PS 11 GeneralPhysics I for the Life Sciences
|
|
- Osborn Campbell
- 5 years ago
- Views:
Transcription
1 PS 11 GeneralPhysics I for the Life Sciences M E C H A N I C S I D R. B E N J A M I N C H A N A S S O C I A T E P R O F E S S O R P H Y S I C S D E P A R T M E N T N O V E M B E R 0 1 3
2 Definition Mechanics is the study of motion and its causes
3 Before discussing the cause of motion, we need to know how to describe motion (kinematics) first.
4 Kinematics How would you describe a moving object?
5 Locate the Object Establish Reference Frame Point of reference needed (origin) Reference direction needed Construct the position vector (magnitude and direction) from the origin to the object We can also call this the displacement of the object from the origin It consists of a magnitude (in meters) and direction
6 1-D Position Vector Only two directions available Can be represented by a signed scalar (magnitude) 1 m O P
7 -D Position Vector Direction goes through a 360 angle 0 angle reference needed Position vector = magnitude, angle Polar Coordinates (r, ) are natural r = magnitude, = direction Polar coordinates to cartesian coordinates and back: P x r cos r = r r y r sin = 0 r x y tan 1 y / x
8 Vector Components Similar to polar coordinate transformation A A A x y tan A Acos Asin x 1 A y A / y A x x coordinate yields the x-component A x of vector A y coordinate yields the y-component A y of vector A
9 Second and Third Quadrant Adjustment The direction is always measured from the +x axis 180 tan 1 A y / A x tan -1 (B y /B x ) < 0 for quadrant II tan -1 (C y /C x ) > 0 for quadrant III
10 3-D Position Vector Direction consists of two angles Choice for two angles Geographer s coordinates Polar angle (longitude) Angle from the horizon (latitude) 0 = horizontal view Spherical coordinates Polar angle Azimuthal Angle 0 = view at the top (azimuth)
11 Geographer s Coordinates
12 Spherical Coordinates
13 Exercise: Position Vector -D Specify the position of the back door. Reference point: Reference direction: Magnitude: Direction: 3-D Specify the position of the projector in the classroom. Reference point: Reference direction: Magnitude: Direction:
14 How fast is the object moving? (Velocity Vector) Average velocity v ave displacement time elapsed Instantaneous velocity Velocity at any instant in time Average velocity over a very short time interval Slope of the position vs. time graph Speed = magnitude of velocity v lim t 0 x x t f t x i dx dt x t
15 Example: Runner s Average Velocity During a 3.00 s time interval, a runner s position changes from x 1 = 50.0 m to x = 30.5 m towards you along a straight track. What is the runner s average velocity? Solution v ave x t 30.5m 50.0m 3.00s 19.5m 3.00s 6.50m / s
16 Is it slowing down or picking up speed? (Acceleration Vector) Average acceleration Instantaneous acceleration a ave v f The acceleration at a particular point in time The average acceleration over a very small time interval The slope of the velocity vs. time graph v dv a lim t 0 t dt t v i v t
17 Example: Accelerating Car A car accelerates along a straight road from from rest to 75 kph in 5.0 s. What is the magnitude of the average acceleration? Solution a ave v f t v i 75kph 5.0s 15 km hs 1000m s 4.m / s
18 When we know the acceleration of an object we can figure out how it is moving! Zero acceleration At rest or moving with a constant velocity Constant acceleration Speed varies linearly (direction remains constant) Position varies parabolically (in time) Variable acceleration Non-linear change in speed or changing direction
19 Motion Graphs Position vs. time Velocity vs. time Velocity = time rate of change of position Slope of position vs. time graph Acceleration vs. time Acceleration = time rate of change of velocity Slope of velocity vs. time graph
20 Constant Velocity Graphs x v t t a = 0
21 Constant Acceleration Graphs
22 Example: Graphical Analysis The velocity of a motorcycle driven by a PNP officer is given by the graph below. How far does the officer go after 5 s? 9 s? 13 s? Solution Consider the area under the curve! t=5 s x=(0 m/s)(5 s)=100m t=9 s x=(0m/s)(9s)+(1/ )(4s)(5m/s) =180 m+50 m=30 m t=13 s x=30 m+(1/)(4s)(45m/s)=30m
23 Variable Acceleration Uniform Circular Motion Launching spaceships/satellites Planetary Orbits Motion in the very general sense
24 Questions and Problems for Contemplation Giancoli (6 th edition) Chapter Questions:, 4, 6, 8, 14, 17, 18, 1 Problems: 3, 7, 8, 0, 4, 6, 35, 39, 46, 50, 56 General Problems: 57, 58, 59, 60, 68, 76, 81 First Long Exam Wednesday, Dec. 4, 013 Submit blue book by Dec. Chapters 1, and 3 including notes, assigned questions and problems
25 Free Fall When an object falls through the air, how fast will it fall down? With no air friction Constant acceleration g = -9.8 m/s g = 9.8 m/s With air friction Variable acceleration
26 Free Fall Demo Falling Objects Galileo s experiment
27 Equations of Motion (No Friction) a(t) = a o = -g = -9.8 m/s v(t) = -gt + v o v o = initial velocity x(t) = -(½)gt + v o t + x o x o = initial displacement
28 Reaction Time Calculation Catch the falling meter stick! v o = 0, x o =? g = 9.8 m/s v(t) = -gt x(t) = -(½)gt + x o
29 Contest! teams (3 persons each) As quickly as you can, catch the falling meter stick between your thumb and pointing finger Only one trial!
30 Throwing Objects Upwards Equations with an initial velocity component x max, time of flight, or v o usually to be determined x o = 0 point where object leaves hand g = 9.8 m/s v(t) = -gt + v o x(t) = -(½)gt + v o t
31 Example Calculate the initial velocity of an object thrown upward to a height of.0 m. Solution Find v o. v(t)=0 at the highest point 0 = -(9.8 m/s )t + v o need to find t! x max =.0 m x(t) = -(½)gt + v o t.0 m = -(4.9m/s )t + v o t From the first equation, t = v o /(9.8 m/s ). Thus.0 m = -(4.9m/s )(v o /(9.8 m/s )) + v o (v o /(9.8 m/s )) Solve for v o.0 m = -v o /(19.6 m/s ) + v o /(9.8 m/s )
32 Example continued.0 m = -v o /(19.6 m/s ) + v o /(9.8 m/s ).0 m = v o /(19.6m/s ) v o = 39. m /s v o = m/s v o = 6. 3 m/s
33 Questions and Problems for Contemplation Giancoli (6 th edition) Chapter 3 Questions: 5, 6, 9, 11, 14, 16, 18 Problems:, 8, 18, 8, 35, 38, 47, 48, 49 General Problems: 53, 57, 63, 69, 75
34 Seatwork: Plot the motion graphs for a bouncing ball. You may work in pairs
35 Motion Graphs for Bouncing Ball
36 -D Motion Projectile Motion
37 With No Air Resistance Horizontal direction Constant velocity Vertical direction Constant acceleration Projectile launched with initial velocity v o at an angle from the horizontal v ox = v o cos v oy = v o sin
38 Equations of Motion Horizontal v(t) = v ox v ox = initial velocity horizontal component x(t) = v ox t + x o x o = initial horizontal displacement Vertical a(t) = a o = -g = -9.8 m/s v y (t) = -gt + v oy v oy = initial velocity vertical component y(t) = -½gt + v oy t + y o y o = initial vertical displacement
39 Horizontal v o Will you be able to jump across to the other building if your initial horizontal velocity is 10 m/s? Solution x o = 0, y o = 0 v oy = 0, v ox = 10 m/s x(t) = (10 m/s)t v y (t) = -(9.8 m/s )t y(t) = -(4.9 m/s )t y(t)= -5.0 m = -(4.9 m/s )t 5.0 t s 1. 0s 4.9 x(1.0s) = (10 m/s)(1.0s) = 10 m 10m 1m You will fall short of the building!! v o 1m 5.0 m
40 Exercise What take-off velocity would you need to jump successfully to the other building? If you cannot go any faster, will you succeed by just varying your take-off angle?
41 -D Trajectory of the Projectile Combine horizontal and vertical motion
42 -D Trajectory x(t) = v ox t (1) y(t) = -½gt + v oy t () From (1), t = x/v ox Substitute into (), y v v oy ox x g v ox x (tan ) x v o g cos x y Ax Bx Isn t this an equation for a parabola?!
43 Plotting the Parabola Roots: y = 0 0 = x(a - Bx) Two roots A tan B g v o cos x = 0 (take-off point) v x = A/B (landing point, range R) o sin R g Vertex: x = A/B x coordinate of y max y max = A /B A /4B = A /4B y max v o sin g
44 Time of flight Time from launching point to landing point t x v ox v o R cos v o v sin o cos g v o sin g Time to reach maximum height y max 0 t v oy vo sin g gt This is just half the time of flight!
45 Range of the Projectile Varying the projection angle
46 Azkal s Football Kick v o = 0.0 m/s, 37.0 Calculate Maximum height Time of flight Range Velocity at the maximum height Velocity as it hits the ground
47 Solution Resolve initial velocity into its components v v ox oy v v At maximum height, v y = 0 With y o = 0 y v o o oy cos37.0 (0.0m / s)(0.799) 16.0m / s sin 37.0 (0.0m / s)(0.60) 1.0m / s t t v oy g gt 1.0m/ s 9.80m/ s 1.s (1.0m / s)(1.s) (4.90m / s )(1.s) 7.35m
48 Solution Time of flight Time to go up done Time to go up = time to go down Time of flight = x time to go up =.44s Alternatively, 0 v oy t gt (1.0m / s) t (4.90m / s ) t 0 t[(1.0m / s) (4.90m / s ) t] 1.0m / s t. 45s 4.90m/ s
49 Solution Range = how far will it go horizontally Horizontal displacement at t = t flight x voxt flight (16.0m / s)(.45s) 39. m
50 Solution Velocity at the maximum point v y = 0 v x = 16.0 m/s v = 16.0 m/s, 0 (horizontal) Velocity as the football hits the ground Velocity at t = t flight v x = 16.0 m/s v y =? v y ( 9.8m/ s )(.45s) 1.0m / s 1.0m / s v ( 1.0m / s) (16.0m / s) 0.0m / s tan 1 1.0m/ s 16.0m/ s 36.9
51 Hang-Time Calculate the fraction of time the football spends on the upper half of its flight. Solution From y=(1/) y max to highest point, y max, back to y=(1/) y max y max = 7.35 m y v oy t gt 7.35m (1.0m / s) t (4.9m / s ) t m (1.0m / s) t (4.9m / s ) t t s 1 t. 090s t t.090s 0.359s s 1 t t t 1 flight 1.73s.45s %
52 Jumping From Building A to Building B Jump at an angle of 15 from the horizontal, 10.0 m/s Time to go up to max height Time to go down Determine y max first vo sin (10m / s)sin 15 t 0. 64s g 9.8m / s Now determine t down (free fall from a height of 5.00m +0.34m = 5.34m) y gt Time of flight = t up + t down = 0.64s s = 1.308s Horizontal distance covered x vo sin (10m / s) sin 15 ymax 0. 34m g (9.8m / s ) ( 5.34m) t down s 9.8m / s You ll make voxt flight ( 10.0m / s)cos15 (1.308s) 1. 6m the jump!
53 Basketball Exercise There are two ways to shoot the ball given the same initial velocity High arc Low arc Determine the angles of projection for the two shots mentioned above for your favorite player
54 Reminders LONG TEST 1 on December 4, 013 (Wednesday) Chapters 1, and 3 Submit Blue Book on Dec. Monday
55 Relative Velocity (1-D) The velocity with respect to a particular reference frame The woman The train The road The bike rider Woman s velocity relative to the train is 1.0 m/s Train s velocity relative to bike rider is 3.0 m/s What is the woman s velocity with respect to the bike rider? v P / A vp / B vb/ A
56 Example You are driving north on a straight road at a constant velocity of 88 kph. A truck is traveling at a constant velocity of 104 kph on the opposite lane. Relative velocity of truck with respect to you v v v T / E T / Y Y / E vt / Y vt / E vy / E 104kph 88kph v Y T / 19kph Your relative velocity with respect to the truck vy / T vt / Y 19kph Relative velocities don t change after the truck has passed you!
57 Relative Velocity (-D) Vector addition required Woman is walking at an angle with respect to the train s displacement Train is moving at an angle with respect to the normal to the bike rider s line of sight Position vector r P / A rp / B rb / A Velocity Vector v P / A vp / B vb/ A
58 Example An airplane is headed north at 40 kph. If there is a wind of 100 kph from west to east, determine the resultant velocity of the airplane with respect to the ground. P=plane, A=air, E=earth v P / A 40kph v A / E 100kph v v From the diagram v P / E P/ A A/ E due due West East v P / E 40kph 100kph 60kph 100kph tan 1 40kph 3 E of N
59 Correcting Flight Path In what direction should you fly the plane so that its resultant direction is northwards? v P / A 40kph direction unknown v A / E 100kph due East v v v P / E P/ A A/ E From the diagram, v P / E 40kph 100kph 18kph 100kph sin 1 5 W of N 40kph
Chapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Addition of Vectors Graphical Methods (One and Two- Dimension) Multiplication of a Vector by a Scalar Subtraction of Vectors Graphical
More informationComponents of a Vector
Vectors (Ch. 1) A vector is a quantity that has a magnitude and a direction. Examples: velocity, displacement, force, acceleration, momentum Examples of scalars: speed, temperature, mass, length, time.
More informationKinematics in Two Dimensions; Vectors
Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors
More informationPH Fall - Section 04 - Version A DRAFT
1. A truck (traveling in a straight line), starts from rest and accelerates to 30 m/s in 20 seconds. It cruises along at that constant speed for one minute, then brakes, coming to a stop in 25 m. Determine
More informationChapter 2. Kinematics in One Dimension. continued
Chapter 2 Kinematics in One Dimension continued 2.6 Freely Falling Bodies Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement
More informationChapter 4. Two-Dimensional Motion
Chapter 4. Two-Dimensional Motion 09/1/003 I. Intuitive (Understanding) Review Problems. 1. If a car (object, body, truck) moves with positive velocity and negative acceleration, it means that its a) speed
More informationProgressive Science Initiative. Click to go to website:
Slide 1 / 246 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
More informationINTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION
INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION (Sections 12.1-12.2) Today s Objectives: Students will be able to find the kinematic quantities (position, displacement, velocity, and acceleration)
More information1) If the acceleration of an object is negative, the object must be slowing down. A) True B) False Answer: B Var: 1
University Physics, 13e (Young/Freedman) Chapter 2 Motion Along a Straight Line 2.1 Conceptual Questions 1) If the acceleration of an object is negative, the object must be slowing down. A) True B) False
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the acceleration of an object is negative, the object must be slowing down. A) True B) False
More information1.1 Graphing Motion. IB Physics 11 Kinematics
IB Physics 11 Kinematics 1.1 Graphing Motion Kinematics is the study of motion without reference to forces and masses. We will need to learn some definitions: A Scalar quantity is a measurement that has
More information5) A stone is thrown straight up. What is its acceleration on the way up? 6) A stone is thrown straight up. What is its acceleration on the way down?
5) A stone is thrown straight up. What is its acceleration on the way up? Answer: 9.8 m/s 2 downward 6) A stone is thrown straight up. What is its acceleration on the way down? Answer: 9.8 m/ s 2 downward
More informationPhys 2425: University Physics I Summer 2016 Practice Exam 1
1. (0 Points) What course is this? a. PHYS 1401 b. PHYS 1402 c. PHYS 2425 d. PHYS 2426 2. (0 Points) Which exam is this? a. Exam 1 b. Exam 2 c. Final Exam 3. (0 Points) What version of the exam is this?
More informationb) (6) How far down the road did the car travel during the acceleration?
General Physics I Quiz 2 - Ch. 2-1D Kinematics June 17, 2009 Name: For full credit, make your work clear to the grader. Show the formulas you use, all the essential steps, and results with correct units
More informationMotion in Two or Three Dimensions
Chapter 3 Motion in Two or Three Dimensions PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 3 To use vectors
More informationVectors. Graphical Method. Graphical Method. SEEMS SIMPLE? = 30.5 m/s. Graphical Method. Graphical Method (TIP TO TAIL) S
Vectors Graphical Method General discussion. Vector - A quantity which has magnitude and direction. Velocity, acceleration, Force, E Field, Mag Field, calar - A quantity which has magnitude only. (temp,
More informationMotion in Two Dimensions. 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.
Motion in Two Dimensions 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.Projectile Motion The position of an object is described by its position
More informationLecture 2. 1D motion with Constant Acceleration. Vertical Motion.
Lecture 2 1D motion with Constant Acceleration. Vertical Motion. Types of motion Trajectory is the line drawn to track the position of an abject in coordinates space (no time axis). y 1D motion: Trajectory
More informationChapter 3 Acceleration
Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide
More information1. (P2.1A) The picture below shows a ball rolling along a table at 1 second time intervals. What is the object s average velocity after 6 seconds?
PHYSICS FINAL EXAM REVIEW FIRST SEMESTER (01/2017) UNIT 1 Motion P2.1 A Calculate the average speed of an object using the change of position and elapsed time. P2.1B Represent the velocities for linear
More informationLecture 2. 1D motion with Constant Acceleration. Vertical Motion.
Lecture 2 1D motion with Constant Acceleration. Vertical Motion. Types of motion Trajectory is the line drawn to track the position of an abject in coordinates space (no time axis). y 1D motion: Trajectory
More informationChapter 2 One-Dimensional Kinematics. Copyright 2010 Pearson Education, Inc.
Chapter 2 One-Dimensional Kinematics Units of Chapter 2 Position, Distance, and Displacement Average Speed and Velocity Instantaneous Velocity Acceleration Motion with Constant Acceleration Applications
More informationDemo: x-t, v-t and a-t of a falling basket ball.
Demo: x-t, v-t and a-t of a falling basket ball. I-clicker question 3-1: A particle moves with the position-versus-time graph shown. Which graph best illustrates the velocity of the particle as a function
More informationJames T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres. Chapter 2 Motion Cengage Learning
James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres Chapter 2 Motion Defining Motion Motion is a continuous change in position can be described by measuring the rate of change of position
More information2-D Kinematics. In general, we have the following 8 equations (4 per dimension): Notes Page 1 of 7
2-D Kinematics The problem we run into with 1-D kinematics, is that well it s one dimensional. We will now study kinematics in two dimensions. Obviously the real world happens in three dimensions, but
More informationKinematics Multiple- Choice Questions (answers on page 16)
Kinematics Multiple- Choice Questions (answers on page 16) 1. An object moves around a circular path of radius R. The object starts from point A, goes to point B and describes an arc of half of the circle.
More informationPHY 1114: Physics I. Quick Question 1. Quick Question 2. Quick Question 3. Quick Question 4. Lecture 5: Motion in 2D
PHY 1114: Physics I Lecture 5: Motion in D Fall 01 Kenny L. Tapp Quick Question 1 A child throws a ball vertically upward at the school playground. Which one of the following quantities is (are) equal
More information3.2 Projectile Motion
Motion in 2-D: Last class we were analyzing the distance in two-dimensional motion and revisited the concept of vectors, and unit-vector notation. We had our receiver run up the field then slant Northwest.
More informationINTRODUCTION. 3. Two-Dimensional Kinematics
INTRODUCTION We now extend our study of kinematics to motion in two dimensions (x and y axes) This will help in the study of such phenomena as projectile motion Projectile motion is the study of objects
More informationChapter 2. Motion In One Dimension
I. Displacement, Position, and Distance Chapter 2. Motion In One Dimension 1. John (Mike, Fred, Joe, Tom, Derek, Dan, James) walks (jogs, runs, drives) 10 m north. After that he turns around and walks
More informationIntroduction to 2-Dimensional Motion
Introduction to 2-Dimensional Motion 2-Dimensional Motion! Definition: motion that occurs with both x and y components.! Example:! Playing pool.! Throwing a ball to another person.! Each dimension of the
More informationPhysics 231. Topic 3: Vectors and two dimensional motion. Alex Brown September MSU Physics 231 Fall
Physics 231 Topic 3: Vectors and two dimensional motion Alex Brown September 14-18 2015 MSU Physics 231 Fall 2014 1 What s up? (Monday Sept 14) 1) Homework set 01 due Tuesday Sept 15 th 10 pm 2) Learning
More informationChapter 8 : Motion. KEY CONCEPTS [ *rating as per the significance of concept ]
Chapter 8 : Motion KEY CONCEPTS [ *rating as per the significance of concept ] 1 Motion **** 2 Graphical Representation of Motion *** & Graphs 3 Equation of motion **** 4 Uniform Circular Motion ** 1 Motion
More informationPhys 2425: University Physics I Spring 2016 Practice Exam 1
1. (0 Points) What course is this? a. PHYS 1401 b. PHYS 140 c. PHYS 45 d. PHYS 46 Survey Questions no points. (0 Points) Which exam is this? a. Exam 1 b. Exam c. Final Exam 3. (0 Points) What version of
More information1-D and 2-D Motion Test Friday 9/8
1-D and -D Motion Test Frida 9/8 3-1 Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocit, force, momentum A scalar has onl a magnitude. Some scalar
More information2. Two Dimensional Kinematics
. Two Dimensional Kinematics A) Overview We will begin by introducing the concept of vectors that will allow us to generalize what we learned last time in one dimension to two and three dimensions. In
More informationWhat does the lab partner observe during the instant the student pushes off?
Motion Unit Review State Test Questions 1. To create real-time graphs of an object s displacement versus time and velocity versus time, a student would need to use a A motion sensor.b low- g accelerometer.
More informationVectors and Scalars. Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction.
Vectors and Scalars Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction. To distinguish a vector from a scalar quantity, it is usually written
More informationGeneral Physics (PHY 170) Chap 2. Acceleration motion with constant acceleration. Tuesday, January 15, 13
General Physics (PHY 170) Chap 2 Acceleration motion with constant acceleration 1 Average Acceleration Changing velocity (non-uniform) means an acceleration is present Average acceleration is the rate
More informationPSI AP Physics 1 Kinematics. Free Response Problems
PSI AP Physics 1 Kinematics Free Response Problems 1. A car whose speed is 20 m/s passes a stationary motorcycle which immediately gives chase with a constant acceleration of 2.4 m/s 2. a. How far will
More informationMOTION (Chapter 2) Student Learning Objectives 2/11/2016. Compare and contrast terms used to describe motion Analyze circular and parabolic motion
MOTION (Chapter 2) https://www.youtube.com/watch?v=oxc-hhqldbe Student Learning Objectives Compare and contrast terms used to describe motion Analyze circular and parabolic motion PHYSICS:THE MOST FUNDAMENTAL
More informationLesson 2. Physics 168. Luis Anchordoqui
Lesson 2 Physics 168 Luis Anchordoqui Deriving Constant-Acceleration Kinematic Equations To obtain an equation for position as a function of time! look at special case of motion with constant velocity!
More informationIn this activity, we explore the application of differential equations to the real world as applied to projectile motion.
Applications of Calculus: Projectile Motion ID: XXXX Name Class In this activity, we explore the application of differential equations to the real world as applied to projectile motion. Open the file CalcActXX_Projectile_Motion_EN.tns
More informationPH Exam 1. Name
PH105-007 Exam 1 Name 1) The figure shows the graph of the position x as a function of time for an object moving in the straight line (the x-axis). Which of the following graphs best describes the velocity
More informationChapter 3. Kinematics in Two Dimensions
Chapter 3 Kinematics in Two Dimensions 3.1 Trigonometry 3.1 Trigonometry sin! = h o h cos! = h a h tan! = h o h a 3.1 Trigonometry tan! = h o h a tan50! = h o 67.2m h o = tan50! ( 67.2m) = 80.0m 3.1 Trigonometry!
More informationLecture4- Projectile Motion Chapter 4
1 / 32 Lecture4- Projectile Motion Chapter 4 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 28 th, 2018 2 / 32 Objectives Vector
More informationCHAPTER 3: Kinematics in Two Dimensions; Vectors
HAPTER 3: Kinematics in Two Dimensions; Vectors Solution Guide to WebAssign Problems 3.1 [] The truck has a displacement of 18 + (16) blocks north and 1 blocks east. The resultant has a magnitude of +
More informationAP Physics Free Response Practice Kinematics ANSWERS 1982B1 2
AP Physics Free Response Practice Kinematics ANSWERS 198B1 a. For the first seconds, while acceleration is constant, d = ½ at Substituting the given values d = 10 meters, t = seconds gives a = 5 m/s b.
More informationReview Session 1. Page 1
Review Session 1 1. Which combination of fundamental units can be used to express the amount of work done on an object? 2. The height of a typical kitchen table is approximately A) 10-2 m B) 10 0 m C)
More informationFormative Assessment: Uniform Acceleration
Formative Assessment: Uniform Acceleration Name 1) A truck on a straight road starts from rest and accelerates at 3.0 m/s 2 until it reaches a speed of 24 m/s. Then the truck travels for 20 s at constant
More informationKinematics. Vector solutions. Vectors
Kinematics Study of motion Accelerated vs unaccelerated motion Translational vs Rotational motion Vector solutions required for problems of 2- directional motion Vector solutions Possible solution sets
More informationAP Physics 1 Summer Assignment 2018 Mrs. DeMaio
AP Physics 1 Summer Assignment 2018 Mrs. DeMaio demaiod@middletownk12.org Welcome to AP Physics 1 for the 2018-2019 school year. AP Physics 1 is an algebra based, introductory college-level physics course.
More informationCHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS
CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS OBJECTIVES After studying the material of this chapter, the student should be able to: represent the magnitude and direction of a vector using a protractor
More informationIntroduction to 1-D Motion Distance versus Displacement
Introduction to 1-D Motion Distance versus Displacement Kinematics! Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.! 1-Dimensional
More informationChapter 3 Motion in two or three dimensions
Chapter 3 Motion in two or three dimensions Lecture by Dr. Hebin Li Announcements As requested by the Disability Resource Center: In this class there is a student who is a client of Disability Resource
More informationBell Ringer: What is constant acceleration? What is projectile motion?
Bell Ringer: What is constant acceleration? What is projectile motion? Can we analyze the motion of an object on the y-axis independently of the object s motion on the x-axis? NOTES 3.2: 2D Motion: Projectile
More informationChapter 3 Acceleration
Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide
More informationPH Fall - Section 05 - Version C DRAFT
1. A truck (traveling in a straight line), starts from rest and accelerates to 30 m/s in 20 seconds. It cruises along at that constant speed for one minute, then brakes, coming to a stop in 25 m. Determine
More informationMotion in One Dimension
Motion in One Dimension Much of the physics we ll learn this semester will deal with the motion of objects We start with the simple case of one-dimensional motion Or, motion in x: As always, we begin by
More informationCHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS
CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS General properties of vectors displacement vector position and velocity vectors acceleration vector equations of motion in 2- and 3-dimensions Projectile motion
More informationKINEMATICS OF A PARTICLE. Prepared by Engr. John Paul Timola
KINEMATICS OF A PARTICLE Prepared by Engr. John Paul Timola Particle has a mass but negligible size and shape. bodies of finite size, such as rockets, projectiles, or vehicles. objects can be considered
More information2-D Vector Equations have the same form as 1-D Kinematics. f i i
2-D Vector Equations have the same form as 1-D Kinematics v = v + at f i 1 r = r + v t+ at f i i 2 2 2-D Vector Equations have the same form as 1-D Kinematics v = viˆ+ v ˆj f x y = ( v + ati ) ˆ+ ( v +
More informationChapter 2: Motion a Straight Line
Formula Memorization: Displacement What is a vector? Average Velocity Average Speed Instanteous Velocity Average Acceleration Instantaneous Acceleration Constant Acceleration Equation (List all five of
More informationChapter 3 Homework Packet. Conceptual Questions
Chapter 3 Homework Packet Conceptual Questions 1) Which one of the following is an example of a vector quantity? A) mass B) area C) distance D) velocity A vector quantity has both magnitude and direction.
More informationWhen we throw a ball :
PROJECTILE MOTION When we throw a ball : There is a constant velocity horizontal motion And there is an accelerated vertical motion These components act independently of each other PROJECTILE MOTION A
More informationProblem: Projectile (CM-1998) Justify your answer: Problem: Projectile (CM-1998) 5 10 m/s 3. Show your work: 3 m/s 2
Physics C -D Kinematics Name: AP Review Packet Vectors have both magnitude and direction displacement, velocity, acceleration Scalars have magnitude only distance, speed, time, mass Unit vectors Specify
More informationINTRODUCTION. 1. One-Dimensional Kinematics
INTRODUCTION Mechanics is the area of physics most apparent to us in our everyday lives Raising an arm, standing up, sitting down, throwing a ball, opening a door etc all governed by laws of mechanics
More informationGraphing Motion Part 2
Kinematics 2: Motion Graphs & Free Fall Sep 5 10:34 AM Sep 5 1:25 PM Graphing Motion Part 2 How do you calculate the slope of a line? What would the slope of a distance vs time graph represent? What would
More informationChapter 2: 1D Kinematics
Chapter 2: 1D Kinematics Description of motion involves the relationship between position, displacement, velocity, and acceleration. A fundamental goal of 1D kinematics is to determine x(t) if given initial
More informationAdding Vectors in Two Dimensions
Slide 37 / 125 Adding Vectors in Two Dimensions Return to Table of Contents Last year, we learned how to add vectors along a single axis. The example we used was for adding two displacements. Slide 38
More informationacceleration versus time. LO Determine a particle s change in position by graphical integration on a graph of velocity versus time.
Chapter: Chapter 2 Learning Objectives LO 2.1.0 Solve problems related to position, displacement, and average velocity to solve problems. LO 2.1.1 Identify that if all parts of an object move in the same
More informationAP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS
AP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS The moment of truth has arrived! To discuss objects that move in something other than a straight line we need vectors. VECTORS Vectors
More informationPractice Test What two units of measurement are necessary for describing speed?
Practice Test 1 1. What two units of measurement are necessary for describing speed? 2. What kind of speed is registered by an automobile? 3. What is the average speed in kilometers per hour for a horse
More informationMultiple-Choice Questions
Multiple-Choice Questions 1. A rock is thrown straight up from the edge of a cliff. The rock reaches the maximum height of 15 m above the edge and then falls down to the bottom of the cliff 35 m below
More informationMotion in 2- and 3-dimensions. Examples: non-linear motion (circles, planetary orbits, etc.) flight of projectiles (shells, golf balls, etc.
Motion in 2- and 3-dimensions Examples: HPTER 3 MOTION IN TWO & THREE DIMENSIONS General properties of vectors the displacement vector position and velocity vectors acceleration vector equations of motion
More informationChapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion
Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors
More informationFour Types of Motion We ll Study
Four Types of Motion We ll Study The branch of mechanics that studies the motion of a body without caring about what caused the motion. Kinematics definitions Kinematics branch of physics; study of motion
More informationBell Ringer. x- direction: Ball and car start with same position and velocity, a=0, so always have same position
Objectives Students should be able to add, subtract, and resolve displacement and velocity vectors so they can: Determine the components of a vector along two specified, mutually perpendicular axes. Determine
More informationVocabulary Preview. Oct 21 9:53 AM. Projectile Motion. An object shot through the air is called a projectile.
Projectile Trajectory Range Launch angle Vocabulary Preview Projectile Motion Projectile Motion An object shot through the air is called a projectile. A projectile can be a football, a bullet, or a drop
More informationMotion Along a Straight Line
PHYS 101 Previous Exam Problems CHAPTER Motion Along a Straight Line Position & displacement Average & instantaneous velocity Average & instantaneous acceleration Constant acceleration Free fall Graphical
More informationPRACTICE TEST for Midterm Exam
South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v o t + ½ at 2 d = v o + v 2 t v = v o + at v 2 = v 2 o + 2ad v = v x 2 + v y 2 = tan 1 v y v v x = v cos
More informationTopic 2.1: Kinematics. How do we analyze the motion of objects?
Topic.1: Kinematics How do we analyze the motion of objects? Characteristic Graphs The most common kinematics problems involve uniform acceleration from rest These have a characteristic shape for each
More informationA. Basic Concepts and Graphs
A. Basic Concepts and Graphs A01 [Qual] [Easy] For each of the following, select if it is a vector or a scalar. a) Speed b) Distance traveled c) Velocity d) (Linear) Displacement A02 [Qual] [Easy] Give
More informationMOTION IN A PLANE. Chapter Four MCQ I. (a) 45 (b) 90 (c) 45 (d) 180
Chapter Four MOTION IN A PLANE MCQ I 4.1 The angle between A = ˆi + ˆj and B = ˆi ˆj is (a) 45 (b) 90 (c) 45 (d) 180 4.2 Which one of the following statements is true? (a) A scalar quantity is the one
More information4 MOTION IN TWO AND THREE DIMENSIONS
Chapter 4 Motion in Two and Three Dimensions 157 4 MOTION IN TWO AND THREE DIMENSIONS Figure 4.1 The Red Arrows is the aerobatics display team of Britain s Royal Air Force. Based in Lincolnshire, England,
More informationClass 11 Physics NCERT Exemplar Solutions Motion in a Straight Line
Class 11 Physics NCERT Exemplar Solutions Motion in a Straight Line Multiple Choice Questions Single Correct Answer Type Q1. Among the four graphs shown in the figure, there is only one graph for which
More informationAP Physics 1 Summer Assignment
Name: Email address (write legibly): AP Physics 1 Summer Assignment Packet 3 The assignments included here are to be brought to the first day of class to be submitted. They are: Problems from Conceptual
More informationPHYSICS Kinematics in One Dimension
PHYSICS Kinematics in One Dimension August 13, 2012 www.njctl.org 1 Motion in One Dimension Return to Table of Contents 2 Distance We all know what the distance between two objects is... So what is it?
More informationThe Science of Physics
Assessment The Science of Physics Chapter Test B MULTIPLE CHOICE In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. A hiker
More informationChapter 2. Motion along a Straight Line
Chapter 2 Motion along a Straight Line 1 2.1 Motion Everything in the universe, from atoms to galaxies, is in motion. A first step to study motion is to consider simplified cases. In this chapter we study
More informationChapter 2 Solutions. = 16.1 m/s. = 11.5 m/s m. 180 km = ( ) h. = 2.5 m/s. = 3.3 m/s
Chapter Solutions *.1 (a) v.30 m/s v x 57.5 m 9.0 m 3.00 s 16.1 m/s (c) v x 57.5 m 0 m 5.00 s 11.5 m/s. (a) Displacement (8.50 10 4 m/h) 35.0 60.0 h + 130 103 m x (49.6 + 130) 10 3 m 180 km Average velocity
More informationMidterm Prep. 1. Which combination correctly pairs a vector quantity with its corresponding unit?
Name: ate: 1. Which combination correctly pairs a vector quantity with its corresponding unit?. weight and kg. velocity and m/s. speed and m/s. acceleration and m 2 /s 2. 12.0-kilogram cart is moving at
More informationPrinciples and Problems. Chapter 6: Motion in Two Dimensions
PHYSICS Principles and Problems Chapter 6: Motion in Two Dimensions CHAPTER 6 Motion in Two Dimensions BIG IDEA You can use vectors and Newton s laws to describe projectile motion and circular motion.
More informationKinematics and One Dimensional Motion
Kinematics and One Dimensional Motion Kinematics Vocabulary Kinema means movement Mathematical description of motion Position Time Interval Displacement Velocity; absolute value: speed Acceleration Averages
More information2. KINEMATICS. By Liew Sau Poh
2. KINEMATICS By Liew Sau Poh 1 OBJECTIVES 2.1 Linear motion 2.2 Projectiles 2.3 Free falls and air resistance 2 OUTCOMES Derive and use equations of motion with constant acceleration Sketch and use the
More informationUnit 1 Motion. Projectile Motion
Unit 1 Motion Projectile Motion Motion to Date Uniform Motion Accelerated Motion Relative Motion Uniform Motion Motion with a constant velocity - Constant speed - Same direction Equation: v d t Problems
More informationPHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009
PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively.
More informationChapter 4 Kinematics II: Motion in Two and Three Dimensions
Chapter 4 Kinematics II: Motion in Two and Three Dimensions Demonstrations: 1) Ball falls down and another falls out 2) Parabolic and straight line motion from two different frames. The truck with a dropping
More informationphysics Chapter 4 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS Chapter 4_Lecture1 THIRD EDITION
Chapter 4 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 4_Lecture1 1 Chapter 4 Kinematics in 2D: Projectile Motion (Sec. 4.2) Which fountain
More informationMotion Along a Straight Line (Motion in One-Dimension)
Chapter 2 Motion Along a Straight Line (Motion in One-Dimension) Learn the concepts of displacement, velocity, and acceleration in one-dimension. Describe motions at constant acceleration. Be able to graph
More information