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 of moving objecs a regular ime inervals. You will invesigae relaionships among quaniies useful for describing he moion of objecs. Deermining hese kinemaic quaniies (posiion, ime, velociy, and acceleraion) under differen condiions allows you o improve your inuiion abou heir quaniaive relaionships. In paricular, you should idenify which relaionships are only valid in some siuaions and which apply o all siuaions. There are many possibiliies for one-dimensional moion of an objec. I migh move a a consan speed, speed up, slow down, or exhibi some combinaion of hese. When making measuremens, you mus quickly undersand your daa o decide if he resuls make sense. If hey don' make sense o you, hen you have no se up he siuaion properly o explore he physics you desire, you are making measuremens incorrecly, or your ideas abou he behavior of objecs in he physical world are incorrec. In any of he above cases, i is a wase of ime o coninue making measuremens. You mus sop, deermine wha is wrong and fix i. If your ideas are wrong, his is your chance o correc hem by discussing he inconsisencies wih your parners, rereading your ex, or alking wih your insrucor. Remember, one of he reasons for doing physics in a laboraory seing is o help you confron and overcome your incorrec ideas abou physics, measuremens, calculaions, and echnical communicaions. Pinpoining and working on your own difficulies will help you in oher pars of his physics course, and perhaps in oher courses. Because people are faser a recognizing paerns in picures han in numbers, he compuer will graph your daa as you go along. Lab I - 1

LAB I: INTRODUCTION OBJECTIVES: Afer you successfully complee his laboraory, you should be able o: Describe compleely he moion of any objec moving in one dimension using posiion, ime, velociy, and acceleraion. Disinguish beween average quaniies and insananeous quaniies for he moion of an objec. Wrie he mahemaical relaionships among posiion, ime, velociy, average velociy, acceleraion, and average acceleraion for differen siuaions. Graphically analyze he moion of an objec. Begin using echnical communicaion skills such as keeping a laboraory journal and wriing a laboraory repor. PREPARATION: Read Serway & Vuille: Chaper 2. Also read Appendix D, he insrucions for doing video analysis. Before coming o he lab you should be able o: Define and recognize he differences among hese conceps: - Posiion, displacemen, and disance. - Insananeous velociy and average velociy. - Insananeous acceleraion and average acceleraion. Find he slope and inercep of a sraigh-line graph. If you need help, see Appendix C. Deermine he slope of a curve a any poin on ha curve. If you need help, see Appendix C. Use he definiions of sin θ, cos θ, and an θ for a righ riangle. Lab I - 2

PROBLEM #1: CONSTANT VELOCITY MOTION Since his physics laboraory design may be new o you, his firs problem, and only his one, conains boh he insrucions o explore consan velociy moion and an explanaion of he various pars of he insrucions. The explanaion of he insrucions is in his fon and is preceded by he double, verical lines seen o he lef. These laboraory insrucions may be unlike any you have seen before. You will no find any workshees or sep-by-sep insrucions. Insead, each laboraory consiss of a se of problems ha you solve before coming o he laboraory by making an organized se of decisions (a problem solving sraegy) based on your iniial knowledge. The predicion and warm-up are designed o help you examine your houghs abou physics. These labs are your opporuniy o compare your ideas abou wha "should" happen wih wha really happens. The labs will have lile value in helping you learn physics unless you ake ime o predic wha will happen before you do somehing. While in he laboraory, ake your ime and ry o answer all he quesions in his lab manual. In paricular, answering each of he exploraion quesions can save you ime and frusraion laer by helping you undersand he behavior and limiaions of your equipmen before you make measuremens. Make sure o complee he laboraory problem, including all analysis and conclusions, before moving on o he nex one. The firs paragraphs of each lab problem describe a real-world siuaion. Before coming o lab, you will solve a physics problem o predic somehing abou ha siuaion. The measuremens and analysis you perform in lab will allow you o es your predicion agains he behavior of he real world. You have aken a job wih he Minneapolis Grand Prix o simulcas one of heir races on he Inerne, using a digial video camera ha sores images direcly on a compuer. Viewers are ineresed in he speeds he cars will be going during he race. Your goal is o deermine hese speeds from he recorded videos. However, you noice ha he image is disored near he edges of he picure and wonder if his affecs he measuremen of a car s speed from he video image. You decide o model he siuaion using a oy car, which moves a a consan velociy. EQUIPMENT This secion conains a brief descripion of he apparaus you can use o es your predicion. Working hrough he exploraion secion will familiarize you wih he deails. If any lab equipmen is missing or broken, submi a problem repor from o he lab coordinaor by clicking he Labhelp icon on any lab compuer deskop. Be sure o include a complee descripion of he problem. You can also file a repor conaining commens abou his lab manual (for example, when you discover errors or inconsisencies in saemens). If you are unable o, please ask your TA o submi a problem repor. For his problem you will use a moorized oy car which moves wih a consan velociy on an aluminum rack. You will also have a sopwach, a meer sick, a video camera, and a compuer wih video analysis applicaions wrien in LabVIEW (VideoRECORDER and VideoTOOL, described in Appendix D) o help you analyze he moion. PREDICTION Everyone has "personal heories" abou he way he world works. One purpose of his lab is o help you clarify your concepions of he physical world by esing he predicions of your personal heory agains wha really happens. For his reason, you will always predic wha will happen before collecing and analyzing he Lab I - 3

PROBLEM #1: CONSTANT VELOCITY MOTION daa. Your predicion should be compleed and wrien in your lab journal before you come o lab. The Warm-up quesions in he nex secion are designed o help you make your predicion and should also be compleed before you come o lab. This may seem a lile backwards. Alhough he Predicion secion appears before he mehod quesions, you should complee he Warm-up before making he predicion. The Predicion secion merely helps you idenify he goal of he lab problem. Spend he firs few minues a he beginning of he lab session comparing your predicion wih hose of your parners. Discuss he reasons for differences in opinion. I is no necessary ha your predicions are correc, bu i is absoluely crucial ha you undersand he basis of your predicion. How would each of he graphs of posiion vs. ime, velociy vs. ime, and acceleraion vs. ime show a disorion of he posiion measuremen? Skech hese graphs o illusrae your answer. How would you deermine he speed of he car from each of he graphs? Which mehod would be he mos sensiive echnique for deermining any disorions? Appendix B migh help you answer his quesion. Someimes, your predicion is an "educaed guess" based on your knowledge of he physical world. In hese problems exac calculaion is oo complicaed and is beyond his course. However, for every problem i s possible o come up wih a qualiaive predicion by making some plausible simplificaions. For oher problems, you will be asked o use your knowledge of he conceps and principles of physics o calculae a mahemaical relaionship beween quaniies in he experimenal problem. WARM-UP The Warm-up secion is inended o help you solve he problem saed in he opening paragraphs. The saemens may help you make he predicion, help you plan how o analyze daa, or help you hink hrough he consequences of a predicion ha is an educaed guess. Warm-up quesions should be answered and wrien in your lab journal before you come o lab. In his case, he Warm-up helps you plan wha daa o ake and how o analyze i. To deermine if he measured speed is affeced by disorion, you need o hink abou how o measure and represen he moion of an objec. The following quesions should help wih he analysis of your daa. Read: Serway & Vuille Chaper 2, Secions 2.1 o 2.5 1. How would you expec an insananeous velociy vs. ime graph o look for an objec wih consan velociy? Make a rough skech and explain your reasoning. Assign appropriae labels and unis o your axes. Wrie an equaion ha describes his graph. Wha is he meaning of each quaniy in your equaion? 2. How would you expec an insananeous acceleraion vs. ime graph o look for an objec moving wih a consan velociy? Make a rough skech and explain your reasoning. Remember axis labels and unis. Wrie down an equaion ha describes his graph. Wha is he meaning of each quaniy in your equaion? Wha is he relaionship beween velociy and acceleraion? 3. How would you expec a posiion vs. ime graph o look for an objec moving wih consan velociy? Make a rough skech and explain your reasoning. Wrie down an equaion ha describes his graph. Wha is he meaning of each quaniy in your equaion? Wha is he relaionship beween posiion and velociy? 4. How would video image disorion near he edges of he picure affec hese graphs? Use a doed line (or a differen color) o draw he expeced disorion effecs on each of your graphs. How would i affec he equaions ha describe hese graphs? How will he uncerainy of your Lab I - 4

PROBLEM #1: CONSTANT VELOCITY MOTION measuremens affec he graphs? How migh you ell he difference beween uncerainy and disorion? 5. Use he simulaion Lab1Sim o approximae he condiions of he car s moion. (See Appendix F for a brief explanaion of how o use he simulaions.) Look a he graphs produced by he simulaion. You will need o experimen wih he seings o find condiions ha will produce a similar consan velociy moion. (See Appendix F for an inroducion o he Simulaion Programs.) The simulaions allow you o creae real ime graphs ha will help you undersand he relaionships beween velociy, posiion, acceleraion and ime furher. Produce simulaed posiion vs. ime and velociy vs. ime graphs of consan velociy moion, and verify ha hey mee your expecaions. Add a small amoun of uncerainy o he posiion measuremens by pressing Add Error in he Graph frame. Noe he effec of error in he posiion vs. ime graph and in he velociy vs. ime graph. EXPLORATION This secion is exremely imporan many insrucions will no make sense, or you may be led asray, if you fail o carefully explore your experimenal plan. In his secion you pracice wih he apparaus and carefully observe he behavior of your physical sysem before you make precise measuremens. You will also explore he range over which your apparaus is reliable. Remember o always rea he apparaus wih care and respec. Sudens in he nex lab secion will use he equipmen afer you are finished wih i. If you are unsure abou how equipmen works, ask your lab insrucor. If a any ime during he course of his lab you find a piece of equipmen is broken, please submi a problem repor using he LabHelp icon on he deskop. Mos equipmen has a range in which is operaion is simple and sraighforward. This is called is range of reliabiliy. Ouside ha range, complicaed correcions are needed. Be sure your planned measuremens fall wihin he range of reliabiliy. You can quickly deermine he range of reliabiliy by making qualiaive observaions a wha he exremes of your measuremen plan. Record hese observaions in your lab journal. If he apparaus does no funcion properly for he ranges you plan o measure, you should modify your plan o avoid he frusraion of useless measuremens. A he end of he exploraion you should have a plan for doing he measuremens ha you need. Record your measuremen plan in your journal. This exploraion secion is much longer han mos. You will record and analyze digial videos several imes during he semeser. Place one of he meal racks on your lab bench and place he moorized oy car on he rack. Turn on he car and observe is moion. Qualiaively deermine if i acually moves wih a consan velociy. Use he meer sick and sopwach o deermine he speed of he car. Esimae he uncerainy in your speed measuremen. Turn on he video camera and look a he moion as seen by he camera on he compuer screen. Go o Appendix D for insrucions abou using he VideoRECORDER sofware. Do you need o focus he camera o ge a clean image? Move he camera closer o he car. How does his affec he video image? Try moving i farher away. Raise he heigh of he camera ripod. How does his affec he image? Decide where you wan o place he camera o ge he mos useful image. Lab I - 5

PROBLEM #1: CONSTANT VELOCITY MOTION Pracice aking videos of he oy car. You will make and analyze many videos in his course! Wrie down he bes siuaion for aking a video in your journal for fuure reference. When you have he bes movie possible, save i in he Lab Daa folder. Qui VideoRECORDER and open VideoTOOL o analyze your movie. Alhough he direcions o analyze a video are given during he procedure in a box wih he ile INSTRUCTIONS, he following is a shor summary of hem ha will be useful o do he exploraion for his and any oher lab video (for more reference you should read Appendix D a leas once). Warning: Be very careful in following hese seps, if you make a misake you may no be able o go backwards; you migh need o resar from he firs sep. 1. Open he video ha you are ineresed in by clicking he Open Video buon. 2. Selec Begin calibraion and advance he video wih he Sep > buon o he frame where he firs daa poin will be aken. This sep is very imporan because i ses up he origin of your ime axis (=0). 3. To ell he analysis program he real size of he video images, selec some objec in he plane of moion ha you can measure. Drag he green cursor, locaed in he op lef corner of he video display, o one end of he calibraion objec. Click he x0, y0 buon when he green cursor is in place. Move he green cursor o he oher end and selec x1, y1. Ener he lengh of he objec in he Lengh box and specify he Unis. Selec he OK buon wice o complee he calibraion sequence. 4. Ener your predicion equaions of how you expec he posiion o behave. Noice ha he symbols used by he equaions in he program are dummy leers, which means ha you have o idenify hose wih he quaniies involved in your predicion. In order o do he bes guess you will need o ake ino accoun he scale and he values from your pracice rials using he sopwach and he meer sick. Once ha your x-posiion predicion is ready, selec Accep x predicion and repea he previous procedure for he y-posiion. 5. To sar your daa collecion, click he Acquire daa buon. Selec a specific poin on he objec whose moion you are analyzing. Drag he green cursor over his poin and click he Accep Daa Poin buon and you will see he daa on he appropriae graph on your compuer screen, afer his he video will advance one frame. Drag again he green cursor over he same poin seleced on he objec and accep he daa poin. Keep doing his unil you have enough daa. 6. Click he Analyze Daa buon and fi your daa. Decide which equaion and consans are he bes approximaions for your daa and accep your x-fi and y-fi. 7. A his level he program will ask you o ener your predicion for velociy in he x- and y- direcions. Choose he appropriae equaions and give your bes approximaions for he consans. Accep your v x - and v y -predicions and you will see he daa on he las wo graphs. 8. Fi your daa for hese velociies in he same way ha you did for posiion. Accep your fi and click he Prin Resuls buon o view a PDF documen of your graphs ha can be e- mailed o you and your group members. Lab I - 6

PROBLEM #1: CONSTANT VELOCITY MOTION Make sure everyone in your group ges he chance o operae he camera and he compuer. Now you are ready o answer some quesions ha will be helpful for planning your measuremens. Wha would happen if you calibrae wih an objec ha is no on he plane of he moion? Wha would happen if you use differen poins on your car o ge your daa poins? MEASUREMENT Now ha you have prediced he resul of your measuremen and have explored how your apparaus behaves, you are ready o make careful measuremens. To avoid wasing ime and effor, make he minimal measuremens necessary o convince yourself and ohers ha you have solved he laboraory problem. 1. Use a sopwach o measure he ime he car akes o ravel a known disance. Esimae he uncerainy in ime and disance measuremens. How many measuremens should you make o accuraely deermine he car s speed? 2. Take a good video of he car s moion using VideoRECORDER. Analyze he video wih VideoTOOL o predic and fi funcions for posiion vs. ime and velociy vs. ime. a. Measure some objec you can see in he video so ha you can ell he analysis program he real size of he video images when i asks you o calibrae. The larger he objec you use he less uncerainy here will be in your calibraion. Try a meer sick or he car iself. b. When you digiize he video, why is i imporan o click on he same poin on he car s image? You migh wan o use a piece of ape on he car so ha you can deermine his poin consisenly. c. Be sure o ake measuremens of he moion of he car in he disored regions (edges) of he video. d. Se he scale for he axes of your graph so you can see he daa poins as you ake hem. Use your measuremens of oal disance he car ravels and oal ime o deermine he maximum and minimum value for each axis before aking daa. If possible, every member of your group should analyze a video. Record your procedures, measuremens, predicion equaions, and fi equaions in a nea and organized manner so ha you can undersand hem a monh from now. Some fuure lab problems will require resuls from earlier ones. Noe: Be sure o record your measuremens wih he appropriae number of significan figures (see Appendix A) and wih your esimaed uncerainy (see Appendix B). Oherwise, he daa are nearly meaningless. ANALYSIS Daa alone is of very limied use. Mos ineresing quaniies are hose derived from he daa, no direc measuremens hemselves. Your predicions may be qualiaively correc bu quaniaively very wrong. To see his you mus process your daa. Lab I - 7

PROBLEM #1: CONSTANT VELOCITY MOTION Always complee your daa processing (analysis) before you ake your nex se of daa. If somehing is going wrong, you shouldn' wase ime aking a lo of useless daa. Afer analyzing he firs collecion of daa, you may need o modify your measuremen plan and re-perform he measuremens. If you do, be sure o record how you changed your plan in your journal. Calculae he average speed of he car from your sopwach and meer sick measuremens. Deermine if he speed is consan wihin your measuremen uncerainies. As you analyze daa from a video, make sure o wrie down each of he predicion and fi equaions for posiion and velociy. When you have finished making a fi equaion for each graph, rewrie he equaions in a able bu now maching he dummy leers wih he appropriae kinemaic quaniies. If you have consan values, assign hem he correc unis. Why do you have fewer daa poins for he velociy vs. ime graph han he posiion vs. ime graph? CONCLUSIONS Afer you have analyzed your daa, you are ready o answer he experimenal problem. Sae your resul in he mos general erms suppored by your analysis. This should all be recorded in your journal in one place before moving on o he nex problem assigned by your lab insrucor. Make sure you compare your resul o your predicion. Compare he car s speed measured wih video analysis o he measuremen using a sopwach. How do hey compare? Did your measuremens and graphs agree wih your answers o he Warm-up? If no, why? Do your graphs mach wha you expeced for consan velociy moion? Wha are he limiaions on he accuracy of your measuremens and analysis? Do measuremens near he edges of he video give he same speed as ha as found in he cener of he image wihin he uncerainies of your measuremen? Wha will you do for fuure measuremens? SIMULATION If your graphs did no perfecly represen wha you expec for consan velociy moion, use he simulaion Lab1Sim (See Appendix F for an inroducion o he Simulaion Programs) o see he effecs of uncerainy in posiion measuremen. In VideoTOOL and Lab1Sim, how do you hink he compuer generaes daa for a velociy graph? How is his relaed o he effec of measuremen uncerainy on velociy (compared o posiion) graphs? Why is here one less daa poin in a velociy vs. ime graph han in he corresponding posiion vs. ime graph? Lab I - 8

PROBLEM #2: MOTION DOWN AN INCLINE You have a summer job working wih a eam invesigaing accidens for he sae safey board. To decide on he cause of one acciden, your eam needs o deermine he acceleraion of a car rolling down a hill wihou any brakes. Everyone agrees ha he car s velociy increases as i rolls down he hill. Your eam s supervisor believes ha he car's acceleraion also increases as i rolls down he hill. Do you agree? To resolve he issue, you decide o measure he acceleraion of a car moving down an inclined rack in he laboraory. EQUIPMENT For his problem you will have a sopwach, meer sick, an adjusable end sop, wood blocks, a video camera, and a compuer wih video analysis applicaions wrien in LabVIEW (VideoRECORDER and VideoTOOL applicaions). You will also have a PASCO car o roll down an aluminum rack. Remember ha if you have broken or missing equipmen, submi a problem repor using he icon on he lab compuer deskop. PREDICTION Skech he insananeous acceleraion vs. ime graph for a car released from res near he op of an inclined rack. Do you hink he car's insananeous acceleraion increases, decreases, or says he same (is consan) as i moves down he rack? Explain your reasoning. WARM-UP Read: Serway & Vuille Chaper 2, Secions 2.1 o 2.5. 1. Skech insananeous acceleraion vs. ime graphs for a car moving (1) wih a consan acceleraion, (2) wih increasing acceleraion, and (3) wih decreasing acceleraion. For easy comparison, draw hese graphs nex o each oher. Wrie down he equaion ha bes represens each of hese graphs. If here are consans in your equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Which graph do you hink bes represens a car rolling down an incline? Lab I - 9

PROBLEM #2: MOTION DOWN AN INCLINE 2. Wrie down a relaionship beween he acceleraion and he velociy of he car. Use his o skech a rough graph of insananeous velociy vs. ime for each of he hree acceleraions you drew in quesion one. Wrie down an equaion ha bes represens each of hese graphs. If here are consans in your equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Can any of he consans be deermined from he equaion represening he acceleraion vs. ime graphs? Which graph do you hink bes represens he velociy of a car rolling down an incline? Change your predicion if necessary. 3. Wrie down a relaionship beween he velociy and he posiion of he car. Use his o consruc posiion vs. ime graphs from he insananeous velociy graphs for he 3 siuaions above. Wrie down an equaion ha bes represens each of hese graphs. If here are consans in your equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Can any of he consans be deermined from your equaion represening he velociy vs. ime graphs? Which graph do you hink bes represens he posiion of a car moving down an incline? Change your predicion if necessary. 4. Use he simulaion Lab1Sim o approximae he condiions of he car s moion. (See Appendix F for a brief explanaion of how o use he simulaions.) Look a he graphs produced by he simulaion. In he real world, fricion or air resisance may affec your resuls. Try increasing and decreasing he fricion and air resisance. Uncerainy in posiion measuremens may affec your resuls. Try increasing and decreasing he measuremen uncerainy. Use he simulaion o compare he resuls wih and wihou measuremen uncerainies. Looking a hese graphs, will reasonable uncerainy affec your abiliy o es he supervisor s saemen? EXPLORATION You will use a wood block and an aluminum rack o creae an incline. Wha is he bes way o change he angle of he incline in a reproducible way? How are you going o measure his angle wih respec o he able? Hin: Think abou rigonomery! Sar wih a small angle and wih he car a res near he op of he rack. Observe he car as i moves down he inclined rack. Try a range of angles. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP! If he angle is oo large, you may no ge enough video frames, and hus enough posiion and ime measuremens o measure he acceleraion accuraely. If he angle is oo small he acceleraion may be oo small o measure accuraely wih he precision of your measuring insrumens. Selec he bes angle for his measuremen. When placing he camera, consider which par of he moion you wish o capure. Try differen camera posiions unil you ge he bes possible video. Hin: Your video may be easier o analyze if he moion on he video screen is purely horizonal. Why? I could be useful o roae he camera! Where is he bes place o release he car so i does no damage he equipmen bu has enough of is moion capured on video? Be sure o cach he car before i collides wih he end sop. Take a few pracice videos using VideoRECORDER and play hem back o make sure you have capured he moion you wan. Lab I - 10

PROBLEM #2: MOTION DOWN AN INCLINE Wha is he oal disance hrough which he car rolls? How much ime does i ake? These measuremens will help you se up he graphs for your compuer daa aking. Wrie down your measuremen plan. MEASUREMENT Use a meer sick and a sopwach o deermine he average acceleraion of he car. Under wha condiion will his average acceleraion be equal o he insananeous acceleraion of he car? How much accuracy from he meer sick and sopwach is necessary o deermine he acceleraion wih a leas wo significan figures? Make a video of he car moving down he inclined rack. Don' forge o measure and record he angle of he rack (wih esimaed uncerainy). You may use i for laer labs. Choose an objec in your picure for calibraion. Choose your coordinae sysem. Is a roaed coordinae sysem he easies o use in his case? Try he measuremen wih and wihou a roaed coordinae sysem. Why is i imporan o click on he same poin on he car s image o record is posiion? Esimae your accuracy in doing so. Make sure you se he scale for he axes of your graph so ha you can see he daa poins as you ake hem. Use your measuremens of oal disance he car ravels and oal ime o deermine he maximum and minimum value for each axis before aking daa. Are any poins missing from he posiion vs. ime graph? If oo many poins are missing, make sure ha he size of your video frame is opimal (see Appendix D). I may also be ha your background is oo busy. Make sure everyone in your group ges he chance o operae he camera and he compuer. Noe: Be sure o record your measuremens wih he appropriae number of significan figures (see Appendix A) and wih your esimaed uncerainy (see Appendix B). Oherwise, he daa are nearly meaningless. ANALYSIS In VideoTOOL, choose a fi funcion o represen he posiion vs. ime graphs in he x and y direcions. How can you esimae he values of he consans of he funcion from he graph? You can wase a lo of ime if you jus ry o guess he consans. Wha kinemaic quaniies do hese consans represen? Choose a fi funcion o represen he velociy vs. ime graphs in he x and y direcions. How can you calculae he values of he consans of his funcion from he funcion represening he posiion vs. ime graph? Check how well his works. You can also esimae he values of he consans from he graph. Jus rying o guess he consans can wase a lo of your ime. Wha kinemaic quaniies do hese consans represen? Lab I - 11

PROBLEM #2: MOTION DOWN AN INCLINE Why do you have fewer daa poins for he velociy vs. ime graphs compared o he posiion vs. ime graphs? Use he daa ables generaed by he compuer o explain how he compuer generaes he graphs. Look a your graphs in VideoTOOL and rewrie all of he fi equaions in a able, bu now maching he dummy leers wih he appropriae kinemaic quaniies. If you have consan values, assign hem he correc unis and explain heir meaning. From he velociy vs. ime graphs deermine if he acceleraion is consan, increasing, or decreasing as he car goes down he ramp. Use he fi equaion represening he velociy vs. ime graph o calculae he acceleraion of he car as a funcion of ime. Make a graph of he acceleraion vs. ime. Is he average acceleraion of he car equal o is insananeous acceleraion in his case? Calculae he average acceleraion of he car from your sopwach and meer sick measuremens. Compare he acceleraions for he car you found wih your video analysis o your acceleraion measuremen using a sopwach. CONCLUSION How does a car accelerae as i moves down an inclined rack? In wha direcion is he acceleraion? Sae your resul in he mos general erms suppored by your analysis. Did your measuremens agree wih your iniial predicions? Why or why no? Wha are he limiaions on he accuracy of your measuremens and analysis? Was your eam supervisor righ abou how a car acceleraes down a hill? If yes, sae your resul in he mos general erms suppored by your analysis. If no, describe how you would convince your supervisor. Address (or re-address if you have already considered hem) he following quesions. In VideoTOOL and Lab1Sim : How do you hink he compuer generaes daa for a velociy graph? How is his relaed o he effec of measuremen uncerainy on velociy (compared o posiion) graphs? Why is here one less daa poin in a velociy vs. ime graph han in he corresponding posiion vs. ime graph? Lab I - 12

PROBLEM #3: MOTION DOWN AN INCLINE WITH AN INITIAL VELOCITY You have a summer job wih a company designing a new bobsled for he U.S. eam o use in he nex Winer Olympics. You know ha he success of he eam depends crucially on he iniial push of he eam members how fas hey can push he bobsled before hey jump ino he sled. You need o know in more deail how ha iniial velociy affecs he moion of he bobsled. In paricular, your boss wans you o deermine if he iniial velociy of he sled affecs is acceleraion down he rack. To solve his problem, you decide o model he siuaion using a car moving down an inclined rack. EQUIPMENT For his problem you will have a sopwach, meer sick, a wood block, a video camera, and a compuer wih video analysis applicaions wrien in LabVIEW (VideoRECORDER and VideoTOOL). You will also have a PASCO car o roll down an inclined aluminum rack. You will slan he ramp a he same angle you used in Problem #2 (Moion Down an Incline) and give he car a genle push down he inclined rack insead of releasing i from res. Remember ha if you have broken or missing equipmen, submi a problem repor using he icon on he lab compuer deskop. PREDICTION From your resuls for Problem #2, make a rough skech of he acceleraion vs. ime graph for a car released from res on an inclined rack. On he same graph skech how you hink he acceleraion vs. ime graph will look when he car is given an iniial velociy down he rack. Do you hink he car launched down he inclined rack will have a larger acceleraion, smaller acceleraion, or he same acceleraion as he car released from res? Explain your reasoning. WARM-UP Read: Serway & Vuille Chaper 2, Secions 2.1 o 2.5. 1. Skech a graph of he insananeous acceleraion vs. ime graph for a car moving down he inclined rack afer an iniial push. Nex o his graph, skech an insananeous acceleraion vs. ime graph for a car released from res using he same scale for he ime axes. Explain your reasoning for each graph. Wrie down an equaion for each graph. If here are consans in your equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? 2. Use your acceleraion vs. ime graphs o skech insananeous velociy vs. ime graphs for each case using he same scale for he ime axes. Wrie down an equaion for each graph. If here are Lab I - 13

PROBLEM #3: MOTION DOWN AN INCLINE WITH AN INITIAL VELOCITY consans in your equaions, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Can any of he consans be deermined from he equaions represening he acceleraion vs. ime graphs? 3. Use your velociy vs. ime graphs o skech insananeous posiion vs. ime graphs for each case using he same scale for he ime axes. Wrie down an equaion for each graph. If here are consans in your equaions, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Can any of hese consans be deermined from he equaions represening he acceleraion vs. ime or velociy vs. ime graphs? 4. Use he simulaion Lab1Sim o explore he approximae he condiions of your experimen. Use a range of iniial velociies and check he affec on he graphs. If you believe air resisance or fricion affeced he resuls, explore he effecs of each wih he simulaion. If you believe ha uncerainy in posiion measuremens may affec your resuls, use he simulaion o compare he resuls wih and wihou error. Remember o check for he effecs of measuremen uncerainy in your VideoTOOL measuremens laer in lab. EXPLORATION Slan he rack a he same angle you used in Problem #2: Moion Down an Incline. Deermine he bes way o genly launch he car down he rack in a consisen way wihou breaking he equipmen. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP! When placing he camera, consider which par of he moion you wish o capure. Try differen camera posiions unil you ge he bes possible video. Hin: Your video may be easier o analyze if he moion on he video screen is purely horizonal. Why? I could be useful o roae he camera! Wha is he oal disance hrough which he car rolls? How much ime does i ake? These measuremens will help you se up he graphs for your compuer daa aking. Wrie down your measuremen plan. MEASUREMENT Using he plan you devised in he Exploraion secion, make a video of he car moving down he rack a your chosen angle. Make sure you ge enough poins for each par of he moion o deermine he behavior of he acceleraion. Don' forge o measure and record he angle (wih esimaed uncerainy). Choose an objec in your picure for calibraion. Choose your coordinae sysem. Is a roaed coordinae sysem he easies o use in his case? Why is i imporan o click on he same poin on he car s image o record is posiion? Esimae your accuracy in doing so. Make sure you se he scale for he axes of your graph so ha you can see he daa poins as you ake hem. Use your measuremens of oal disance he car ravels and oal ime o deermine he maximum and minimum value for each axis before aking daa. Make sure everyone in your group ges he chance o operae he camera and he compuer. Lab I - 14

PROBLEM #3: MOTION DOWN AN INCLINE WITH AN INITIAL VELOCITY ANALYSIS Using VideoTOOL, deermine he fi funcions ha bes represen he posiion vs. ime graphs in he x and y direcions. How can you esimae he values of he consans of he funcion from he graph? You can wase a lo of ime if you jus ry o guess he consans. Wha kinemaic quaniies do hese consans represen? Choose a fi funcion o represen he velociy vs. ime graphs in he x and y direcions. How can you calculae he values of he consans of his funcion from he funcion represening he posiion vs. ime graph? Check how well his works. You can also esimae he values of he consans from he graph. Jus rying o guess he consans can wase a lo of your ime. Wha kinemaic quaniies do hese consans represen? Are any of he quaniies relaed o he posiion vs. ime graphs? From eiher he velociy or posiion versus ime graph, deermine he acceleraion of he car as a funcion of ime as i goes down he ramp afer he iniial push. Make a graph of ha funcion. CONCLUSIONS Did he car launched down he inclined rack have a larger acceleraion, smaller acceleraion, or he same acceleraion as he car released from res? Did your measuremens agree wih your iniial predicions? Why or why no? Wha are he limiaions on he accuracy of your measuremens and analysis? Wha will you ell your boss? Does he acceleraion of he bobsled down he rack depend on he iniial velociy he eam can give i? Does he velociy of he bobsled down he rack depend on he iniial velociy he eam can give i? Sae your resul in he mos general erms suppored by your analysis. If your daa did no mach your expecaions, you should use he simulaion o explore wha could have happened. A scheme for doing so is oulined a he end of Problem 2 in his lab. Lab I - 15

PROBLEM #4: MOTION UP AND DOWN AN INCLINE A proposed ride a he Valley Fair amusemen park launches a roller coaser car up an inclined rack. Near he op of he rack, he car reverses direcion and rolls backwards ino he saion. As a member of he safey commiee, you have been asked o compue he acceleraion of he car hroughou he ride and deermine if he acceleraion of an objec moving up a ramp is differen from ha of an objec moving down he same ramp. To check your resuls, you decide o build a laboraory model of he ride. EQUIPMENT You will have a sopwach, meer sick, an end sop, a wood block, a video camera, and a compuer wih video analysis applicaions wrien in LabVIEW TM (VideoRECORDER and VideoTOOL). You will also have a PASCO car o roll on an inclined aluminum rack. Remember ha if you have broken or missing equipmen, submi a problem repor using he icon on he lab compuer deskop. PREDICTION Based on your resuls for Problem #2, make a rough skech of he acceleraion vs. ime graph for he car moving down he inclined rack. On he same graph, skech how you hink he acceleraion vs. ime graph will look for he car moving up he rack a he same angle. Do you hink he magniude of he car s acceleraion as i moves up an inclined rack will increase, decrease, or say he same? Wha abou he magniude of he car s acceleraion as i moves down a rack inclined a he same angle? Explain your reasoning. Does he direcion of he car s acceleraion change hroughou is moion, or say he same? Remember, for a direc comparison o Problem #2, you should use he same coordinae sysem. WARM-UP Read: Serway & Vuille Chaper 2, Secions 2.1 o 2.5 1. Draw a picure of he car rolling up he ramp. Draw arrows above he car o show he direcion of he velociy and he direcion of he acceleraion. Choose a coordinae sysem and include his in your picure. 2. Draw a new picure of he car rolling down he ramp. Draw arrows above he car o show he direcion of he velociy and he direcion of he acceleraion. Label your coordinae sysem. 3. Skech a graph of he insananeous acceleraion vs. ime for he enire moion of he car as i rolls up and hen back down he rack afer an iniial push. Label he insan where he car reverses is moion near he op of he rack. Explain your reasoning. Wrie down he equaion(s) ha Lab I - 16

PROBLEM #4: MOTION UP AND DOWN AN INCLINE bes represens his graph. If here are consans in your equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? 4. From your acceleraion vs. ime graph, answer Warm-up quesion 3. for insananeous velociy vs. ime insead. Hin: Be sure o consider boh he direcion and he magniude of he velociy as he car rolls up and down he rack. Use he same scale for your ime axes. Can any of he consans in he velociy equaion(s) be deermined from he consans in he acceleraion equaion(s)? 5. Now do he same for posiion vs. ime. 6. Use he simulaion Lab1Sim o approximae he condiions of he car s moion. (See Appendix F for a brief explanaion of how o use he simulaions.) Look a he graphs produced by he simulaion. If you believe fricion or air resisance may affec your resuls, explore he effecs of each wih he simulaion. If you believe ha uncerainy in posiion measuremens may affec your resuls, use he simulaion o compare he resuls wih and wihou error. Noe he difference in he effec in he posiion vs. ime and velociy vs. ime graph. Remember o check for he effecs of measuremen uncerainy in your VideoTOOL measuremens laer in lab. EXPLORATION Wha is he bes way o change he angle of he inclined rack in a reproducible way? How are you going o measure his angle wih respec o he able? Hin: Think abou rigonomery. How seep of an incline do you wan o use? Sar he car up he rack wih a genle push. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP ON ITS WAY DOWN! Observe he car as i moves up he inclined rack. A he insan he car reverses direcion, wha is is velociy? Is acceleraion? Observe he car as i moves down he inclined rack. Do your observaions agree wih your predicion? If no, his is a good ime o discuss wih your group and modify your predicion. When placing he camera, consider which par of he moion you wish o capure. Try differen camera posiions unil you ge he bes possible video. Hin: Your video may be easier o analyze if he moion on he video screen is purely horizonal. Why? I could be useful o roae he camera! Try several differen angles. If he angle is oo large, he car may no go up very far and give you oo few video frames for he measuremen. If he angle is oo small i will be difficul o measure he acceleraion. Deermine he useful range of angles for your rack. Take a few pracice videos and play hem back o make sure you have capured he moion you wan. Wha is he oal disance hrough which he car rolls? How much ime does i ake? These measuremens will help you se up he graphs for your compuer daa aking. Wrie down your measuremen plan. MEASUREMENT Follow your measuremen plan from he Exploraion secion o make a video of he car moving up and hen down he rack a your chosen angle. Make sure you ge enough poins for each par of he moion o deermine he behavior of he acceleraion. Record he ime duraion of he car s rip, and he disance raveled. Don' forge o measure and record he angle (wih esimaed uncerainy). Lab I - 17

PROBLEM #4: MOTION UP AND DOWN AN INCLINE Choose an objec in your picure for calibraion. Choose your coordinae sysem. Is a roaed coordinae sysem he easies o use in his case? Why is i imporan o click on he same poin on he car s image o record is posiion? Esimae your accuracy in doing so. Make sure you se he scale for he axes of your graph so ha you can see he daa poins as you ake hem. Use your measuremens of oal disance he car ravels and oal ime o deermine he maximum and minimum value for each axis before aking daa. ANALYSIS From he ime given by he sopwach (or he ime samp on he video) and he disance raveled by he car, calculae he average acceleraion. Esimae he uncerainy. Using VideoTOOL, deermine he fi funcions ha bes represen he posiion vs. ime graphs in he x and y direcions. How can you esimae he values of he consans of he funcion from he graph? You can wase a lo of ime if you jus ry o guess he consans. Wha kinemaic quaniies do hese consans represen? Can you ell from your graph where he car reaches is highes poin? Do he same for he velociy vs. ime graphs in he x and y direcions. Compare hese funcions wih he posiion vs. ime funcions. Wha was he velociy when he car reached is maximum heigh on he rack? How do you know? Deermine he acceleraion as a funcion of ime as he car goes up and hen down he ramp. Make a graph of he acceleraion vs. ime. Can you ell from your graph where he car reaches is highes poin? Is he average acceleraion of he car equal o is insananeous acceleraion in his case? As you analyze your video, make sure everyone in your group ges he chance o operae he compuer. Compare he acceleraion funcion you jus graphed wih he average acceleraion you calculaed from he ime and he disance he car raveled. CONCLUSIONS How do your posiion vs. ime and velociy vs. ime graphs compare wih your answers o he warmup and he predicion? Wha are he limiaions on he accuracy of your measuremens and analysis? How did he acceleraion of he car up he rack compare o he acceleraion down he rack? Did he acceleraion change magniude or direcion a any ime during is moion? Was he acceleraion zero, or nonzero a he maximum heigh of is moion? Explain how you reached your conclusions abou he car s moion. If your daa did no mach your expecaions, you should go back and use he simulaion o explore wha could have happened. A scheme for doing so is oulined a he end of Problem 2 in his lab. Lab I - 18

PROBLEM #5: MASS AND MOTION DOWN AN INCLINE Before he end of summer arrives, you and some friends drive o a local amusemen park o ride he new roller coaser. During he busy afernoon, he roller coaser is always full of people. Bu as he day comes o an end and he park is less crowded, you wan o go down he roller coaser once more. However, your friends say ha he ride down he firs hill won' be as fas as i was earlier, because here is less mass in he roller coaser, so hey don' wan o go. Wha do you hink? To deermine how he acceleraion of an objec down a ramp depends on is mass, you decide o model he siuaion using a car moving down an inclined rack. EQUIPMENT You will have a sopwach, meer sick, an adjusable end sop, a wood block, a video camera, and a compuer wih video analysis applicaions wrien in LabVIEW (VideoRECORDER and VideoTOOL). You will also have a PASCO car o roll down an inclined aluminum rack and a mass se o vary he mass of he car. For his problem you will slan he ramp a he same angle you used in Problem #2 (Moion Down an Incline) and release he car from res. PREDICTION Make a skech of how you hink he acceleraion vs. mass graph will look for cars wih differen masses released from res from he op of an inclined rack. Do you hink he acceleraion of he car increases, decreases, or says he same as he mass of he car increases? Explain your reasoning. WARM-UP Read: Serway & Vuille Chaper 2, Secions 2.1 o 2.5 1. Skech a graph of how you would expec an insananeous acceleraion vs. ime graph o look for a car released from res on an inclined rack. Nex o his graph, skech a new graph of he acceleraion vs. ime for a car wih a much larger mass. Explain your reasoning. Wrie down he equaion(s) ha bes represen each of hese graphs. If here are consans in your Lab I - 19

PROBLEM #5: MASS AND MOTION DOWN AN INCLINE equaion, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? 2. Skech a graph of insananeous velociy vs. ime for each case. Use he same scale for he ime axes as he acceleraion graphs. Wrie down he equaion(s) for each graph. If here are consans in your equaions, wha kinemaic quaniies do hey represen? How would you deermine hese consans from your graph? Can any of he consans be deermined from he equaions represening he acceleraion vs. ime graphs? 3. Now do he same for posiion vs. ime. Can any of he consans in your funcions be deermined from he equaions represening he acceleraion vs. ime or velociy vs. ime graphs? 4. Use he simulaion Lab1Sim o explore he approximae he condiions of your experimen. Use a range of values for he mass of he car and check he affec on he graph. EXPLORATION Slan he rack a he same angle you used in Problem #2: Moion Down an Incline. Observe he moion of several cars of differen mass when released from res a he op of he rack. BE SURE TO CATCH THE CART BEFORE IT HITS THE END STOP! From your esimae of he size of he effec, deermine he range of mass ha will give he bes resuls in his problem. Deermine he firs wo masses you should use for he measuremen. How do you deermine how many differen masses do you need o use o ge a conclusive answer? How will you deermine he uncerainy in your measuremens? How many imes should you repea hese measuremens? Explain. When placing he camera, consider which par of he moion you wish o capure. Try differen camera posiions unil you ge he bes possible video. Hin: Your video may be easier o analyze if he moion on he video screen is purely horizonal. Why? I could be useful o roae he camera! Wha is he oal disance hrough which he car rolls? How much ime does i ake? These measuremens will help you se up he graphs for your compuer daa aking. Wrie down your measuremen plan. Make sure everyone in your group ges he chance o operae he camera and he compuer. MEASUREMENT Using he measuremen plan you devised in he Exploraion secion, make a video of he car moving down he rack a your chosen angle. Make sure you ge enough poins for each par of he moion o deermine he behavior of he acceleraion. Record he ime duraion of he car s rip, and he disance raveled. Don' forge o measure and record he angle (wih esimaed uncerainy). Choose an objec in your picure for calibraion. Choose your coordinae sysem. Is a roaed coordinae sysem he easies o use in his case? Lab I - 20

PROBLEM #5: MASS AND MOTION DOWN AN INCLINE Why is i imporan o click on he same poin on he car s image o record is posiion? Esimae your accuracy in doing so. Make sure you se he scale for he axes of your graph so ha you can see he daa poins as you ake hem. Make several videos wih cars of differen mass o check your qualiaive predicion. If you analyze your daa from he firs wo masses you use before you make he nex video, you can deermine which mass o use nex. As usual you should minimize he number of measuremens you need. ANALYSIS From he ime given by he sopwach (or he ime samp on he video) and he disance raveled by he car, calculae he average acceleraion. Esimae he uncerainy. Using VideoTOOL, deermine he fi funcions ha bes represen he posiion vs. ime graphs in he x and y direcions. How can you esimae he values of he consans of he funcion from he graph? You can wase a lo of ime if you jus ry o guess he consans. Wha kinemaic quaniies do hese consans represen? Do he same for he velociy vs. ime graphs in he x and y direcions. Compare hese funcions wih he posiion vs. ime funcions. Deermine he acceleraion as he car goes down he rack for differen masses. Make a graph of he acceleraion vs. mass. Is he average acceleraion of he car equal o is insananeous acceleraion in his case? As you analyze your video, make sure everyone in your group ges he chance o operae he compuer. Compare he acceleraion of he car you found from he video analysis wih he average acceleraion you calculaed from he ime and he disance he car raveled. Do you have enough daa o convince ohers of your conclusion abou how he acceleraion of he car depends on is mass? If he acceleraion does indeed depend on he mass of he car, wha migh be causing his difference? CONCLUSION How will you respond o your friend? Does he acceleraion down a nearly fricionless roller coaser depend on he mass of he people in he coaser? Does he velociy of he coaser depend on is mass? (Will he roller coaser be jus as fas wih fewer people?) Sae your resul in he mos general erms suppored by your analysis. Did your measuremens of he car agree wih your iniial predicions? Why or why no? Wha are he limiaions on he accuracy of your measuremens and analysis? If your daa did no mach your expecaions, you should use he simulaion o explore wha could have happened. A scheme for doing so is oulined a he end of Problem 2 in his lab. Lab I - 21