Kinematics in two Dimensions


 Cameron Ross
 4 years ago
 Views:
Transcription
1 Lecure 5 Chaper 4 Phsics I Kinemaics in wo Dimensions Course websie: hp://facul.uml.edu/andri_danlo/teachin/phsicsi PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
2 Toda we are oin o discuss: Chaper 4: Moion in Two Dimensions: Secion 4.1 Projecile moion: Secion 4. PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
3 Moion in Two Dimensions (Vecor Kinemaics) We use he ecor mahemaics o consider moion in more han one dimension. Preiousl described 1D displacemen as Δ, where moion could onl be posiie or neaie. In more han 1D, displacemen are D ecors r r r r r() () PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
4 Displacemen in wo dimensions Posiion of an objec r ( )ˆ i ( ) ĵ î Rabbi s pah r 1 1 r r r r r 1 displacemen (in uni ecor noaion): r In wo dimensions, he displacemen is a ecor: r iˆ r iˆ 1 1 ( 1 )ˆ i ( 1) 1 PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
5 r 1 Insananeous Veloci in wo dimensions 1 Tanen 1 r r r r r Aerae eloci is he displacemen diided b he elapsed ime r r1 1 r As Δ and Δr become smaller and smaller, he aerae eloci approaches he insananeous eloci. lim r d r d The insananeous eloci indicaes how fas he objec moes and he direcion of moion a each insan of ime dr d dr d d iˆ d d d iˆ PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
6 Insananeous acceleraion in wo dimensions r r Aerae acceleraion a The insananeous acceleraion is in he direcion of,and is ien b: lim 1 d d 1 1 a d r d a d d iˆ d d d iˆ d d d PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
7 () r Posiion of an objec r ( )ˆ i ( ) Insananeous eloci dr d d iˆ iˆ d d d () a Insananeous acceleraion d d iˆ d d d d d iˆ d r,, a wrien in erm of iˆ, ˆ, j kˆ PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
8 Eample A rabbi runs across a parkin lo on which a se of coordinae aes has, sranel enouh, been drawn. The coordinaes as funcions of ime are ien The, coordinaes are componens of he rabbi s posiion ecor ( ) (4 1) ( ) 3 r( ) ( )ˆ i ( ) r ( ) (4 1)ˆ i 3j ˆ PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
9 Projecile moion A projecile is an objec moin in wo dimensions under he influence of Earh's rai; is pah is a parabola. () r () a a?,? PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
10 r r a B spliin he equaions of moion ino componen form, we can sole problems one direcion a a ime 1 a a a f ( ) Veloci equaion o Posiion equaion 1 a No ime equaion a (1) () (3) f ( ) Veloci equaion o Posiion equaion 1 a No ime equaion a (1) () (3) There is onl one parameer, which connecs X and Y moion: ime PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics X and Y moions are compleel independen Work he problem as wo onedimensional problems
11 Equaions in he X  direcion No forces in direcion (air resisance is neleced), as a resul, no acceleraion is consan!!!! f ( ) Veloci equaion o Posiion equaion 1 a No ime equaion a (1) () (3) a = So, from here, we can e onl one equaion. PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
12 Deparmen of Phsics and Applied Phsics PHYS.141 Lecure 5 Danlo Equaions in he Y direcion a = a = if hen if hen ) ( 1 ) ( 1 1 a f (3) No ime equaion Posiion equaion a o ) ( Veloci equaion () (1)
13 Rescue Helicoper Helicoper flin horizonall a 7m/s wans o drop supplies on mounain op m below. How far in adance (horizonal disance) should he packae be dropped? Draw diaram, choose coordinaes Knowns and unknowns Diide equaions ino and Sole, noin ha in he and calculaions he common parameer is he ime ineral PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
14 ConcepTes 1 From he same heih (and a he same ime), one ball is dropped and anoher ball is fired horizonall. Which one will hi he round firs? Droppin he Ball I A) he dropped ball B) he fired ball C) he boh hi a he same ime D) i depends on how hard he ball was fired E) i depends on he iniial heih OR Boh of he balls are fallin ericall under he influence of rai. The boh fall from he same heih. Therefore, he will hi he round a he same ime. The fac ha one is moin horizonall is irrelean remember ha he and moions are compleel independen!! 1
15 Eample (Golf Ball) A olf ball is hi wih iniial eloci a an anle θ aboe he horizonal. Draw diaram and choose coordinae ssem Fill in knowns cos sin a a PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
16 Con. Eample (Golf Ball). A olf ball is hi wih iniial eloci a an anle θ aboe he horizonal. Find: he ime of flih (how lon he ball is in he air) This depends onl on he componen equaions, as he moion in direcion sops he flih. o o 1 a Since boh and are zero a he beinnin/end = when he ball was hi PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics o 1 ( o ) The second is he ime of flih 1 and = when he ball landed
17 Con. Eample (Golf Ball) A olf ball is hi wih iniial eloci a an anle θ aboe he horizonal. Find: Rane (how far does ball rael on fla round) ime of flih Rane when Use consan eloci o calculae how far ball raels horizonall durin ime of flih (Rane) Consan eloci R PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics sin 1 or 45 cos R sin o R ma o Rane sin coso Maimum Rane o sin
18 Con. Eample (Golf Ball) A olf ball is hi wih iniial eloci a an anle θ aboe he horizonal. Find: rajecor (heih as a funcion of posiion ) o 1 Since common parameer is ime, eliminae o e () Equaion of parabola A B PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
19 ConcepTes. Puns I Which of he hree puns has he lones han ime? A B C D) all hae he same han ime h The ime in he air is deermined b he erical moion! Because all of he puns reach he same heih, he all sa in he air for he same ime. ( ) o o 1 a
20 ConcepTes 3 Puns II A baleship simulaneousl fires wo shells a wo enem submarines. The shells are launched wih he same iniial eloci. If he shells follow he rajecories shown, which submarine es hi firs? The flih ime is fied b he moion in he direcion. The hiher an objec oes, he loner i sas in flih. The shell hiin submarine # oes less hih, herefore i sas in flih for less ime han he oher shell. Thus, submarine # is hi firs. A B C) boh a he same ime
21 Solin Problems Inolin Projecile Moion 1. Read he problem carefull, and choose he objec(s) ou are oin o analze.. Draw a diaram. 3. Choose an oriin and a coordinae ssem. 4. Decide on he ime ineral; his is he same in boh direcions, and includes onl he ime he objec is moin wih consan acceleraion. 5. Eamine he and moions separael. 6. Lis known and unknown quaniies. Remember ha neer chanes, and ha = a he hihes poin. 7. Plan how ou will proceed. Use he appropriae equaions; ou ma hae o combine some of hem. PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics
22 PHYS.141 Lecure 5 Danlo Deparmen of Phsics and Applied Phsics Thank ou See ou on Monda
Kinematics in two dimensions
Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5
More informationChapter 3 Kinematics in Two Dimensions
Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Twodimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo
More informationUnit 1 Test Review Physics Basics, Movement, and Vectors Chapters 13
A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 13 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:
More informationand v y . The changes occur, respectively, because of the acceleration components a x and a y
Week 3 Reciaion: Chaper3 : Problems: 1, 16, 9, 37, 41, 71. 1. A spacecraf is raveling wih a veloci of v0 = 5480 m/s along he + direcion. Two engines are urned on for a ime of 84 s. One engine gives he
More informationWEEK3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationPhys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole
Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen
More informationPhysics Unit Workbook Two Dimensional Kinematics
Name: Per: L o s A l o s H i g h S c h o o l Phsics Uni Workbook Two Dimensional Kinemaics Mr. Randall 1968  Presen adam.randall@mla.ne www.laphsics.com a o 1 a o o ) ( o o a o o ) ( 1 1 a o g o 1 g o
More information2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance
Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion
More informationDEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS LESSON 1C PROJECTILE MOTION FLUID RESISTANCE Inroducion Videos Projecile Moion 1 Useful Applicaions of Projecile Moion Essenial Idea: Moion ma be described
More informationOneDimensional Kinematics
OneDimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
More informationEquations of motion for constant acceleration
Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
More informationReview Equations. Announcements 9/8/09. Table Tennis
Announcemens 9/8/09 1. Course homepage ia: phsics.bu.edu Class web pages Phsics 105 (Colon J). (Classwide email sen) Iclicker problem from las ime scores didn ge recorded. Clicker quizzes from lecures
More information1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a
Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.
More informationVersion 053 Midterm 1 OConnor (05141) 1
Version 053 Miderm 1 OConnor (05141) 1 This prinou should have 36 quesions. Muliplechoice quesions ma coninue on he ne column or pae find all choices before answerin. V1:1, V:1, V3:3, V4:1, V5:4. 001
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More informationPhysics Notes  Ch. 2 Motion in One Dimension
Physics Noes  Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,
More informationBrock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension
Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiionime graphs, elociyime graphs, and heir
More informationVectors and TwoDimensional Motion
3 Vecors and TwoDimensional Moion QUICK QUIZZES. Choice (c). The lares possible maniude of he resulan occurs when he wo ecors are in he same direcion. In his case, he maniude of he resulan is he sum of
More informationEx: An object is released from rest. Find the proportion of its displacements during the first and second seconds. y. g= 9.8 m/s 2
FREELY FALLING OBJECTS Free fall Acceleraion If e only force on an objec is is wei, e objec is said o be freely fallin, reardless of e direcion of moion. All freely fallin objecs (eay or li) ae e same
More informationKinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.
Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages
More informations in boxe wers ans Put
Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs
More informationExam #2 PHYSICS 211 Monday July 6 th, 2009 Please write down your name also on the back page of this exam
Exa #2 PHYSICS 211 Monday July 6 h, 29 NME Please wrie down your nae also on he back pae of his exa 1. The fiure ives how he force varies as a funcion of he posiion. Such force is acin on a paricle, which
More informationIn this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should
Cambridge Universiy Press 97836600337 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion
More informationQ2.4 Average velocity equals instantaneous velocity when the speed is constant and motion is in a straight line.
CHAPTER MOTION ALONG A STRAIGHT LINE Discussion Quesions Q. The speedomeer measures he magniude of he insananeous eloci, he speed. I does no measure eloci because i does no measure direcion. Q. Graph (d).
More informationLAB 05 Projectile Motion
PHYS 154 Universi Phsics Laboraor PreLab Spring 18 LAB 5 Projecile Moion CONTENT: 1. Inroducion. Projecile moion A. Seup B. Various characerisics 3. Prelab: A. Aciviies B. Preliminar info C. Quiz 1.
More informationChapter 12: Velocity, acceleration, and forces
To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable
More information2d Motion: Constant Acceleration
d Moion: Consan Acceleaion Kinemaic Equaions o Moion (eco Fom Acceleaion eco (consan eloci eco (uncion o Posiion eco (uncion o The eloci eco and posiion eco ae a uncion o he ime. eloci eco a ime. Posiion
More informationPage 1 o 13 1. The brighes sar in he nigh sky is α Canis Majoris, also known as Sirius. I lies 8.8 lighyears away. Express his disance in meers. ( lighyear is he disance coered by ligh in one year. Ligh
More informationPhysics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension
Physics for Scieniss and Engineers Chaper Kinemaics in One Dimension Spring, 8 Ho Jung Paik Kinemaics Describes moion while ignoring he agens (forces) ha caused he moion For now, will consider moion in
More informationChapter 5 Kinematics
Chaper 5 Kinemaics In he firs place, wha do we mean b ime and space? I urns ou ha hese deep philosophical quesions have o be analzed ver carefull in phsics, and his is no eas o do. The heor of relaivi
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationMain Ideas in Class Today
Main Ideas in Class Toda Inroducion o Falling Appl Consan a Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs Refers o objecs
More informationPhysics 218 Exam 1 with Solutions Spring 2011, Sections ,526,528
Physics 18 Exam 1 wih Soluions Sprin 11, Secions 513515,56,58 Fill ou he informaion below bu do no open he exam unil insruced o do so Name Sinaure Suden ID E mail Secion # Rules of he exam: 1. You have
More informationPhysics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.
Physics 180A Fall 2008 Tes 1120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers
More information1. VELOCITY AND ACCELERATION
1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. DisplacemenTime Graph Gradien = speed 1.3 VelociyTime Graph Gradien = acceleraion Area under
More informationDisplacement ( x) x x x
Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1Dimensional Kinemaics (or 1 Dimensional moion) refers o moion in a sraigh
More informationIB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
More informationINSTANTANEOUS VELOCITY
INSTANTANEOUS VELOCITY I claim ha ha if acceleraion is consan, hen he elociy is a linear funcion of ime and he posiion a quadraic funcion of ime. We wan o inesigae hose claims, and a he same ime, work
More informationPhysics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)
Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.13.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as
More informationAP Calculus BC Chapter 10 Part 1 AP Exam Problems
AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a
More informationMotion along a Straight Line
chaper 2 Moion along a Sraigh Line verage speed and average velociy (Secion 2.2) 1. Velociy versus speed Cone in he ebook: fer Eample 2. Insananeous velociy and insananeous acceleraion (Secions 2.3, 2.4)
More informationPHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections
PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.22.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
More informationCourse II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle
Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s
More informationUNIT # 01 (PART I) BASIC MATHEMATICS USED IN PHYSICS, UNIT & DIMENSIONS AND VECTORS. 8. Resultant = R P Q, R P 2Q
JPhsics UNI # 0 (PAR I) ASIC MAHMAICS USD IN PHYSICS, UNI & DIMNSIONS AND VCORS XRCIS I. nclosed area : A r so da dr r Here r 8 cm, dr da 5 cm/s () (8) (5) 80 cm /s. Slope d d 6 9 if angen is parallel
More informationSPH3U1 Lesson 03 Kinematics
SPH3U1 Lesson 03 Kinemaics GRAPHICAL ANALYSIS LEARNING GOALS Sudens will Learn how o read values, find slopes and calculae areas on graphs. Learn wha hese values mean on boh posiionime and velociyime
More informationPhysics 20 Lesson 5 Graphical Analysis Acceleration
Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiionime graph is equal o he velociy of
More informationVelocity is a relative quantity
Veloci is a relaie quani Disenangling Coordinaes PHY2053, Fall 2013, Lecure 6 Newon s Laws 2 PHY2053, Fall 2013, Lecure 6 Newon s Laws 3 R. Field 9/6/2012 Uniersi of Florida PHY 2053 Page 8 Reference Frames
More informationPhysics for Scientists and Engineers I
Physics for Scieniss and Engineers I PHY 48, Secion 4 Dr. Beariz Roldán Cuenya Universiy of Cenral Florida, Physics Deparmen, Orlando, FL Chaper  Inroducion I. General II. Inernaional Sysem of Unis III.
More informationUniversity Physics with Modern Physics 14th Edition Young TEST BANK
Universi Phsics wih Modern Phsics 14h Ediion Young SOLUTIONS MANUAL Full clear download (no formaing errors) a: hps://esbankreal.com/download/universiphsicsmodernphsics 14hediionoungsoluionsmanual/
More informationGuest Lecturer Friday! Symbolic reasoning. Symbolic reasoning. Practice Problem day A. 2 B. 3 C. 4 D. 8 E. 16 Q25. Will Armentrout.
Pracice Problem day Gues Lecurer Friday! Will Armenrou. He d welcome your feedback! Anonymously: wrie somehing and pu i in my mailbox a 111 Whie Hall. Email me: sarah.spolaor@mail.wvu.edu Symbolic reasoning
More informationCheck in: 1 If m = 2(x + 1) and n = find y when. b y = 2m n 2
7 Parameric equaions This chaer will show ou how o skech curves using heir arameric equaions conver arameric equaions o Caresian equaions find oins of inersecion of curves and lines using arameric equaions
More informationSPH3U: Projectiles. Recorder: Manager: Speaker:
SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0
More informationLecture 21 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure  Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationIntegration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum.
Inegraion of he equaion of moion wih respec o ime raher han displacemen leads o he equaions of impulse and momenum. These equaions greal faciliae he soluion of man problems in which he applied forces ac
More informationFundamental Units. Then, watch out. Page 1. SPH4UI: Lecture 1 Course Info & Advice. Kinematics
SPH4UI: Lecure 1 Course Info & Adice Course has seeral componens: Lecure: (me alkin, demos and ou askin quesions) Discussion secions (uorials, problem solin, quizzes) Homework Web based Labs: (roup eploraion
More informationWelcome Back to Physics 215!
Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure012 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion
More informationParametrics and Vectors (BC Only)
Paramerics and Vecors (BC Only) The following relaionships should be learned and memorized. The paricle s posiion vecor is r() x(), y(). The velociy vecor is v(),. The speed is he magniude of he velociy
More information!!"#"$%&#'()!"#&'(*%)+,&',)./0)1*23)
"#"$%&#'()"#&'(*%)+,&',)./)1*) #$%&'()*+,&',.%,/)*+,&1*#$)()5*6$+$%*,7&*'&1*(,&*6&,7.$%$+*&%'(*8$&',,%'&1*(,&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',9*(&,%)?%*,('&5
More informationTopic 1: Linear motion and forces
TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor
More informationt A. 3. Which vector has the largest component in the ydirection, as defined by the axes to the right?
Ke Name Insrucor Phsics 1210 Exam 1 Sepember 26, 2013 Please wrie direcl on he exam and aach oher shees of work if necessar. Calculaors are allowed. No noes or books ma be used. Muliplechoice problems
More information4.5 Constant Acceleration
4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x componen of he velociy is a linear funcion (Figure 4.8(a)),
More informationBest test practice: Take the past test on the class website
Bes es pracice: Take he pas es on he class websie hp://communiy.wvu.edu/~miholcomb/phys11.hml I have posed he key o he WebAssign pracice es. Newon Previous Tes is Online. Forma will be idenical. You migh
More information2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s freefall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:
More informationPHYSICS 149: Lecture 9
PHYSICS 149: Lecure 9 Chaper 3 3.2 Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1 Velociy (m/s) The
More informationWave Motion Sections 1,2,4,5, I. Outlook II. What is wave? III.Kinematics & Examples IV. Equation of motion Wave equations V.
Secions 1,,4,5, I. Oulook II. Wha is wave? III.Kinemaics & Eamples IV. Equaion of moion Wave equaions V. Eamples Oulook Translaional and Roaional Moions wih Several phsics quaniies Energ (E) Momenum (p)
More informationPosition, Velocity, and Acceleration
rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME9493 1 Car ME9454 1 Fan Accessory ME9491 1 Moion Sensor II CI6742A 1 Track Barrier Purpose The purpose
More informationPhysics 101 Fall 2006: Exam #1 PROBLEM #1
Physics 101 Fall 2006: Exam #1 PROBLEM #1 1. Problem 1. (+20 ps) (a) (+10 ps) i. +5 ps graph for x of he rain vs. ime. The graph needs o be parabolic and concave upward. ii. +3 ps graph for x of he person
More informationMechanics Acceleration The Kinematics Equations
Mechanics Acceleraion The Kinemaics Equaions Lana Sheridan De Anza College Sep 27, 2018 Las ime kinemaic quaniies graphs of kinemaic quaniies Overview acceleraion he kinemaics equaions (consan acceleraion)
More informationConceptual Physics Review (Chapters 2 & 3)
Concepual Physics Review (Chapers 2 & 3) Soluions Sample Calculaions 1. My friend and I decide o race down a sraigh srech of road. We boh ge in our cars and sar from res. I hold he seering wheel seady,
More informationPhysics 101 Lecture 4 Motion in 2D and 3D
Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd
More informationSuggested Practice Problems (set #2) for the Physics Placement Test
Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More information10.6 Parametric Equations
0_006.qd /8/05 9:05 AM Page 77 Secion 0.6 77 Parameric Equaions 0.6 Parameric Equaions Wha ou should learn Evaluae ses of parameric equaions for given values of he parameer. Skech curves ha are represened
More informationKinematics Motion in 1 Dimension and Graphs
Kinemaics Moion in 1 Dimension and Graphs Lana Sheridan De Anza College Sep 27, 2017 Las ime moion in 1dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics
More informationx i v x t a dx dt t x
Physics 3A: Basic Physics I Shoup  Miderm Useful Equaions A y A sin A A A y an A y A A = A i + A y j + A z k A * B = A B cos(θ) A B = A B sin(θ) A * B = A B + A y B y + A z B z A B = (A y B z A z B y
More informationPhysics 3A: Basic Physics I Shoup Sample Midterm. Useful Equations. x f. x i v x. a x. x i. v xi v xf. 2a x f x i. y f. a r.
Physics 3A: Basic Physics I Shoup Sample Miderm Useful Equaions A y Asin A A x A y an A y A x A = A x i + A y j + A z k A * B = A B cos(θ) A x B = A B sin(θ) A * B = A x B x + A y B y + A z B z A x B =
More information3 Motion with constant acceleration: Linear and projectile motion
3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr
More information15. Vector Valued Functions
1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,
More informationDynamics. Option topic: Dynamics
Dynamics 11 syllabusref Opion opic: Dynamics eferenceence In his cha chaper 11A Differeniaion and displacemen, velociy and acceleraion 11B Inerpreing graphs 11C Algebraic links beween displacemen, velociy
More informationPhysics 5A Review 1. Eric Reichwein Department of Physics University of California, Santa Cruz. October 31, 2012
Physics 5A Review 1 Eric Reichwein Deparmen of Physics Universiy of California, Sana Cruz Ocober 31, 2012 Conens 1 Error, Sig Figs, and Dimensional Analysis 1 2 Vecor Review 2 2.1 Adding/Subracing Vecors.............................
More informationTwo Dimensional Dynamics
Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Exam I Physics 11: Lecure 6, Pg 1 Brie Reiew Thus Far Newon s Laws o moion: SF=ma Kinemaics: x = x + + ½ a Dynamics Today
More informationA. Using Newton s second law in one dimension, F net. , write down the differential equation that governs the motion of the block.
Simple SIMPLE harmonic HARMONIC moion MOTION I. Differenial equaion of moion A block is conneced o a spring, one end of which is aached o a wall. (Neglec he mass of he spring, and assume he surface is
More informationMEI Mechanics 1 General motion. Section 1: Using calculus
Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = , so he iniial displacemen =  m. s v 4 When = 0, v = so he iniial velociy
More informationTwo Dimensional Dynamics
Physics 11: Lecure 6 Two Dimensional Dynamics Today s lecure will coer Chaper 4 Saring Wed Sep 15, WF oice hours will be in 3 Loomis. Exam I M oice hours will coninue in 36 Loomis Physics 11: Lecure 6,
More informationPhysics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008
Physics 221 Fall 28 Homework #2 Soluions Ch. 2 Due Tues, Sep 9, 28 2.1 A paricle moving along he xaxis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly
More information1.6. Slopes of Tangents and Instantaneous Rate of Change
1.6 Slopes of Tangens and Insananeous Rae of Change When you hi or kick a ball, he heigh, h, in meres, of he ball can be modelled by he equaion h() 4.9 2 v c. In his equaion, is he ime, in seconds; c represens
More informationFundamental Units. Then, watch out. Page 1. SPH4UI: Lecture 1 Course Info & Advice. Kinematics
SPH4UI: Lecure 1 Course Info & Adice Course has seeral componens: Lecure: (me alkin, demos and ou askin quesions) Discussion secions (uorials, problem solin, quizzes) Homework Web based Labs: (roup eploraion
More informationGiambattista, Ch 3 Problems: 9, 15, 21, 27, 35, 37, 42, 43, 47, 55, 63, 76
Giambaisa, Ch 3 Problems: 9, 15, 21, 27, 35, 37, 42, 43, 47, 55, 63, 76 9. Sraeg Le be direced along he +xaxis and le be 60.0 CCW from Find he magniude of 6.0 B 60.0 4.0 A x 15. (a) Sraeg Since he angle
More informationSolution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration
PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationLAB 5  PROJECTILE MOTION
Lab 5 Projecile Moion 71 Name Dae Parners OVEVIEW LAB 5  POJECTILE MOTION We learn in our sudy of kinemaics ha wodimensional moion is a sraighforward exension of onedimensional moion. Projecile moion
More information4.6 One Dimensional Kinematics and Integration
4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a nonconsan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x componen of
More informationWeek 1 Lecture 2 Problems 2, 5. What if something oscillates with no obvious spring? What is ω? (problem set problem)
Week 1 Lecure Problems, 5 Wha if somehing oscillaes wih no obvious spring? Wha is ω? (problem se problem) Sar wih Try and ge o SHM form E. Full beer can in lake, oscillaing F = m & = ge rearrange: F =
More informationChapter 2. Motion along a straight line
Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics
More informationv x + v 0 x v y + a y + v 0 y + 2a y + v y Today: Projectile motion Soccer problem Firefighter example
Thurs Sep 10 Assign 2 Friday SI Sessions: Moron 227 Mon 8:109:10 PM Tues 8:109:10 PM Thur 7:058:05 PM Read Read Draw/Image lay ou coordinae sysem Wha know? Don' know? Wan o know? Physical Processes?
More informationx y θ = 31.8 = 48.0 N. a 3.00 m/s
4.5.IDENTIY: Vecor addiion. SET UP: Use a coordinae sse where he dog A. The forces are skeched in igure 4.5. EXECUTE: + ais is in he direcion of, A he force applied b =+ 70 N, = 0 A B B A = cos60.0 =
More informationToday: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time
+v Today: Graphing v (miles per hour ) 9 8 7 6 5 4   Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class. Do yourself a favor! Prof Sarah s failsafe
More informationk 1 k 2 x (1) x 2 = k 1 x 1 = k 2 k 1 +k 2 x (2) x k series x (3) k 2 x 2 = k 1 k 2 = k 1+k 2 = 1 k k 2 k series
Final Review A Puzzle... Consider wo massless springs wih spring consans k 1 and k and he same equilibrium lengh. 1. If hese springs ac on a mass m in parallel, hey would be equivalen o a single spring
More informationa. Show that these lines intersect by finding the point of intersection. b. Find an equation for the plane containing these lines.
Mah A Final Eam Problems for onsideraion. Show all work for credi. Be sure o show wha you know. Given poins A(,,, B(,,, (,, 4 and (,,, find he volume of he parallelepiped wih adjacen edges AB, A, and A.
More information