Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!

Size: px
Start display at page:

Download "Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!"

Transcription

1 Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed Vector: Mgntude nd Drecton Poton, Dplcement,, Accelerton Don t Forget Unt! Coordnte Sytem Etblh the coordnte ytem ruler A number lne wth n ndcton howng pote drecton. Any drecton you chooe. The 0 (or y0) locton dented. Agn t cn be ny plce your chooe. 0 Poton Etblh the coordnte ytem ruler Red the poton rom the ruler Don t orget the unt nd drecton Negte Poton Pote Poton Etblh the coordnte ytem ruler drecton pote n drecton o coordnte ytem. drecton cn lo be clculted rom dplcement becue Pote Negte 1

2 Denton o g. elocty Both de o equton re equl Mgntude Unt Drecton (t ector!) Mgntude Mgntude Unt Unt Drecton Drecton Rte o Chnge o Rte o Chnge o Poton Slope Re/Run (m) t() Chngng All thee Velocte? Fndng the Aerge 1, 4, 7, 8, 9, 15, 35 1, 4, 7, 10, 13, 16, 19 4, 8, 1, 16, 0, 4, 8 Requlrly chngng elocty: Aerge the 1 t nd Lt The mddle lue ncree rom 10 to 0 m/: g.? + Chnge n : lter elocty mnu erler elocty Aerge : Between ny tme I elocty ncree regulrly then nd erge o nd. Slope o trght lne between pont Intntneou Between tme jut bt ter/beore t Slope o tngent lne t t Δ lter erler ( + ) Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Δ Mgntude Mgntude Unt Unt Drecton Drecton Rte o Chnge o Rte o Chnge o Slope Re/Run (m/) Δ t()

3 Accelerton Etblh the coordnte ytem ruler Drw elocty rrow. Accelerton drecton cn be clculted rom elocty becue Δ 0 Mke up mple number: 1-5 m/ -8 m/ V-1 [ -8 (-5)] m/ Δ -3 m/ o negte Accel. I negte Sgn? Depend on Coordnte Sytem Choce 0 Wht the gn o:,,,,, Δ,? 0, +, +, +, +, -, - Sgn? Depend on Coordnte Sytem Choce Sgn? Depend on Coordnte Sytem Choce 0 Wht the gn o:,,,,, Δ,? -, +, +, +, +, -, - 0 Wht the gn o:,,,,, Δ,? +, -, -, -, -, +, + Red rom Grph Red rom Grph UNITS Ge u the CLUES! Coordnte On n t grph the coordnte tell u the poton () nd the tme ntnt (t). Slope On n t grph the lope tell u the elocty. Are UNITS Ge u the CLUES! X(m) Slope m Slope m t () t () t () Are Are 3

4 Plot ll three grph Equton Notton 0. t. t. t Common n other tet Smply by ettng t 10 Thnk o t t Other mpled notton nd umpton g nd Contnt Δ Δ t t Δ t t + t 0 0 Equton: rom your tet A combnton or rerrnged My be ued only : Accelerton contnt ( ) ( ) + Δ t Fundmentl denton 1 1 Δ + t + t + Δ ( ) + ( ) ( ) ( ) Δ Problem Solng Proce Problem Decrpton: Th generlly gen. You mut denty n the tet gen, the queton tht mut be nwered. Phyc Decrpton: Dgrm nd equton relent to the tuton. Soluton: The lgebr, grph, etc. And the nwer to the queton! Elutton: Check your unt, mgntude, drecton nd mtchng between repreentton.. Elute A peron trelng let t 10 m/ or mn. How r doe th peron trel? Unt Anly m m Mgntude 100 m bout 3/4 m Mut be rdng n ehcle Emple: 1 prt problem Problem Decrpton A peron trelng let begnnng t 10 m/ nd lowng down or mn. beore toppng. How r doe th peron trel? 4

5 Dgrm nd Pctorl Dgrm Speclzed Dgrm tht nclude mot o the knemtc normton. Ued tool to ole knemtc t problem. /Pctorl Dgrm templte re lble to prnt rom the cl webte. Dgrm Type I Contnt or Speed up or Slow Type II Contnt or Speed up or Slow Type III Contnt or Speed up or Slow t t Prt I: Equton Crcle the known lue Prt II: Equton Crcle the known lue Prt III: Equton Crcle the known lue t Phyc Decrpton Slowng 0 0 m/ -10 m/ t 10 ec t 0 Δ t 1 + t Note: Velocte re neg. Accelerton + nce Δ + Slowng 0 0 m/ -10 m/ t 10 ec t 0 Δ 1 t Soluton Ue crcled equton Fnd erge elocty rt m m m 5 Now nd dplcement m 5 (10 0) 600m Elute A peron trelng let begnnng t 10 m/ nd lowng down or mn. beore toppng. How r doe th peron trel? Unt Anly m m Mgntude 600 m le thn wht t would be t contnt peed (100m3/4 m). Sgn negte whch mtche dgrm. Emple : Mult-Prt Prob Problem Decrpton A truck on trght rod trt rom ret nd ccelerte t.0 m/ untl t reche peed o 0 m/. Then the truck trel or 0 t contnt peed untl the brke re ppled, toppng the truck n unorm mnner n n ddtonl 5.0. Wht the erge elocty o the truck durng the moton decrbed? Phyc Decrpton: 3 Prt Speed Up Contnt Slow Down 0 0 m/ 0 m/ 0 m/ 0 t 0 ec t t t (nother t (nother 5) m/ 0 0) Δ Δ Δ 1 t 1 t 1 t 5

6 Soluton Elute Speed Up Contnt Slow Down 0 0 m/ t 0 ec m/ 100 m 0 m/ t t m 0 m/ t 30-4 m/ 550 m 0 t 35 Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? Δ Δ Δ 1 t 1 t 1 t Emple 3: Free Fll Problem Decrpton An pple ll rom tree rom dtnce o.0 m boe the top o the gr below. Whle llng, t h downwrd ccelerton o 9.8 m/. A the pple nk nto the gr, t peed decree untl t top ter nkng m nto the gr. Sole or eerythng. Soluton Crcle thng known n equton Sole or wht you cn Keep gong untl eerythng known Coordnte + down, y0 md Type I Speed up Type II Slow y -.0 m 0 t m/ y m/ t m/ y m 0 t 0.66 Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + Coordnte + down, y0 bottom Type I Speed up Type II Slow y -.05 m 0 t m/ y m +6.6 m/ t m/ y 0 m 0 t 0.66 Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + 6

7 Coordnte + up, y0 bottom Elute Type I Speed up Type II Slow y +.05 m 0 t m/ y m -6.6 m/ t m/ Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? y 0 m 0 t

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,

More information

a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114

a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114 Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module

More information

Linear Motion. Kinematics Quantities

Linear Motion. Kinematics Quantities Liner Motion Physics 101 Eyres Kinemtics Quntities Time Instnt t Fundmentl Time Interl Defined Position x Fundmentl Displcement Defined Aerge Velocity g Defined Aerge Accelertion g Defined 1 Kinemtics

More information

v v at 1 2 d vit at v v 2a d

v v at 1 2 d vit at v v 2a d SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton

More information

Motion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.

Motion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration. Motion ccelertion Prt : Constnt ccelertion ccelertion ccelertion ccelertion is the rte of chnge of elocity. = - o t = Δ Δt ccelertion = = - o t chnge of elocity elpsed time ccelertion is ector, lthough

More information

Physics for Scientists and Engineers I

Physics for Scientists and Engineers I Phscs for Scentsts nd Engneers I PHY 48, Secton 4 Dr. Betr Roldán Cuen Unverst of Centrl Flord, Phscs Deprtment, Orlndo, FL Chpter - Introducton I. Generl II. Interntonl Sstem of Unts III. Converson of

More information

E-Companion: Mathematical Proofs

E-Companion: Mathematical Proofs E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth

More information

Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds

Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds The speed o a nere mpulse n the human body s about 100 m/s. I you accdentally stub your toe n the dark, estmatethe tme t takes the nere mpulse to trael to your bran. Tps: pcture, poste drecton, and lst

More information

8. INVERSE Z-TRANSFORM

8. INVERSE Z-TRANSFORM 8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere

More information

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton

More information

ESCI 342 Atmospheric Dynamics I Lesson 1 Vectors and Vector Calculus

ESCI 342 Atmospheric Dynamics I Lesson 1 Vectors and Vector Calculus ESI 34 tmospherc Dnmcs I Lesson 1 Vectors nd Vector lculus Reference: Schum s Outlne Seres: Mthemtcl Hndbook of Formuls nd Tbles Suggested Redng: Mrtn Secton 1 OORDINTE SYSTEMS n orthonorml coordnte sstem

More information

19.1 Electrical Potential Energy. Special Case 1. v B

19.1 Electrical Potential Energy. Special Case 1. v B 9. lectcl Potentl neg Specl Ce We elee tet chge between the plte o cpcto. Dung ome tme t moe om to B How e the ntl nd nl peed nd B elted? pp Sole th poblem b ung the concept o electcl potentl eneg B 9.

More information

Chapter Newton-Raphson Method of Solving a Nonlinear Equation

Chapter Newton-Raphson Method of Solving a Nonlinear Equation Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson

More information

Chapter 2. Pythagorean Theorem. Right Hand Rule. Position. Distance Formula

Chapter 2. Pythagorean Theorem. Right Hand Rule. Position. Distance Formula Chapter Moton n One Dmenson Cartesan Coordnate System The most common coordnate system or representng postons n space s one based on three perpendcular spatal axes generally desgnated x, y, and z. Any

More information

Let us look at a linear equation for a one-port network, for example some load with a reflection coefficient s, Figure L6.

Let us look at a linear equation for a one-port network, for example some load with a reflection coefficient s, Figure L6. ECEN 5004, prng 08 Actve Mcrowve Crcut Zoy Popovc, Unverty of Colordo, Boulder LECURE 5 IGNAL FLOW GRAPH FOR MICROWAVE CIRCUI ANALYI In mny text on mcrowve mplfer (e.g. the clc one by Gonzlez), gnl flow-grph

More information

VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors

VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors 1. Defnton A vetor s n entt tht m represent phsl quntt tht hs mgntude nd dreton s opposed to slr tht ls dreton.. Vetor Representton A vetor n e represented grphll n rrow. The length of the rrow s the mgntude

More information

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden Poton nd Speed Control Lund Unverty, Seden Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton.

More information

Uniform Circular Motion

Uniform Circular Motion Unfom Ccul Moton Unfom ccul Moton An object mong t constnt sped n ccle The ntude of the eloct emns constnt The decton of the eloct chnges contnuousl!!!! Snce cceleton s te of chnge of eloct:!! Δ Δt The

More information

Chapter Newton-Raphson Method of Solving a Nonlinear Equation

Chapter Newton-Raphson Method of Solving a Nonlinear Equation Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson

More information

6 Roots of Equations: Open Methods

6 Roots of Equations: Open Methods HK Km Slghtly modfed 3//9, /8/6 Frstly wrtten t Mrch 5 6 Roots of Equtons: Open Methods Smple Fed-Pont Iterton Newton-Rphson Secnt Methods MATLAB Functon: fzero Polynomls Cse Study: Ppe Frcton Brcketng

More information

Introduction to Mechanics Practice using the Kinematics Equations

Introduction to Mechanics Practice using the Kinematics Equations Introduction to Mechnics Prctice using the Kinemtics Equtions Ln Sheridn De Anz College Jn 24, 2018 Lst time finished deriing the kinemtics equtions some problem soling prctice Oeriew using kinemtics equtions

More information

DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)

DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x) DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng

More information

ragsdale (zdr82) HW6 ditmire (58335) 1 the direction of the current in the figure. Using the lower circuit in the figure, we get

ragsdale (zdr82) HW6 ditmire (58335) 1 the direction of the current in the figure. Using the lower circuit in the figure, we get rgsdle (zdr8) HW6 dtmre (58335) Ths prnt-out should hve 5 questons Multple-choce questons my contnue on the next column or pge fnd ll choces efore nswerng 00 (prt of ) 00 ponts The currents re flowng n

More information

Review of linear algebra. Nuno Vasconcelos UCSD

Review of linear algebra. Nuno Vasconcelos UCSD Revew of lner lgebr Nuno Vsconcelos UCSD Vector spces Defnton: vector spce s set H where ddton nd sclr multplcton re defned nd stsf: ) +( + ) (+ )+ 5) λ H 2) + + H 6) 3) H, + 7) λ(λ ) (λλ ) 4) H, - + 8)

More information

Modeling motion with VPython Every program that models the motion of physical objects has two main parts:

Modeling motion with VPython Every program that models the motion of physical objects has two main parts: 1 Modelng moton wth VPython Eery program that models the moton o physcal objects has two man parts: 1. Beore the loop: The rst part o the program tells the computer to: a. Create numercal alues or constants

More information

Physics 111. CQ1: springs. con t. Aristocrat at a fixed angle. Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468.

Physics 111. CQ1: springs. con t. Aristocrat at a fixed angle. Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468. c Announcement day, ober 8, 004 Ch 8: Ch 10: Work done by orce at an angle Power Rotatonal Knematc angular dplacement angular velocty angular acceleraton Wedneday, 8-9 pm n NSC 118/119 Sunday, 6:30-8 pm

More information

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations Dynm o Lnke Herrhe Contrne ynm The Fethertone equton Contrne ynm pply ore to one omponent, other omponent repotone, rom ner to r, to ty tne ontrnt F Contrne Boy Dynm Chpter 4 n: Mrth mpule-be Dynm Smulton

More information

PHYSICS 211 MIDTERM I 22 October 2003

PHYSICS 211 MIDTERM I 22 October 2003 PHYSICS MIDTERM I October 3 Exm i cloed book, cloed note. Ue onl our formul heet. Write ll work nd nwer in exm booklet. The bck of pge will not be grded unle ou o requet on the front of the pge. Show ll

More information

Applied Statistics Qualifier Examination

Applied Statistics Qualifier Examination Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng

More information

Definition of Tracking

Definition of Tracking Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,

More information

Prof. Dr. I. Nasser T /16/2017

Prof. Dr. I. Nasser T /16/2017 Pro. Dr. I. Nasser T-171 10/16/017 Chapter Part 1 Moton n one dmenson Sectons -,, 3, 4, 5 - Moton n 1 dmenson We le n a 3-dmensonal world, so why bother analyzng 1-dmensonal stuatons? Bascally, because

More information

Momentum. Momentum. Impulse. Momentum and Collisions

Momentum. Momentum. Impulse. Momentum and Collisions Momentum Momentum and Collsons From Newton s laws: orce must be present to change an object s elocty (speed and/or drecton) Wsh to consder eects o collsons and correspondng change n elocty Gol ball ntally

More information

Work is the change in energy of a system (neglecting heat transfer). To examine what could

Work is the change in energy of a system (neglecting heat transfer). To examine what could Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes

More information

Name: PHYS 110 Dr. McGovern Spring 2018 Exam 1. Multiple Choice: Circle the answer that best evaluates the statement or completes the statement.

Name: PHYS 110 Dr. McGovern Spring 2018 Exam 1. Multiple Choice: Circle the answer that best evaluates the statement or completes the statement. Name: PHYS 110 Dr. McGoern Sprng 018 Exam 1 Multple Choce: Crcle the answer that best ealuates the statement or completes the statement. #1 - I the acceleraton o an object s negate, the object must be

More information

Physics 120. Exam #1. April 15, 2011

Physics 120. Exam #1. April 15, 2011 Phyc 120 Exam #1 Aprl 15, 2011 Name Multple Choce /16 Problem #1 /28 Problem #2 /28 Problem #3 /28 Total /100 PartI:Multple Choce:Crclethebetanwertoeachqueton.Anyothermark wllnotbegvencredt.eachmultple

More information

Name: SID: Discussion Session:

Name: SID: Discussion Session: Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether

More information

4. Eccentric axial loading, cross-section core

4. Eccentric axial loading, cross-section core . Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we

More information

Identify graphs of linear inequalities on a number line.

Identify graphs of linear inequalities on a number line. COMPETENCY 1.0 KNOWLEDGE OF ALGEBRA SKILL 1.1 Identify grphs of liner inequlities on number line. - When grphing first-degree eqution, solve for the vrible. The grph of this solution will be single point

More information

Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:

Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions: Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the

More information

Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers

Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for

More information

PHYSICS 211 MIDTERM I 21 April 2004

PHYSICS 211 MIDTERM I 21 April 2004 PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of

More information

Physics 207 Lecture 5

Physics 207 Lecture 5 Phsics 07 Lecture 5 Agend Phsics 07, Lecture 5, Sept. 0 Chpter 4 Kinemtics in or 3 dimensions Independence of, nd/or z components Circulr motion Cured pths nd projectile motion Frmes of reference dil nd

More information

Artificial Intelligence Markov Decision Problems

Artificial Intelligence Markov Decision Problems rtificil Intelligence Mrkov eciion Problem ilon - briefly mentioned in hpter Ruell nd orvig - hpter 7 Mrkov eciion Problem; pge of Mrkov eciion Problem; pge of exmple: probbilitic blockworld ction outcome

More information

HO 40 Solutions ( ) ˆ. j, and B v. F m x 10-3 kg = i + ( 4.19 x 10 4 m/s)ˆ. (( )ˆ i + ( 4.19 x 10 4 m/s )ˆ j ) ( 1.40 T )ˆ k.

HO 40 Solutions ( ) ˆ. j, and B v. F m x 10-3 kg = i + ( 4.19 x 10 4 m/s)ˆ. (( )ˆ i + ( 4.19 x 10 4 m/s )ˆ j ) ( 1.40 T )ˆ k. .) m.8 x -3 g, q. x -8 C, ( 3. x 5 m/)ˆ, and (.85 T)ˆ The magnetc force : F q (. x -8 C) ( 3. x 5 m/)ˆ (.85 T)ˆ F.98 x -3 N F ma ( ˆ ˆ ) (.98 x -3 N) ˆ o a HO 4 Soluton F m (.98 x -3 N)ˆ.8 x -3 g.65 m.98

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

PRACTICE EXAM 2 SOLUTIONS

PRACTICE EXAM 2 SOLUTIONS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Phyic Phyic 8.01x Fll Term 00 PRACTICE EXAM SOLUTIONS Proble: Thi i reltively trihtforwrd Newton Second Lw problem. We et up coordinte ytem which i poitive

More information

Rigid Body Dynamics. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018

Rigid Body Dynamics. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018 Rg Bo Dnmcs CSE169: Compute Anmton nstucto: Steve Roteneg UCSD, Wnte 2018 Coss Pouct k j Popetes of the Coss Pouct Coss Pouct c c c 0 0 0 c Coss Pouct c c c c c c 0 0 0 0 0 0 Coss Pouct 0 0 0 ˆ ˆ 0 0 0

More information

Physics 105: Mechanics Lecture 13

Physics 105: Mechanics Lecture 13 Physcs 05: Mechancs Lecture 3 Wenda Cao NJIT Physcs Department Momentum and Momentum Conseraton Momentum Impulse Conseraton o Momentum Collsons Lnear Momentum A new undamental quantty, lke orce, energy

More information

AP Physics C: Mechanics

AP Physics C: Mechanics 08 AP Phyc C: Mechnc ee-repone Queton 08 The College Bod. College Bod, Advnced Plcement Pogm, AP, AP Centl, nd the con logo e egteed tdemk of the College Bod. Vt the College Bod on the Web: www.collegebod.og.

More information

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses

More information

1. The number of significant figures in the number is a. 4 b. 5 c. 6 d. 7

1. The number of significant figures in the number is a. 4 b. 5 c. 6 d. 7 Name: ID: Anwer Key There a heet o ueul ormulae and ome converon actor at the end. Crcle your anwer clearly. All problem are pont ecept a ew marked wth ther own core. Mamum core 100. There are a total

More information

Partially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism

Partially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism CS294-40 Lernng for Rootcs nd Control Lecture 10-9/30/2008 Lecturer: Peter Aeel Prtlly Oservle Systems Scre: Dvd Nchum Lecture outlne POMDP formlsm Pont-sed vlue terton Glol methods: polytree, enumerton,

More information

Projectile Motion. Parabolic Motion curved motion in the shape of a parabola. In the y direction, the equation of motion has a t 2.

Projectile Motion. Parabolic Motion curved motion in the shape of a parabola. In the y direction, the equation of motion has a t 2. Projectle Moton Phc Inentor Parabolc Moton cured oton n the hape of a parabola. In the drecton, the equaton of oton ha a t ter Projectle Moton the parabolc oton of an object, where the horzontal coponent

More information

PHUN. Phy 521 2/10/2011. What is physics. Kinematics. Physics is. Section 2 1: Picturing Motion

PHUN. Phy 521 2/10/2011. What is physics. Kinematics. Physics is. Section 2 1: Picturing Motion /0/0 Wh phyc Phy 5 Phyc he brnch o knowledge h ude he phycl world. Phyc nege objec mll om nd lrge glxe. They udy he nure o mer nd energy nd how hey re reled. Phyc he udy o moon nd energy. Phyc nd oher

More information

EMU Physics Department.

EMU Physics Department. Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons

More information

2. Work each problem on the exam booklet in the space provided.

2. Work each problem on the exam booklet in the space provided. ECE470 EXAM # SOLUTIONS SPRING 08 Intructon:. Cloed-book, cloed-note, open-mnd exm.. Work ech problem on the exm booklet n the pce provded.. Wrte netly nd clerly for prtl credt. Cro out ny mterl you do

More information

2.12 Pull Back, Push Forward and Lie Time Derivatives

2.12 Pull Back, Push Forward and Lie Time Derivatives Secton 2.2 2.2 Pull Bck Push Forwrd nd e me Dertes hs secton s n the mn concerned wth the follown ssue: n oserer ttched to fxed sy Crtesn coordnte system wll see mterl moe nd deform oer tme nd wll osere

More information

" = #N d$ B. Electromagnetic Induction. v ) $ d v % l. Electromagnetic Induction and Faraday s Law. Faraday s Law of Induction

 = #N d$ B. Electromagnetic Induction. v ) $ d v % l. Electromagnetic Induction and Faraday s Law. Faraday s Law of Induction Eletromgnet Induton nd Frdy s w Eletromgnet Induton Mhel Frdy (1791-1867) dsoered tht hngng mgnet feld ould produe n eletr urrent n ondutor pled n the mgnet feld. uh urrent s lled n ndued urrent. The phenomenon

More information

Math 2142 Homework 2 Solutions. Problem 1. Prove the following formulas for Laplace transforms for s > 0. a s 2 + a 2 L{cos at} = e st.

Math 2142 Homework 2 Solutions. Problem 1. Prove the following formulas for Laplace transforms for s > 0. a s 2 + a 2 L{cos at} = e st. Mth 2142 Homework 2 Solution Problem 1. Prove the following formul for Lplce trnform for >. L{1} = 1 L{t} = 1 2 L{in t} = 2 + 2 L{co t} = 2 + 2 Solution. For the firt Lplce trnform, we need to clculte:

More information

Section 6.4 Graphs of the sine and cosine functions

Section 6.4 Graphs of the sine and cosine functions Section 6. Grphs of the sine nd cosine functions This is the grph of the sine function f() sin f() sin Domin All rel numbers (, ) Rnge [ 1,1] Amplitute 1 Period π This sine function hs Period of π mens

More information

ONE-DIMENSIONAL COLLISIONS

ONE-DIMENSIONAL COLLISIONS Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal

More information

i-clicker i-clicker A B C a r Work & Kinetic Energy

i-clicker i-clicker A B C a r Work & Kinetic Energy ork & c Energ eew of Preou Lecture New polc for workhop You are epected to prnt, read, and thnk about the workhop ateral pror to cong to cla. (Th part of the polc not new!) There wll be a prelab queton

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

Chapter 2 Linear Mo on

Chapter 2 Linear Mo on Chper Lner M n .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s

More information

( ) ( )()4 x 10-6 C) ( ) = 3.6 N ( ) = "0.9 N. ( )ˆ i ' ( ) 2 ( ) 2. q 1 = 4 µc q 2 = -4 µc q 3 = 4 µc. q 1 q 2 q 3

( ) ( )()4 x 10-6 C) ( ) = 3.6 N ( ) = 0.9 N. ( )ˆ i ' ( ) 2 ( ) 2. q 1 = 4 µc q 2 = -4 µc q 3 = 4 µc. q 1 q 2 q 3 3 Emple : Three chrges re fed long strght lne s shown n the fgure boe wth 4 µc, -4 µc, nd 3 4 µc. The dstnce between nd s. m nd the dstnce between nd 3 s lso. m. Fnd the net force on ech chrge due to the

More information

Calculus - Activity 1 Rate of change of a function at a point.

Calculus - Activity 1 Rate of change of a function at a point. Nme: Clss: p 77 Mths Helper Plus Resource Set. Copright 00 Bruce A. Vughn, Techers Choice Softwre Clculus - Activit Rte of chnge of function t point. ) Strt Mths Helper Plus, then lod the file: Clculus

More information

Physics 101 Lecture 9 Linear Momentum and Collisions

Physics 101 Lecture 9 Linear Momentum and Collisions Physcs 0 Lecture 9 Lnear Momentum and Collsons Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum and Collsons q q q q q q q Conseraton o Energy Momentum Impulse Conseraton o Momentum -D Collsons

More information

A-Level Mathematics Transition Task (compulsory for all maths students and all further maths student)

A-Level Mathematics Transition Task (compulsory for all maths students and all further maths student) A-Level Mthemtics Trnsition Tsk (compulsory for ll mths students nd ll further mths student) Due: st Lesson of the yer. Length: - hours work (depending on prior knowledge) This trnsition tsk provides revision

More information

Logarithms. Logarithm is another word for an index or power. POWER. 2 is the power to which the base 10 must be raised to give 100.

Logarithms. Logarithm is another word for an index or power. POWER. 2 is the power to which the base 10 must be raised to give 100. Logrithms. Logrithm is nother word for n inde or power. THIS IS A POWER STATEMENT BASE POWER FOR EXAMPLE : We lred know tht; = NUMBER 10² = 100 This is the POWER Sttement OR 2 is the power to which the

More information

Distance And Velocity

Distance And Velocity Unit #8 - The Integrl Some problems nd solutions selected or dpted from Hughes-Hllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl

More information

Variable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia

Variable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng

More information

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Relative velocity. to x f along x - axis at time t i

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Relative velocity. to x f along x - axis at time t i Ensten Clsses, Unt No. 0, 03, Vrdhmn Rn Rod Plz, Vks Pr Etn., New Delh -8 Ph. : 9369035, 857, E-ml enstenclsses003@ml.com, PK K I N E M AT I C S Syllbs : CONCEPTS The prt of mechncs tht dels wth the descrpton

More information

_3-----"/- ~StudI_G u_id_e_-..,...-~~_~

_3-----/- ~StudI_G u_id_e_-..,...-~~_~ e- / Dte Period Nme CHAPTR 3-----"/- StudIG uide-..,...- [-------------------- Accelerted Motion Vocbulry Review Write the term tht correctly completes the sttement. Use ech term once. ccelertion verge

More information

Solutions Problem Set 2. Problem (a) Let M denote the DFA constructed by swapping the accept and non-accepting state in M.

Solutions Problem Set 2. Problem (a) Let M denote the DFA constructed by swapping the accept and non-accepting state in M. Solution Prolem Set 2 Prolem.4 () Let M denote the DFA contructed y wpping the ccept nd non-ccepting tte in M. For ny tring w B, w will e ccepted y M, tht i, fter conuming the tring w, M will e in n ccepting

More information

Math 1431 Section M TH 4:00 PM 6:00 PM Susan Wheeler Office Hours: Wed 6:00 7:00 PM Online ***NOTE LABS ARE MON AND WED

Math 1431 Section M TH 4:00 PM 6:00 PM Susan Wheeler Office Hours: Wed 6:00 7:00 PM Online ***NOTE LABS ARE MON AND WED Mth 43 Section 4839 M TH 4: PM 6: PM Susn Wheeler swheeler@mth.uh.edu Office Hours: Wed 6: 7: PM Online ***NOTE LABS ARE MON AND WED t :3 PM to 3: pm ONLINE Approimting the re under curve given the type

More information

Chapter 5 1. = on [ 1, 2] 1. Let gx ( ) e x. . The derivative of g is g ( x) e 1

Chapter 5 1. = on [ 1, 2] 1. Let gx ( ) e x. . The derivative of g is g ( x) e 1 Chpter 5. Let g ( e. on [, ]. The derivtive of g is g ( e ( Write the slope intercept form of the eqution of the tngent line to the grph of g t. (b Determine the -coordinte of ech criticl vlue of g. Show

More information

? plate in A G in

? plate in A G in Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0

More information

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1 The Fundmentl Theorem of Clculus As we continue to study the re problem, let s think bck to wht we know bout computing res of regions enclosed by curves. If we wnt to find the re of the region below the

More information

The Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve.

The Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve. Clculus Li Vs The Fundmentl Theorem of Clculus. The Totl Chnge Theorem nd the Are Under Curve. Recll the following fct from Clculus course. If continuous function f(x) represents the rte of chnge of F

More information

4-6 ROTATIONAL MOTION

4-6 ROTATIONAL MOTION Chpter 4 Motions in Spce 51 Reinforce the ide tht net force is needed for orbitl motion Content We discuss the trnsition from projectile motion to orbitl motion when bll is thrown horizontlly with eer

More information

2.4 Linear Inequalities and Interval Notation

2.4 Linear Inequalities and Interval Notation .4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or

More information

Lecture 4: Piecewise Cubic Interpolation

Lecture 4: Piecewise Cubic Interpolation Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml

More information

Chapter 9 Linear Momentum and Collisions

Chapter 9 Linear Momentum and Collisions Chapter 9 Lnear Momentum and Collsons m = 3. kg r = ( ˆ ˆ j ) P9., r r (a) p m ( ˆ ˆj ) 3. 4. m s = = 9.. kg m s Thus, p x = 9. kg m s and p y =. kg m s (b) p px p y p y θ = tan = tan (.33) = 37 px = +

More information

CENTROID (AĞIRLIK MERKEZİ )

CENTROID (AĞIRLIK MERKEZİ ) CENTOD (ĞLK MEKEZİ ) centrod s geometrcl concept rsng from prllel forces. Tus, onl prllel forces possess centrod. Centrod s tougt of s te pont were te wole wegt of pscl od or sstem of prtcles s lumped.

More information

Basic Derivative Properties

Basic Derivative Properties Bsic Derivtive Properties Let s strt this section by remining ourselves tht the erivtive is the slope of function Wht is the slope of constnt function? c FACT 2 Let f () =c, where c is constnt Then f 0

More information

Smart Motorways HADECS 3 and what it means for your drivers

Smart Motorways HADECS 3 and what it means for your drivers Vehcle Rentl Smrt Motorwys HADECS 3 nd wht t mens for your drvers Vehcle Rentl Smrt Motorwys HADECS 3 nd wht t mens for your drvers You my hve seen some news rtcles bout the ntroducton of Hghwys Englnd

More information

INTRODUCTION TO COMPLEX NUMBERS

INTRODUCTION TO COMPLEX NUMBERS INTRODUCTION TO COMPLEX NUMBERS The numers -4, -3, -, -1, 0, 1,, 3, 4 represent the negtve nd postve rel numers termed ntegers. As one frst lerns n mddle school they cn e thought of s unt dstnce spced

More information

Chapter Twelve. Integration. We now turn our attention to the idea of an integral in dimensions higher than one. Consider a real-valued function f : D

Chapter Twelve. Integration. We now turn our attention to the idea of an integral in dimensions higher than one. Consider a real-valued function f : D Chapter Twelve Integraton 12.1 Introducton We now turn our attenton to the dea of an ntegral n dmensons hgher than one. Consder a real-valued functon f : R, where the doman s a nce closed subset of Eucldean

More information

Introduction to Numerical Integration Part II

Introduction to Numerical Integration Part II Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w

More information

Chemical Reaction Engineering

Chemical Reaction Engineering Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F 0 E 0 F E Q W

More information

Gravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)

Gravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11) Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng

More information

PHYS Summer Professor Caillault Homework Solutions. Chapter 2

PHYS Summer Professor Caillault Homework Solutions. Chapter 2 PHYS 1111 - Summer 2007 - Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement

More information

1. Find the derivative of the following functions. a) f(x) = 2 + 3x b) f(x) = (5 2x) 8 c) f(x) = e2x

1. Find the derivative of the following functions. a) f(x) = 2 + 3x b) f(x) = (5 2x) 8 c) f(x) = e2x I. Dierentition. ) Rules. *product rule, quotient rule, chin rule MATH 34B FINAL REVIEW. Find the derivtive of the following functions. ) f(x) = 2 + 3x x 3 b) f(x) = (5 2x) 8 c) f(x) = e2x 4x 7 +x+2 d)

More information

Sample pages. 9:04 Equations with grouping symbols

Sample pages. 9:04 Equations with grouping symbols Equtions 9 Contents I know the nswer is here somewhere! 9:01 Inverse opertions 9:0 Solving equtions Fun spot 9:0 Why did the tooth get dressed up? 9:0 Equtions with pronumerls on both sides GeoGebr ctivity

More information

Principle Component Analysis

Principle Component Analysis Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler -T Sytem: Ung Bode Plot EEE 30 Sgnal & Sytem Pro. Mark Fowler Note Set #37 /3 Bode Plot Idea an Help Vualze What rcut Do Lowpa Flter Break Pont = / H ( ) j /3 Hghpa Flter c = / L Bandpa Flter n nn ( a)

More information

Effect of Wind Speed on Reaction Coefficient of Different Building Height. Chunli Ren1, a, Yun Liu2,b

Effect of Wind Speed on Reaction Coefficient of Different Building Height. Chunli Ren1, a, Yun Liu2,b 4th Interntonl Conference on Senor, Meurement nd Intellgent Mterl (ICSMIM 015) Effect of Wnd Speed on Recton Coeffcent of Dfferent Buldng Heght Chunl Ren1,, Yun Lu,b 1 No.9 Dxuexdo. Tnghn Cty, Hebe Provnce,

More information

UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II

UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )

More information

The meaning of d Alembert s principle for rigid systems and link mechanisms

The meaning of d Alembert s principle for rigid systems and link mechanisms De Bedeutung de d Alembertchen Prnzpe für trre Syteme und Gelenkmechnmen (Fortetzung) Arch der Mth und Phy () (90) 98-6 The menng of d Alembert prncple for rgd ytem nd lnk mechnm By KARL HEUN n Berln Trnlted

More information

MEG 741 Energy and Variational Methods in Mechanics I

MEG 741 Energy and Variational Methods in Mechanics I EG 74 Energy nd rton ethod n echnc I Brendn J. O Tooe, Ph.D. Aocte Profeor of echnc Engneerng Hord R. Hughe Coege of Engneerng Unerty of Ned eg TBE B- (7) 895-885 j@me.un.edu Chter 4: Structur Any ethod

More information