LAB 5 - PROJECTILE MOTION

Size: px
Start display at page:

Download "LAB 5 - PROJECTILE MOTION"

Transcription

1 Lab 5 Projecile Moion 71 Name Dae Parners OVEVIEW LAB 5 - POJECTILE MOTION We learn in our sudy of kinemaics ha wo-dimensional moion is a sraighforward exension of one-dimensional moion. Projecile moion under he influence of graviy is a subjec wih which we are all familiar. We learn o shoo baskeballs in an arc o swish hrough he baske or o bounce off he backboard. We learn how o lob in volleyball and ennis. These are examples of projecile moion. The force of graviy acs in he verical direcion, and air resisance acs in boh he horizonal and verical direcions, bu we ofen neglec air resisance for small objecs. In his experimen we will explore how he moion depends upon he body s iniial velociy and elevaion angle. Consider a body wih an iniial speed v a angle α wih respec o he horizonal axis. We analyze he body s moion in wo independen coordinaes x (horizonal) and y (verical). [As we are free o choose his origin of our coordinae sysem, we choose x = and y = when = so as o simplify our calculaions.] Figure 1 hen shows ha he componens of he velociy vecor along he x and y axes are respecively: v x = v cosα and v y = v sinα (1) If we neglec air resisance, he only force affecing he moion of he objec is graviy, which near he Earh s surface acs purely in he verical direcion ( F ˆ g = mg = mgy ). There is no force a all in he horizonal direcion. Since here is no horizonally applied force, here is no acceleraion in he horizonal direcion; hence he x direcion of he velociy will remain unchanged forever. The horizonal posiion of he body is hen described by he expression for consan velociy: x ) = v x ( v cosα ) () ( = The force in he y (verical) direcion is graviaion ( Fy = mg ). Since F = ma, ay Inegraing his wih respec o ime yields he verical componen of he velociy: v y ( V V y α = g. ) = v y g = v sinα g. (3) The verical componen of he posiion can be obained by inegraing Equaion (3) wih respec o ime, yielding he resul: V x Figure y( ) = v y g = ( v sinα ) g. (4) PHYS 14W, Spring 7

2 7 Lab 5 Projecile Moion We can use hese equaions o deermine he acual rajecory of he body in erms of he x and y variables, wih no explici reference o he ime. The equaion has a parabolic form y C x C x = 1 (5) where C1 = an ( α) and C = g / v cos ( α). We are ineresed in he range, he horizonal disance ha he projecile ravels on level ground. We can ge he range from Equaion (5) by noing ha y sars a zero when x = and is once again zero when x =. We ge v sin( ) α = (6) g Alhough we won measure hem in his experimen, we can similarly show ha he ime of fligh (T ) is given by T v g and he maximum heigh (reached when = T / ) is given by h α = sin ( ) (7) v sin ( α) g INVESTIGATION 1: MEASUEMENT OF ANGE = (8) You will need he following maerials: projecile moion apparaus landing pad opical bench digial phoogae imer meer sick masking ape plasic ruler 3 m ape measure level spark (pressure-sensiive) paper Figure 1. Before saring he measuremens, familiarize yourself wih he apparaus. The cenral feaure of he seup is a spring-loaded gun mouned on a plae marked in degrees, as shown in Figure. The plae can be roaed around a horizonal axis o se he iniial PHYS 14W, Spring 7

3 Lab 5 Projecile Moion 73 direcion of moion: a desired angle can be se by loosening he knurled screw aached o he plae, aligning he required angle mark wih he horizonal mark on he sand and hen ighening he screw. The iniial speed of he projecile (a seel ball) can be se o hree differen values by drawing back he spring-loaded firing pin unil i is locked in one of he hree prese posiions. Noice he cable-release rigger and make sure ha is plunger is fully wihdrawn (his is achieved by pressing on he small ring near he end of he rigger cable), hen ry drawing back he firing pin and lisen o he hree disinc clicks corresponding o he hree posiions. Unforunaely, someimes he cablerelease becomes disconneced, somehing you wan o avoid, because i is difficul o reconnec i! Press he rigger s plunger and he pin will fire. Now you can pracice launching he projecile: ry differen angles and differen velociies o ge a feeling of which angular range will land he projecile ono he able. When doing your measuremens, record he landing spo of he ball on he able by means of a pressure sensiive paper aped o he board. Do no ape he paper in posiion unil you are ready o sar your measuremens, because i is expensive and we can afford o wase any.. Now you will wan o verify ha he apparaus is level and ha he landing able is a he same heigh as he pivo poin (which is where we believe he ball also leaves he spring). Firs, place he level on he back of he gun apparaus and, if needed, use he wo screws holding up he apparaus o level he gun apparaus. Use a meer sick and he level o make sure ha he able op surface is a he same heigh as he pivo poin of he angle mark (he iming apparaus can easily be pulled ou o see where he pivo poin acually is) and ha he able is level. Ask your TA for assisance if his procedure is no clear. Aciviy 1-1: Deermining he Iniial Speed 1. As he final preparaion, we wan o measure he iniial speed of he projecile. As i leaves he gun, he projecile crosses he ligh beam of wo ligh bulbs (acually ligh emiing diodes or LED s), shining ono wo phoocells, which are conneced o a imer uni. When in pulse mode, he imer will sar couning when he firs ligh beam is inerruped, and i will keep couning unil he second beam is obscured. Make sure he imer is se o.1 ms resoluion and se he angle o. Wihdraw he firing pin o one of he hree posiions and place he ball ino he gun. If he imer is running, press he ESET buon. Launch he ball and use a Syrofoam cup o cach he ball. The imer will record he ime in seconds i ook he projecile o go from he firs o he second ligh. Knowing he disance d beween he wo (i is marked on he apparaus), you can deermine he average speed of he ball as i ravels beween he lighs. Take one half of he leas significan digi in d as, your esimae of your uncerainy in d. d d : d : PHYS 14W, Spring 7

4 74 Lab 5 Projecile Moion Quesion 1-1: Can you hink of a beer way o measure he iniial speed? Discuss among your group why we use his procedure ( angle) o deermine he iniial speed. Wrie your conclusions here. Measure he ime ( ) for a leas four rials for each click seing. Ener your daa ino Table 1-1. Use hese daa and he posiion beween he phoocells o deermine he speed. For each seing calculae he average ime, ( ) and he sandard deviaion,. Le your uncerainy in ( ), be he larger of he sandard error in he mean or one-half of he leas significan digi (.5 ms). Calculae he iniial speed, v = d, and is uncerainy, v o, based on your esimaes of d and Click Posiion 1 3 (ms) Trial 1 Trial Trial 3 Trial 4. Table 1-1 Iniial Speed (ms) Aciviy 1-: ange as a Funcion of Iniial Angle (ms) (ms) v (m/s) v (m/s) For his aciviy you will choose one of he hree values of he launch speed and execue a se of launches for a leas five differen values of he launch angle, say 15, 3, 45, 6, and 75. We sugges ha you ake daa wih highes iniial speed. Quesion 1-: Wrie down wo reasons why i migh be bes o use he highes speed o ake hese daa. Predicion 1-1: Fix your coordinae sysem such ha he x and y coordinaes are boh zero when he ball passes hrough he pivo and adjus he op of he landing board o ha level ( y = ). The ball hen sars a y = and reaches y = again when landing on he PHYS 14W, Spring 7

5 Lab 5 Projecile Moion 75 board. The range will simply be he x coordinae where i his. Draw your predicions for he rajecory on he following graph for each of your chosen angles 3 Projecile Moion Trajecory y [cm] x [cm] Predicion 1-: Draw your heoreical predicions for he range as a funcion of he iniial angle α on he following graph. 1 1 ange [cm] a [degrees] Quesion 1-3: If you waned o plo he range versus a quaniy ha depends on angle (ha is, you are going o vary he angle) and ha would heoreically resul in a sraigh line for all five iniial angles, wha would you choose for he independen funcion variable (funcion variable ploed along he horizonal axis)? Explain. PHYS 14W, Spring 7

6 76 Lab 5 Projecile Moion 1. emove he phoogae so ha you can more easily measure he disances. Turn off he phoogae s power.. For each launch, he range of he projecile will be recorded by a do on he pressuresensiive paper. You will noice ha even if you keep he iniial speed and inclinaion fixed, he landing posiions will be spread over several millimeers. The acual range you will use for ploing your daa will be he average of he measured poins. To avoid confusions due o spurious marks on he paper caused by bounces of he projecile, i is advisable, firs, o label each mark as he ball makes i and, second, o perform he measuremens wih he longes ranges firs. You migh, for example, circle each mark o disinguish i from he newer ones. Do no ake daa unil insruced o do so! Quesion 1-4: Can you deermine from he formula derived earlier which angle corresponds o he longes range? Explain. Tha should be your firs angle. 3. ecord your iniial speed: v 4. Now ake your daa for his same v and inser your values ino he following able: Trial Table 1- ange (in cm) for each projecile launch Angle PHYS 14W, Spring 7

7 Lab 5 Projecile Moion For each angle, calculae he average range,, and he sandard deviaion,. Le your uncerainy in,, be he larger of he sandard error in he mean or one half of he leas significan digi. Quesion 1-5: For which angle is he range he larges? Does his agree wih your predicion? Explain. Quesion 1-6: Does i appear from your daa ha he ranges for any of he angles are he same (wihin he probable errors)? If so, for which ses of daa are his rue? Discuss. 6. Now ha you have your daa, compare hem wih he heoreical predicions. You wan o plo your daa using he funcion you decided in Quesion 1-3 ha produces a sraigh line. For each angular seing, use he expression you derived earlier o compue he expeced projecile range as some funcion of angle. Produce he line for he heoreical predicions (see = [ v sin( α)]/ g ) and use your measured values of v and he known value of g. Calculae for each angle and pu he resuls and your daa ino Excel. Then you can connec he daa poins wih a line, bu choose in Excel o no display he calculaed daa poins. Show only he heoreical line and he experimenal daa versus a suiable parameer ha depends on he iniial angle α (see Quesion 1-3) using Excel. The resul should be a linear plo. 7. Prin ou and include he graph wih your repor. 8. By hand, add error bars o he measured daa on your graph. These should be shor lines of lengh ha exend above and below he daa poin. Ofen hese lines have T like ends. PHYS 14W, Spring 7

8 78 Lab 5 Projecile Moion Quesion 1-7: How well do your measuremens agree wih your predicions? Are he deviaions consisen o wihin he accuracy you expec of your measuremens? Explain why or why no. Discuss possible sources of sysemaic errors ha may be presen. Aciviy 1-3: ange as a Funcion of Iniial Speed 1. Now you wan o choose one suiable angle and measure he range for each of he hree iniial speeds ha you deermined earlier. Wrie down your chosen angle: Launch angle Quesion 1-8: Wha crieria did you use for choosing your launch angle? Would i beer o use a shallow or high angle? Does i maer for any reason?. Take a leas four readings for each of he hree iniial speeds. Inser your resuls ino Table 1-3. PHYS 14W, Spring 7

9 Lab 5 Projecile Moion 79 Trial Table 1-3 ange (in cm) as a Funcion of Iniial Speed Iniial Velociy 1: : 3: Quesion 1-9: I would be insrucive o plo your resuls again on a graph ha produces a linear line. Look a he equaion for range and deermine wha you should plo he range versus. Sae your choice and give an explanaion: 3. Plo your experimenal values for he range on a graph versus he parameer you chose in he previous quesion and compare hem as before wih a line drawn by he heoreical values prediced by he expression you derived. 4. Prin ou your graph, add error bars and aach he graph o your repor. Quesion 1-1: Do your daa agree reasonably well wih your heoreical predicions? How many of your daa poins have error bars ha overlap your heoreical calculaion? Is his wha you expec? Do you believe your errors are saisical or sysemaic? Explain. PHYS 14W, Spring 7

10 8 Lab 5 Projecile Moion PHYS 14W, Spring 7

LAB 4: PROJECTILE MOTION

LAB 4: PROJECTILE MOTION 55 Name Dae Parners LAB 4: POJECTILE MOTION A famous illusraion from Newon s Principia showing he relaionship beween projecile moion and orbial moion OVEVIEW We learned in our sudy of kinemaics ha wo-dimensional

More information

Lab 4: Projectile Motion

Lab 4: Projectile Motion 59 Name Date Partners OVEVIEW Lab 4: Projectile Motion We learn in our study of kinematics that two-dimensional motion is a straightforward extension of one-dimensional motion. Projectile motion under

More information

Lab 5: Projectile Motion

Lab 5: Projectile Motion Lab 5 Projectile Motion 47 Name Date Partners Lab 5: Projectile Motion OVERVIEW We learn in our study of kinematics that two-dimensional motion is a straightforward application of onedimensional motion.

More information

Lab #2: Kinematics in 1-Dimension

Lab #2: Kinematics in 1-Dimension Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion

More information

d = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time

d = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In 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 978--36-60033-7 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 information

Constant Acceleration

Constant Acceleration Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion

More information

LAB 4: PROJECTILE MOTION

LAB 4: PROJECTILE MOTION 57 Name Date Partners LAB 4: POJECTILE MOTION A famous illustration from Newton s Principia showing the relationship between projectile motion and orbital motion OVEVIEW We learned in our study of kinematics

More information

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 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 information

SPH3U: Projectiles. Recorder: Manager: Speaker:

SPH3U: 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 information

IB Physics Kinematics Worksheet

IB 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 information

KINEMATICS IN ONE DIMENSION

KINEMATICS 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 information

LAB 6: SIMPLE HARMONIC MOTION

LAB 6: SIMPLE HARMONIC MOTION 1 Name Dae Day/Time of Lab Parner(s) Lab TA Objecives LAB 6: SIMPLE HARMONIC MOTION To undersand oscillaion in relaion o equilibrium of conservaive forces To manipulae he independen variables of oscillaion:

More information

Chapter 3 Kinematics in Two Dimensions

Chapter 3 Kinematics in Two Dimensions Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional 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 information

NEWTON S SECOND LAW OF MOTION

NEWTON 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 information

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 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 information

Position, Velocity, and Acceleration

Position, Velocity, and Acceleration rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose

More information

1. Kinematics I: Position and Velocity

1. Kinematics I: Position and Velocity 1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his

More information

Displacement ( x) x x x

Displacement ( x) x x x Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh

More information

Kinematics in two dimensions

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 information

Physics 101 Fall 2006: Exam #1- PROBLEM #1

Physics 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 information

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs. Physics 180A Fall 2008 Tes 1-120 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 information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 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 information

Guest Lecturer Friday! Symbolic reasoning. Symbolic reasoning. Practice Problem day A. 2 B. 3 C. 4 D. 8 E. 16 Q25. Will Armentrout.

Guest 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 information

1. VELOCITY AND ACCELERATION

1. 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. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

Some Basic Information about M-S-D Systems

Some Basic Information about M-S-D Systems Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,

More information

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan

Ground 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 information

k 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

k 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 information

15210 RECORDING TIMER - AC STUDENT NAME:

15210 RECORDING TIMER - AC STUDENT NAME: CONTENTS 15210 RECORDING TIMER - AC STUDENT NAME: REQUIRED ACCESSORIES o C-Clamps o Ruler or Meer Sick o Mass (200 g or larger) OPTIONAL ACCESSORIES o Ticker Tape Dispenser (#15225) o Consan Speed Vehicle

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

Solution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration

Solution: 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 information

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.

Kinematics 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 information

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a

1. 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 information

UNC resolution Uncertainty Learning Objectives: measurement interval ( You will turn in two worksheets and

UNC resolution Uncertainty Learning Objectives: measurement interval ( You will turn in two worksheets and UNC Uncerainy revised Augus 30, 017 Learning Objecives: During his lab, you will learn how o 1. esimae he uncerainy in a direcly measured quaniy.. esimae he uncerainy in a quaniy ha is calculaed from quaniies

More information

9702/1/O/N/02. are set up a vertical distance h apart. M 1 M 2. , it is found that the ball takes time t 1. to reach M 2 ) 2

9702/1/O/N/02. are set up a vertical distance h apart. M 1 M 2. , it is found that the ball takes time t 1. to reach M 2 ) 2 PhysicsndMahsTuor.com 7 car is ravelling wih uniform acceleraion along a sraigh road. The road has marker poss every 1 m. When he car passes one pos, i has a speed of 1 m s 1 and, when i passes he nex

More information

x i v x t a dx dt t x

x 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 information

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0. PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard

More information

Phys1112: DC and RC circuits

Phys1112: DC and RC circuits Name: Group Members: Dae: TA s Name: Phys1112: DC and RC circuis Objecives: 1. To undersand curren and volage characerisics of a DC RC discharging circui. 2. To undersand he effec of he RC ime consan.

More information

15. Bicycle Wheel. Graph of height y (cm) above the axle against time t (s) over a 6-second interval. 15 bike wheel

15. Bicycle Wheel. Graph of height y (cm) above the axle against time t (s) over a 6-second interval. 15 bike wheel 15. Biccle Wheel The graph We moun a biccle wheel so ha i is free o roae in a verical plane. In fac, wha works easil is o pu an exension on one of he axles, and ge a suden o sand on one side and hold he

More information

Physics 131- Fundamentals of Physics for Biologists I

Physics 131- Fundamentals of Physics for Biologists I 10/3/2012 - Fundamenals of Physics for iologiss I Professor: Wolfgang Loser 10/3/2012 Miderm review -How can we describe moion (Kinemaics) - Wha is responsible for moion (Dynamics) wloser@umd.edu Movie

More information

Q.1 Define work and its unit?

Q.1 Define work and its unit? CHP # 6 ORK AND ENERGY Q.1 Define work and is uni? A. ORK I can be define as when we applied a force on a body and he body covers a disance in he direcion of force, hen we say ha work is done. I is a scalar

More information

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance

2.1: 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 information

Today: Falling. v, a

Today: Falling. v, a Today: Falling. v, a Did you ge my es email? If no, make sure i s no in your junk box, and add sbs0016@mix.wvu.edu o your address book! Also please email me o le me know. I will be emailing ou pracice

More information

LAB 05 Projectile Motion

LAB 05 Projectile Motion PHYS 154 Universi Phsics Laboraor Pre-Lab Spring 18 LAB 5 Projecile Moion CONTENT: 1. Inroducion. Projecile moion A. Seup B. Various characerisics 3. Pre-lab: A. Aciviies B. Preliminar info C. Quiz 1.

More information

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5)

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5) Physics 18 Exam 1 wih Soluions Fall 1, Secions 51-54 Fill ou he informaion below bu o no open he exam unil insruce o o so! Name Signaure Suen ID E-mail Secion # ules of he exam: 1. You have he full class

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

Matlab and Python programming: how to get started

Matlab and Python programming: how to get started Malab and Pyhon programming: how o ge sared Equipping readers he skills o wrie programs o explore complex sysems and discover ineresing paerns from big daa is one of he main goals of his book. In his chaper,

More information

Physics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008

Physics 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 x-axis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly

More information

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed?

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed? 1 1 The graph relaes o he moion of a falling body. y Which is a correc descripion of he graph? y is disance and air resisance is negligible y is disance and air resisance is no negligible y is speed and

More information

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3 A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:

More information

AP Calculus BC Chapter 10 Part 1 AP Exam Problems

AP 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 information

04. Kinetics of a second order reaction

04. Kinetics of a second order reaction 4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, Arrhenius

More information

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx

More information

Conceptual Physics Review (Chapters 2 & 3)

Conceptual 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 information

LabQuest 24. Capacitors

LabQuest 24. Capacitors Capaciors LabQues 24 The charge q on a capacior s plae is proporional o he poenial difference V across he capacior. We express his wih q V = C where C is a proporionaliy consan known as he capaciance.

More information

Practicing Problem Solving and Graphing

Practicing Problem Solving and Graphing Pracicing Problem Solving and Graphing Tes 1: Jan 30, 7pm, Ming Hsieh G20 The Bes Ways To Pracice for Tes Bes If need more, ry suggesed problems from each new opic: Suden Response Examples A pas opic ha

More information

Physics 5A Review 1. Eric Reichwein Department of Physics University of California, Santa Cruz. October 31, 2012

Physics 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 information

Physics 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 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 information

Parametrics and Vectors (BC Only)

Parametrics 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

Testing What You Know Now

Testing What You Know Now Tesing Wha You Know Now To bes each you, I need o know wha you know now Today we ake a well-esablished quiz ha is designed o ell me his To encourage you o ake he survey seriously, i will coun as a clicker

More information

Two Coupled Oscillators / Normal Modes

Two Coupled Oscillators / Normal Modes Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own

More information

LABORATORY I: DESCRIPTION OF MOTION IN ONE DIMENSION

LABORATORY I: DESCRIPTION OF MOTION IN ONE DIMENSION LABORATORY I: DESCRIPTION OF MOTION IN ONE DIMENSION In his laboraory you will measure and analyze one-dimensional moion; ha is, moion along a sraigh line. Wih digial videos, you will measure he posiions

More information

Chapter 2. Motion in One-Dimension I

Chapter 2. Motion in One-Dimension I Chaper 2. Moion in One-Dimension I Level : AP Physics Insrucor : Kim 1. Average Rae of Change and Insananeous Velociy To find he average velociy(v ) of a paricle, we need o find he paricle s displacemen

More information

15. Vector Valued Functions

15. 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 information

Physics 20 Lesson 5 Graphical Analysis Acceleration

Physics 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 posiion-ime graph is equal o he velociy of

More information

Welcome Back to Physics 215!

Welcome Back to Physics 215! Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion

More information

Acceleration. Part I. Uniformly Accelerated Motion: Kinematics & Geometry

Acceleration. Part I. Uniformly Accelerated Motion: Kinematics & Geometry Acceleraion Team: Par I. Uniformly Acceleraed Moion: Kinemaics & Geomery Acceleraion is he rae of change of velociy wih respec o ime: a dv/d. In his experimen, you will sudy a very imporan class of moion

More information

Today: 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

Today: 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 fail-safe

More information

Kinematics in two Dimensions

Kinematics in two Dimensions 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 Toda we are oin o discuss:

More information

4.5 Constant Acceleration

4.5 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 information

LAB 5 - PROJECTILE MOTION

LAB 5 - PROJECTILE MOTION Lab 4 Projectile Motion L4-1 Name Date Partners L05-1 L05-1 Name Date Partners Name Date Partners Lab 4 - Projectile Motion LAB 5 - PROJECTILE MOTION LAB 5 - PROJECTILE MOTION A famous illustration from

More information

HOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.

HOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures. HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =

More information

Biol. 356 Lab 8. Mortality, Recruitment, and Migration Rates

Biol. 356 Lab 8. Mortality, Recruitment, and Migration Rates Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese

More information

Acceleration. Part I. Uniformly Accelerated Motion: Kinematics & Geometry

Acceleration. Part I. Uniformly Accelerated Motion: Kinematics & Geometry Acceleraion Team: Par I. Uniformly Acceleraed Moion: Kinemaics & Geomery Acceleraion is he rae of change of velociy wih respec o ime: a dv/d. In his experimen, you will sudy a very imporan class of moion

More information

Week Exp Date Lecture topic(s) Assignment. Course Overview. Intro: Measurements, uncertainties. Lab: Discussion of Exp 3 goals, setup

Week Exp Date Lecture topic(s) Assignment. Course Overview. Intro: Measurements, uncertainties. Lab: Discussion of Exp 3 goals, setup Schedule for Physics BL - Fall 01 Find relevan Lab Guides on he course web sie o prepare for Quizzes. Reading maerial and pracice problems are from Taylor, Error Analysis. Week Exp Dae Lecure opic(s) Assignmen

More information

Lab 5 - Projectile Motion

Lab 5 - Projectile Motion Lab 5 Projectile Motion L5-1 Name Date Partners L05-1 L05-1 Name Date Partners Lab 5 - Projectile Motion Name Date Partners LAB 5 - PROJECTILE MOTION LAB 5 - PROJECTILE MOTION A famous illustration from

More information

Section A: Forces and Motion

Section A: Forces and Motion I is very useful o be able o make predicions abou he way moving objecs behave. In his chaper you will learn abou some equaions of moion ha can be used o calculae he speed and acceleraion of objecs, and

More information

Kinematics in One Dimension

Kinematics in One Dimension Kinemaics in One Dimension PHY 7 - d-kinemaics - J. Hedberg - 7. Inroducion. Differen Types of Moion We'll look a:. Dimensionaliy in physics 3. One dimensional kinemaics 4. Paricle model. Displacemen Vecor.

More information

2001 November 15 Exam III Physics 191

2001 November 15 Exam III Physics 191 1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall 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 information

EE100 Lab 3 Experiment Guide: RC Circuits

EE100 Lab 3 Experiment Guide: RC Circuits I. Inroducion EE100 Lab 3 Experimen Guide: A. apaciors A capacior is a passive elecronic componen ha sores energy in he form of an elecrosaic field. The uni of capaciance is he farad (coulomb/vol). Pracical

More information

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4 Homework #2. Ph 231 Inroducory Physics, Sp-03 Page 1 of 4 2-1A. A person walks 2 miles Eas (E) in 40 minues and hen back 1 mile Wes (W) in 20 minues. Wha are her average speed and average velociy (in ha

More information

Physics 218 Exam 1 with Solutions Spring 2011, Sections ,526,528

Physics 218 Exam 1 with Solutions Spring 2011, Sections ,526,528 Physics 18 Exam 1 wih Soluions Sprin 11, Secions 513-515,56,58 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 information

MEI STRUCTURED MATHEMATICS 4758

MEI STRUCTURED MATHEMATICS 4758 OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon

More information

Starting from a familiar curve

Starting from a familiar curve In[]:= NoebookDirecory Ou[]= C:\Dropbox\Work\myweb\Courses\Mah_pages\Mah_5\ You can evaluae he enire noebook by using he keyboard shorcu Al+v o, or he menu iem Evaluaion Evaluae Noebook. Saring from a

More information

Of all of the intellectual hurdles which the human mind has confronted and has overcome in the last fifteen hundred years, the one which seems to me

Of all of the intellectual hurdles which the human mind has confronted and has overcome in the last fifteen hundred years, the one which seems to me Of all of he inellecual hurdles which he human mind has confroned and has overcome in he las fifeen hundred years, he one which seems o me o have been he mos amazing in characer and he mos supendous in

More information

Suggested Practice Problems (set #2) for the Physics Placement Test

Suggested 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 information

Brock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension

Brock 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 posiion-ime graphs, elociy-ime graphs, and heir

More information

1.6. Slopes of Tangents and Instantaneous Rate of Change

1.6. 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 information

Lab 10: RC, RL, and RLC Circuits

Lab 10: RC, RL, and RLC Circuits Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in

More information

One-Dimensional Kinematics

One-Dimensional Kinematics One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion

More information

Equations of motion for constant acceleration

Equations 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 information

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B) SCORING GUIDELINES (Form B) Quesion A blood vessel is 6 millimeers (mm) long Disance wih circular cross secions of varying diameer. x (mm) 6 8 4 6 Diameer The able above gives he measuremens of he B(x)

More information

A man pushes a 500 kg block along the x axis by a constant force. Find the power required to maintain a speed of 5.00 m/s.

A man pushes a 500 kg block along the x axis by a constant force. Find the power required to maintain a speed of 5.00 m/s. Coordinaor: Dr. F. hiari Wednesday, July 16, 2014 Page: 1 Q1. The uniform solid block in Figure 1 has mass 0.172 kg and edge lenghs a = 3.5 cm, b = 8.4 cm, and c = 1.4 cm. Calculae is roaional ineria abou

More information

3, so θ = arccos

3, so θ = arccos Mahemaics 210 Professor Alan H Sein Monday, Ocober 1, 2007 SOLUTIONS This problem se is worh 50 poins 1 Find he angle beween he vecors (2, 7, 3) and (5, 2, 4) Soluion: Le θ be he angle (2, 7, 3) (5, 2,

More information

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole

Phys 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 information

Motion along a Straight Line

Motion 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 information

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16.

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16. 1. For which one of he following siuaions will he pah lengh equal he magniude of he displacemen? A) A jogger is running around a circular pah. B) A ball is rolling down an inclined plane. C) A rain ravels

More information

SOLUTIONS TO CONCEPTS CHAPTER 3

SOLUTIONS TO CONCEPTS CHAPTER 3 SOLUTIONS TO ONEPTS HPTER 3. a) Disance ravelled = 50 + 40 + 0 = 0 m b) F = F = D = 50 0 = 30 M His displacemen is D D = F DF 30 40 50m In ED an = DE/E = 30/40 = 3/4 = an (3/4) His displacemen from his

More information

FITTING EQUATIONS TO DATA

FITTING EQUATIONS TO DATA TANTON S TAKE ON FITTING EQUATIONS TO DATA CURRICULUM TIDBITS FOR THE MATHEMATICS CLASSROOM MAY 013 Sandard algebra courses have sudens fi linear and eponenial funcions o wo daa poins, and quadraic funcions

More information