be used to predict the results of future experiments.

19 What is Important? Learn how to think critically. Learn how to describe motion: 1. Visually (where 90% of the problem is solved) 2. Reasoning (decide which equations to use) 3. Equations (math) 4. Graphs (interpretation) Learn how to assess: 1. Check your answer and check your units. 2. Think outside the box.

20 II. Visualization

21 Drill (Do not Copy!) There are six people in a room; their names are, Bob, Carrie, Larry, Marie, Mary, and Rob. Three people are aligned in a roll near the north end of the room; one of them is named Larry. Marie is standing the furthest south in the room. One person is standing in in the southwest portion of the room, and Rob is standing in the southeast portion of the room. The person eating an apple stands at opposite ends from the person drinking a Snapple. Carrie, is standing between two men. The person standing to the left of Carrie is Bob. The closest people to Mary are Bob and Marie. The person with the radio stands closest to Carrie and Rob. No woman has a drink, one has a phone, and one woman hold nothing.

22 Questions Which person is standing toward the very west end of the room? Which two people are in the middle of the room? Which two people are on the phone? Who is drinking the snapple?

23 W N S (1)Visualization Drill/Due Today E Carrie Bob Larry radio Mary apple Marie Rob snapple Which person is standing toward the very west end of the room? Which two people are in the middle of the room? Which two people are on the phone? Who is drinking the snapple?

24 car Sketches person

25 Math Solution ( ) ( ) ) C P(H C P ) C P(H C P ) C P(H ) C (H P Z Y Z Y Z Y Z Y Y Z + = ) C P(H ) C (H P Z Y Y Z = + = + Bayes Theorem What s the Assessment?

26 Let s Make a Deal Assessment of Bayes Theorem

27 Visualization Solution 1 2 3

28 Physics Drill/Due Today A ball is tossed upwards from the ground with an initial speed of 29.4 m/s. Determine the highest point the ball reaches, and the time it takes to reach the highest point. Determine how long the ball was in the air. Determine the two times the ball was 25 meters high.

29 Visual Solution Determine the highest point the ball reaches, and the time it takes to reach the highest point. 50 Height (m) Time (s)

30 Visual Solution Determine how long the ball was in the air. 50 Height (m) Time (s)

31 Visual Solution Determine the two times the ball was 25 meters high. 50 Height (m) Time (s)

32 Motion Examples Simplest motion to explain: An object at rest remains at rest.

33 Visual Drill/Due Today Draw the sketch that best represents an object at rest remains at rest. Include the important details. v = i, x 0 a = i, x 0 O Origin x i

34 Second Simplest Motion

35 Visualization Drill/Due Today A person travels from the origin moves 100 m in 80 s. Draw a detailed sketch of the motion. O x i = 0 x f =100m t = 80s

36 III. Motion Terminology 1. Displacement 2. Velocity 3. Acceleration

37 1. Displacement Displacement is the change in position 0m 1m 2m 3m x i x f x FYI Textbook uses x 0 xx = xx ff xx ii

38 Position Position is the location of an object at a specific time. 0m 1m 2m 3m 0s 1s 2s 3s

39 2. Origin A fixed reference frame where the number zero is established. O 0m 1m 2m 3m

40 Origin Right of the origin is a positive number and left of the origin is a negative number. O -2m -1m 0m 1m

41 2. Position vs. Time Graph x(m)

42 2. Velocity Velocity measures the displacement during a time interval. Unit: Dimensions distance time m s mi hr Velocity is a vector and requires a direction. Speed is how fast the object moves. or

43 Speed vs. Velocity Speed is how fast t he object moves. Velocity is speed and direction. speed = Velocity = distance traveled in a given time interval time interval displacement time interval = x t = dx dt

44 Speed vs. Velocity In 1-Dimensional motion, both speed and velocity are numerically the same, except if the object moves in the negative direction the velocity will have a negative value.

45 Speed vs. Velocity Speed and velocity differ in 2-D motion. L x i x f L L x f = x i L v speed = x f = t 4L t x i = 0

46 Speed vs. Velocity Speed and velocity differ in 2-D motion. r speed = 2πr t v = x f x i = 0 t x i x f x f = x i

47 Do You Know the Facts Which of the following is fatal to you? A. 100,000 mph B. 9.8 m/s 2 C. 100 mph D. 100 m/s 2

48 3. Acceleration Acceleration measures how much velocity changes during a time interval.

49 Acceleration Acceleration is the rate of change of velocity. Change in velocity acceleration v r v dv a = = t dt a v Change in time Arrow indicates vector

50 Common Mistakes 9.8 m/s 2 is a faster acceleration than 4 m/s 2. Acceleration is not a speed nor velocity, so words like fast or slow cannot be used. 9.8 m/s 2 is a larger acceleration than 4 m/s 2. The coordinate system determines whether acceleration is positive or negative.

51 Do You Know the Facts Which of the following is fatal to you? A. 100,000 mph B. 9.8 m/s 2 C. 100 mph D. 100 m/s 2

52 IV. Particle Model

53 Particle Model Particle model replaces the object with a dot. Particle Model

54 Assessing the Particle Model Constant Speed/ Zero Acceleration Speeding up/ Constant Acceleration Slowing down/ Constant Acceleration

55 Assessment Drill/Due Today Which car is going faster, A or B? Assume there are equal intervals of time between the frames of both videos.

56 Motion Visual Example You ve made a video of a car as it skids to a halt... Draw a motion diagram for the car Skid starts Car Stopped Reasoning: The distances between the dots getting smaller indicate the car is slowing down. x

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

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

59 Displacement Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Rank from largest to smallest the total displacement of the objects from the origin. Assume the first dot is at the origin. a. B > A > D > C b. C > D > A> B c. B > D > A > C d. none of the above

60 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin.. Draw a position vs. time graphs for motions A, B, C, and D.

61 Velocity Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Rank the velocity of the objects from largest to smallest. Assume the first dot is at the origin. a. B > A > D > C b. C > D > A> B c. B > D > A > C d. none of the above

62 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin. Draw a velocity vs. time graphs for motions A, B, C, and D.

63 Acceleration Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Rank the acceleration of the objects from largest to smallest. Assume the first dot is at the origin. a. B > A > D > C b. C > D > A> B c. B > D > A > C d. none of the above

64 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin. Draw an acceleration vs. time graphs for motions A, B, C, and D.

65 Displacement Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Rank from largest to smallest the total displacement of the objects from the origin. Assume the first dot is at the origin. a. B > A > D > C b. C > A > D> B c. B > D > A > C d. none of the above

66 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin. Draw a position vs. time graphs for motions A, B, C, and D.

67 Velocity Each dot represents the distance an object traveled in the same amount of time. Rank the final velocity of the objects from largest to smallest. Assume the first dot is at the origin. a. B > A > D > C b. C > A > D> B c. A > D > B > C d. none of the above

68 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin.. Draw a velocity vs. time graphs for motions A, B, C, and D.

69 Acceleration Each dot represents the distance an object traveled in the same amount of time. Rank the acceleration of the objects from largest to smallest. Assume the first dot is at the origin. a. B > A > D > C b. C > A > B> D c. B > D > A > C d. none of the above

70 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin. Draw an acceleration vs. time graphs for motions A, B, C, and D.

71 Acceleration Each dot represents the distance an object traveled in the same amount of time. Rank the magnitude of the acceleration of the objects from largest to smallest. Assume the first dot is at the origin. a. B > A > D > C b. C > A > B> D c. A > D > B > C d. none of the above

72 Graph Drill/Due Today Each dot represents the distance an object traveled in the same amount of time. Assume the first dot is at the origin. Draw an acceleration vs. time graphs for motions A, B, C, and D.

Spring 2015, Math 111 Lab 4: Kinematics of Linear Motion

Spring 2015, Math 111 Lab 4: Kinematics of Linear Motion Spring 2015, Math 111 Lab 4: William and Mary February 24, 2015 Spring 2015, Math 111 Lab 4: Learning Objectives Today, we will be looking at applications of derivatives in the field of kinematics. Learning