b Lab 2 Posiion and Velociy Wha You Need To Know: Working Wih Slope In las week s lab you deal wih a lo of graphing ideas. You will coninue o use one of hese ideas in his week s lab, namely slope. Howeer, insead of dealing wih a lo of calculaions we will be concenraing on geing a beer feel for he idea of slope so you can apply i o he physics you will be learning oday. FIGURE 1 s. graph In graphing here are always wo aes ha you deal wih, a horizonal ais and a erical ais. In grade school you were inroduced o graphs ha were probably y s. graphs where he y alues were placed on he erical ais and he alues were placed on he horizonal ais. This does no always hae o be he case. In his lab you will be dealing wih s. graphs which means ha he alues will be placed on he erical ais and he alues will be placed on he horizonal ais. The alues will represen an objec s posiion and he alues will represen he ime a which he objec is a ha posiion. See Figure 1. You know ha slope is defined by he change in your erical alue oer a corresponding change in your horizonal alue (i.e. he rise oer he run ). So, for he ype of graphs you will be using oday, he slope will equal slope = is he change in posiion [rise] (in meers, m) is he change in ime [run] (in seconds, s) Seep and Shallow One of he main hings you wan o ge a good feel for in his lab is when you hae a large slope and when you hae a small slope. From he equaion aboe you can see ha when your is greaer han your hen your slope is large. See Figure 2. You can see ha when your line is seep you hae a large slope. Howeer, when your is smaller han your hen your slope is small. See Figure 3. You can see ha when your line is shallow you hae a small slope. FIGURE 2 Large slope FIGURE 3 Small slope 2-1
Posiion and Velociy Posiie and Negaie Anoher imporan idea is o deermine if you hae a posiie or a negaie slope. If your erical alue is increasing (going up) as your horizonal alue is increasing (going righ) hen you hae a posiie slope. See Figure 4. If your erical alue is decreasing (going down) as you horizonal alue is increasing (going righ) hen you hae a negaie slope. See Figure 5. FIGURE 4 FIGURE 5 Posiie slope Negaie slope To ie all his ogeher you can use his analogy. Think of yourself as hiker who is hiking some hills. The lines on he graphs are a side iew of he hill. You can only hike moing o he righ. Le s say you were hiking he line in Figure 3 (from he preious page). In moing o he righ you would say ha you were hiking upwards a a prey shallow incline. Therefore you would conclude ha he line has a posiie and small slope, respeciely. Now le s say you were hiking he line in Figure 5. In moing o he righ you would say ha you were hiking downwards a a prey seep incline. Therefore you would conclude ha he line has a negaie and large slope. Wha You Need To Do: Emier/ Receier FIGURE 6 Moion Sensor The Equipmen For his lab you will be using a moion sensor (See Figure 6) aached o a compuer. (Open Posiion and Velociy on he deskop.) The moion sensor will emi a pulse ha raels ou from he sensor unil i his an objec. I hen reflecs off he objec and comes back o he sensor and is receied. Depending on how long i akes he pulse o reurn will deermine he disance from he sensor o he objec. Based on his informaion, he compuer will make a graph of he objec s posiion s. ime (i.e. an s. graph). Since you will be using he moion sensor quie ofen during he semeser i is imporan ha you learn how o use i effeciely. In his lab you will be he objec ha is moing back and forh in fron of he sensor. If he pulse does no hae a nice surface o reflec off of i will scaer and no go back o he sensor. You need, hen, o hold a solid fla surface in fron of you. A noebook will do fine. Also, when you hold up he noebook make sure you aim i a he sensor, oherwise he signal will bounce off o he side and he sensor will no read i. The pulse fans ou a bi when raeling from he sensor. If here are oher objecs close by, like your lab parner or books sacked on he lab able, hen hey migh reflec back he pulse and you will ge spikes on your graph. Make sure he area is clear before you begin. 2-2
Posiion and Velociy Ok, so now you can ry i ou. Pu he sensor a he edge of your lab able poining a he wall. Ge a fla surface o hold and sand somewhere in fron of he sensor. Hae your lab parner push he green COLLECT buon on he compuer screen. There is a sligh pause afer pushing he buon before he sensor sars emiing pulses. When i sars you can hear he pulses. Moe back and forh in fron of he sensor and obsere wha happens on he compuer screen. Le each lab parner hae a go. Pracice a geing a nice, smooh graph. If you are geing spikes on your graph hen reread he las couple of paragraphs. If ha doesn clear up your problem hen grab your TA for assisance. Noice ha you will neer be able o ge a reading of 0 on he graph. 0 posiion would be righ a he sensor. The sensor doesn regiser objecs ha are closer han 40 cm from i. If an objec is less han 40 cm from he sensor, hen he graph will show an objec righ a 40 cm no maer wha small disance i is from he sensor. Try moing closer han 40 cm from he sensor and see wha happens. Par 1 - Velociy In his lab one lab parner will run he compuer and he oher will moe in fron of he sensor. Try o alernae hese jobs. Moe he sensor abou 40 cm from he edge of he lab able. (I can regiser you wihin ha disance anyway.) A) Hae one of you sand in fron of he sensor a any disance from he able. Push COLLECT. Do no moe for he enire ime he sensor is acie. Noice on he compuer screen ha a any ime (horizonal ais) you are a he same posiion (erical ais) relaie o he sensor. Skech he graph ha you see on your compuer screen in your lab repor. Quesion 1 Based on your graph, is your locaion posiie or negaie relaie o he sensor? How do you know his? Is here any way you can ge boh posiie and negaie locaions gien how he sysem is se up righ now? Quesion 2 Wha is he slope of your line (shallow, seep, or zero)? B) Sand close o he able. Once you push COLLECT and he sensor is pulsing moe away from he sensor ery slowly ( baby seps ) and seadily. (Do no moe any faser or slower as you walk.) Skech he graph ha you see on your screen in your lab repor. Ignore Afer doing a run on he compuer, you migh hae some spikes a he beginning or end of your moion. You can jus ignore hese and Focus focus only on he main par of your run in which you hae a nice smooh line. See Figure 7. FIGURE 7 Quesion 3 Wha is he slope of your line (shallow, seep, or zero)? C) Sand close o he able. Once you push COLLECT and he sensor is pulsing moe away from he sensor rapidly and seadily. Skech he relean par of he graph ha you see on your screen in your lab repor. 2-3
Posiion and Velociy Quesion 4 Wha is he slope of your line (shallow, seep, or zero)? Quesion 5 Looking back a your answers o Quesions 2-4, wha do you conclude abou he relaionship beween your differen moions and he slope of he each of he corresponding graphs? D) The firs concep you will be learning abou in physics is called elociy. An objec s elociy is defined by aking an objec s change in posiion and diiding i by is change in ime. is he elociy (in meers per seconds, m/s) = is he change in posiion (in meers, m) is he change in ime (in seconds, s) This operaion is eacly he same as finding he slope of an s. graph. So, he slope of such a graph is equal o he elociy of an objec. rise = = = slope run Go back o your hree skeches ha you made and ne o each graph wrie down wha kind of elociy you had. Wrie eiher large elociy, small elociy, or zero elociy. E) In his lab you will be dealing wih elociies ha are eiher consan or changing. You can ell from your graphs if your elociy is consan or changing by looking o see if your slope is consan or changing. If your line is sraigh hen i is consan. If your line is cured hen your elociy is changing. Go back o your hree skeches ha you made and ne o each graph wrie down if you had a consan elociy or a changing elociy. NOTE: If you hae a zero elociy hen you don hae eiher kind since you are no moing. Par 2 - Velociy and Direcion There is one more idea we need o look a relaie o elociy and ha is wheher you hae a posiie or negaie elociy. A) Sand far from he able. Once you push COLLECT and he sensor is pulsing moe owards he sensor ery slowly and seadily. Skech he graph ha you see on your screen in your lab repor. There should be somehing differen abou your graph compared o he las ones. Based on wha you learned in he Inroducion of he lab, can you ell wha he difference is? You now hae a negaie slope. This also means ha you mus hae a negaie elociy. Quesion 6 Based on your obseraions for his run and he ones you did in Par 1, wha does haing a posiie or negaie elociy mean? Some people hink ha haing a negaie elociy means ha you are slowing down bu you can see ha his is no he case. The only hing ha a posiie or negaie elociy indicaes is if you are moing in one direcion or he opposie direcion. 2-4
Posiion and Velociy B) There are now hree differen commens you can make abou an objec s elociy. You can hae a posiie or negaie elociy, a consan or a changing elociy, and you can hae a large, small, or zero elociy. For he graph you jus creaed wrie down wha kind of elociy you hae. (You should wrie down hree differen commens.) Also, go back o he graphs you made in Par 1 and complee your commens for he elociies. (Three oal commens.) C) Sand far from he able. Once you push COLLECT and he sensor is pulsing moe owards he sensor rapidly and seadily. Skech he graph ha you see on your screen in your lab repor. Wrie down ne o he graph wha kind of elociy you hae. D) For he moion you jus did in C) and using informaion only from he graph, eplain in words how you knew wha o wrie down for he hree differen commens abou he elociy. E) Eplain he same hing again (as in D)) bu base your answers relaie o your moion. Some of yours answers will be really obious bu wrie hem down anyway. For eample, I know ha I had a small elociy because I was walking slowly. Par 3 Finding a Slope Once you hae a graph of your moion i is possible o ge a number alue for your slope. This procedure is somehing ha you will be doing a lo of during he semeser. If you are confused abou any of his hen make sure you grab your TA for clarificaion. Ignore Focus FIGURE 7 A) To find he slope of your graph you should firs highligh he region in which you wan o find he slope. You only wan o highligh he region ha has a nice, smooh line like he region of focus in Figure 7. Using he las graph you made from Par 2, place your mouse on he lef end of his region and click and hold. Drag he mouse o he righ end of he region and unclick. A he op middle of he screen you should see a buon R=. If you click his buon i will open a small window wih seeral pieces of informaion, one of which is he slope of your highlighed region. Wrie down he slope alue and eplain how i agrees wih any elociy commens you made earlier for his graph. Ask your TA for help if you are confused on his process. B) Close he small window. Do a run for moing away from he sensor ery slowly and seadily. Using he same mehod you jus used, find he slope of his line and eplain how his agrees wih your moion. Par 4 Velociy Graphs We e discussed how o describe he elociy of an objec based on is posiion s. ime graph. Now we re going o alk abou how o make a elociy s. ime graph based on a posiion s. ime graph. Le s say you hae an objec whose posiion s. ime graph is like he one in Figure 8a. The slope of his line is zero which ells you ha he elociy is zero. (The dashed lines signify he beginning and he end of he moion. ) FIGURE 8 (a) 2-5
Posiion and Velociy You would hen draw a elociy s. ime graph ha shows zero elociy. See Figure 8b. NOTE: In oher cases you hae possibiliies of posiie or negaie elociies, so he graphs are drawn wih an opion of a posiie or a negaie elociy (i.e. aboe or below he ime ais). For anoher eample, le s say you hae an objec whose posiion s. ime graph is like he one in Figure 9a. The slope of his line is large, negaie, and consan. In your elociy s. ime graph, Figure 9b, you would draw a line ha has a high alue (farher from he ime ais), is negaie (below he ime ais, no aboe), and is a horizonal line (i has he same elociy alue a any ime, i.e. consan). FIGURE 8 (b) (a) FIGURE 9 (b) A) Copy he ne hree ses of graphs ino your lab repor and complee he elociy s. ime graphs. Also, ne o each se of graphs, describe in words wha kind of elociy he objec has. ( I ) ( II ) ( III ) Par 5 Graph Maching Close ou of Logger Pro and open up Graph Maching on he deskop. You should see a posiion s. ime graph wih a ligh blue line on i ha represens seeral differen moions. Moe he sensor abou 70 cm from he edge of able. A) For each of he differen ypes of moion oer each incremen of ime, wrie ou wha you would hae o do in fron of he moion sensor o mach he blue line. Also sae wha kind of elociy you hae for each moion. For eample From 0 o 0.5 seconds I would sand a res a disance of 1 meer away from he moion sensor. I would hae a elociy of zero. 2-6
Posiion and Velociy B) Now ry o mach he graph by acually doing wha you wroe ou in A). Take no more han en minues o do his. Par 6 Changing Velociy So far, eeryhing you hae done has been eiher zero elociy or consan elociy. Now you are going o be doing a changing elociy. Close ou of Logger Pro and open back up Posiion and Velociy on he deskop. A) Sar close o he sensor, push COLLECT, and moe away from i a a seadily increasing rae. HINT: Sar ou wih ery small baby-seps and hen increase your sride. You should ge a graph ha looks similar o he one in Figure 10. Skech your graph in your lab repor. FIGURE 10 B) Highligh he firs 0.5 seconds of your graph in which you hae a smooh cure. Push R= and record your elociy. Do he same for he las 0.5 seconds. Quesion 7 Wha happened o your elociy from he beginning of your moion o he end of your moion? Describe your elociy fully. (i.e. consan, increasing, or decreasing; posiie or negaie) C) Make a elociy s. ime graph of your moion. NOTE: No maer wha your s. graph looks like you will neer hae a cured line in your s. graph. I will always be eiher a horizonal sraigh line or angled sraigh line. D) Sar far from he sensor, push COLLECT, and walk owards i a a seadily increasing rae. Skech your graph. Describe your elociy. Make a s. graph for your moion. E) Copy he ne wo ses of graphs ino your lab repor. Do he following for each se For each s. graph describe how you would moe in fron of he sensor in order o achiee he graph. Based on each s. graph, sae wha kind of elociy he objec has. Complee he s. graph. ( I ) ( II ) 2-7
Posiion and Velociy Par 7 A Few Quesions Jus o es wha you hae learned, answer he following quesions Quesion 8 Gien a posiion s. ime graph for a moion, how can you ell wheher your elociy is consan? Quesion 9 Gien a elociy s. ime graph for a moion, how can you ell wheher he elociy is consan? Quesion 10 Gien a posiion s. ime graph for a moion, how can you ell he direcion of moion? Quesion 11 Gien a elociy s. ime graph for a moion, how can you ell he direcion of moion? Wha You Need To Turn In: On a separae shee of paper from his lab manual answer all of he quesions, including all of he graphs ha you are asked o draw. 2008 by Michael J. Dubuque 2-8