b Lab 3 Acceleraion Wha You Need To Know: The Physics In he previous lab you learned ha he velociy of an objec can be deermined by finding he slope of he objec s posiion vs. ime graph. x v ave. = v ave. is he average velociy (in meers per seconds, m/s) x is he change in posiion [rise] (in meers, m) is he change in ime [run] (in seconds, s) The nex concep in moion, acceleraion, can be found in a similar fashion. An objec is acceleraing when i is changing is velociy. The equaion for average acceleraion is v a ave. = a ave. is he average acceleraion (in, m/s 2 ) v is he change in velociy [rise] (in, m/s) is he change in ime [run] (in seconds, s) v v FIGURE 1 Posiive slope FIGURE 2 Negaive slope This equaion ells you ha, in looking a a velociy vs. ime graph, you will be able o deermine he acceleraion of an objec. Therefore, in his lab, you can use all of he conceps you learned in he previous lab on deermining slopes. However, in his case, you will be using a v vs. graph insead of an x vs. graph. Le s review some of hose ideas. The firs hing you learned in las week s lab was ha in moving away from he sensor you are moving in he posiive direcion hus you have a posiive velociy. The opposie is also rue. In moving owards he sensor you have a negaive velociy. You learned ha if your verical value on he graph is increasing while moving o he righ along he horizonal axis, hen you have a posiive slope. See Figure 1. The opposie is also rue. If your verical value decreases while moving o he righ along he horizonal axis hen you have a negaive slope. See Figure 2. You also learned ha if your ploed line is sraigh hen you will have a consan slope and herefore a consan velociy. You will sill be using hese ideas for his lab. Common Acceleraion Ideas One idea ha is ofen incorrecly believed is ha when an objec s velociy a a paricular ime is zero hen he acceleraion of he objec is also zero. This is no always he case. Acceleraion is he CHANGE in velociy over a period of ime (a = v/ ) no jus velociy over ime (no a = v/). For example, when you hrow a ball up in he air i sops briefly a he peak before i comes back down. We would say ha v = 0. However he acceleraion is no zero because he velociy is sill changing as he ball sops for an insan of ime. You will be doing an experimen in his lab o show his idea. 3-1
Wha You Need To Do: The Equipmen For his lab you will be using a rack, a car wih an acceleraion fan, and a moion sensor. See Figure 3. Aach he fan o he car using wo rubber bands as shown below. Place he car wih he fan on he rack and make sure i is in working order. Since he baeries drain quickly, only urn on he fan when performing an experimen. FAN RUBBER BAND + CART MOTION SENSOR TRACK FIGURE 3 - Equipmen Se-up (NOT DRAWN TO SCALE) ADJUSTABLE FEET There are colored arrow sickers on boh sides of he fan ha poin in he direcion of he acceleraion caused by he fan. If he arrow is poining away from he sensor hen he acceleraion of he car is posiive. If he arrow is poining owards he sensor hen he acceleraion is negaive. See Figure 4 for a char of all sign convenions. Descripion Car moving away from sensor Car moving owards sensor Descripion Arrow poining away from sensor Arrow poining owards sensor FIGURE 4 - Sign Convenions Velociy + Acceleraion + v FIGURE 5 - v vs. graph Before you begin, you should level he rack. Wih he fan off, place he car on he rack and le i go from res. If he rack is level he car will no move. If he car moves hen adjus he fee underneah he rack (See Figure 3) o level he rack. Par 1 Consan Velociy You should already know, based on las week s lab, wha a graph of consan velociy looks like in a v vs. graph. Begin your lab repor by making wo v vs. graphs: one of a posiive consan velociy and one of a negaive consan velociy. Quesion 1 Below each graph wrie down wha he acceleraion would be. How do you know his? Par 2 Changing Velociy Away From The Sensor Take your car and place i 50 cm from he moion sensor. Make sure he arrow on he fan is poining away from he sensor. Make a v vs. graph like he one in Figure 5. Turn on he fan and release he car. NOTE: Make sure someone is always ready o cach he car a he end of he rack. Examine he moion of he car and fill in your v vs. graph based on your observaions for wha you hink he moion of he car is. 3-2
Now you are going o use he compuer o make a graph of he car s moion. Open he file ACCELERATION. You will see a v vs. graph he same as in Figure 5. Se your car up as you did before. Push Collec on he compuer. Once he moion sensor sars clicking, release he car. If you are no geing a good signal on your screen i is probably because he moion sensor is no poined direcly down he line of he rack. Re-aim he sensor and ry again. Skech he graph on he compuer screen nex o he one you made righ before using he compuer. Compare he wo graphs. Are he graphs he same? If no, hen wha error did you make in your reasoning? Quesion 2 In examining he graph on he compuer, is he velociy of he car posiive or negaive? How can you ell from he graph? Quesion 3 In examining he graph on he compuer, do you have an increasing, decreasing, or consan velociy? How can you ell from he graph? On he compuer screen, highligh he area of your graph ha corresponds o he main moion of he car unil jus before you sopped i. A he op-middle of he screen here is a buon, R=. This will give you a linear fi o your highlighed region. A lile window will also pop up o ell you he slope of he line and he y-inercep. Also, noe ha here is a fain black line ha will overlay your graph. Quesion 4 Based on he linear fi line, do you have a posiive or negaive acceleraion? How can you ell from he graph? Quesion 5 Based on he linear fi line, do you have an increasing, decreasing, or consan acceleraion? How can you ell from he graph? From he informaion in he lile window, record he acceleraion of he car. Do wo more rial runs and record hose acceleraions. Quesion 6 Wha do you conclude abou he acceleraion offered by he fan? Is i changing or roughly consan? Make a char like Figure 6. (You will fill in he char as you progress hrough he lab. Do no fill ou he enire char now.) The firs row is for he moion you are currenly doing (i.e. Par 2) in which your car sared close o he sensor and moved away. Pu in a + or a in he v and a columns for he firs row. In he fourh column, wrie down he moion of he car; was i speeding up or slowing down? Keep in mind he sign convenions ha were given o you in Figure 4 on he previous page. Fill in he firs row now. Par v a Moion of car 2 3 4 5 FIGURE 6 Moion Char 3-3
v Acceleraion FIGURE 5 - v vs. graph Par 3 Changing Velociy Towards The Sensor Take your car and place i abou 140 cm from he moion sensor. Make sure he arrow on he fan is poining owards he sensor. Make a v vs. graph like he one in Figure 5. Turn on he fan and release he car WITHOUT THE COMPUTER SOFTWARE RUNNING. NOTE: Make sure someone is always ready o cach he car a he end of he rack before i his he moion sensor. Examine he moion of he car and fill in your v vs. graph based on your observaions on he moion of he car. Repea he above procedure wih he compuer racking he car. Skech he graph on he compuer screen nex o he one ha you jus made. Compare he wo graphs. Are he graphs he same? If no, hen wha error did you make in your reasoning? Quesion 7 In examining he graph on he compuer, is he velociy of he car posiive or negaive? How can you ell from he graph? Quesion 8 In examining he graph on he compuer, do you have an increasing, decreasing, or consan velociy? How can you ell from he graph? On he compuer screen, highligh he area of your graph ha maches he moion from when your released he car unil jus before you sopped i. Click on R= for your linear fi. Quesion 9 Based on he linear fi line, do you have a posiive or negaive acceleraion? How can you ell from he graph? Quesion 10 Based on he linear fi line, do you have an increasing, decreasing, or consan acceleraion? How can you ell from he graph? Go back o your moion char ha you made like Figure 6. For he row Par 3, fill in he columns for v, a, and Moion. I is ofen believed ha when an objec has a negaive acceleraion ha he objec will slow down. Is his he case for Par 3? Par 4 Opposie Velociy And Acceleraion NOTE: You do no need he compuer sofware for his par. Take he car and place i a 50 cm away from he sensor wih he arrow poining owards he sensor. Turn on he fan and give he car a push away from he sensor. Cach he car when i sops. Based on wha you observed, fill in he row corresponding o Par 4 in your moion char. (Do no ake ino accoun he acceleraion of he car due o your hand pushing on he car. Only ake ino accoun he acceleraion due o he fan.) Was he car s velociy +/? How can you ell? Was he car s acceleraion +/? How can you ell? Wha kind of moion did he car have? Par 5 Opposie Velociy And Acceleraion Again Take he car and place i 140 cm away from he sensor wih he arrow poining away from he sensor. Turn on he fan and give he car a push owards he sensor. Cach he car when i sops. Based on wha you observed, fill in he final row in your moion char. Before answering he nex quesion, ask your TA o come over and check o make sure ha your moion char is correc. 3-4
Quesion 11 Upon examining your compleed moion char, wrie down an overall saemen ha you can make abou he relaionship beween velociy of an objec, acceleraion of an objec, and is moion. Par 6 Freefall Have your insrucor do a demonsraion run of an objec in freefall and hen bring he srip of whie paper wih he freefall daa back o your able. Remove he car and moion sensor from he rack. Using some ape from he fron of he lab room, aach he srip of paper wih he free-fall daa o he rack wih he firs do on he srip in line wih a convenien poin on he rack. You will be using he ruler on he rack so don cover i wih he srip bu aach i close for easier reading. If you have some kind of card in your walle hen you can use ha o line up he dos wih he rulings on he rack. Nex, in your lab repor, make a daa char like he one in Figure 7. n 2 3 4 5 6 7 8 9 10 11 n y n y v FIGURE 7 - Freefall daa In he char, n is he do number (i.e. he 2 nd do is n = 2), n is he ime for he n h do, y n is he locaion of he n h do. Don worry abou he res of he char for now. Sar aking daa from your second do on he srip and pu he measuremens in he y n column in your char. NOTE: We are going o define our sysem wih he direcion downwards as posiive. So, all of your y n daa will be posiive. Take daa on en dos so ha you will fill he column. DO NOT MAKE MARKS ON THE STRIP. The spark machine was se so ha he ime beween each spark (or do) was 1/30 of a second. Fill he n column wih your imes in decimal form. (Keep hree significan figures.). DO NOT fill ou he res of he char now. You will be insruced on how o fill ou he res of he char afer Quesion 12. On he compuer, open Graphical Analysis from he deskop. Make a plo of y vs.. Once you have ploed your daa, make a rough skech of he graph in your lab repor. Quesion 12 Based on wha you learned in las week s lab and he graph you jus made, wha kind of velociy is his graph showing? (i.e. pos./neg. and inc/dec/consan?) Make a skech of wha you hink he v vs. graph will look like. You are now going o fill in he res of he char from Figure 7. In order o calculae and y you will use every oher daa poin. For example, in order o calculae he firs un-shaded box for he column (i.e. he n = 3 row) you will use 4 and 2, for he n = 4 row, you will use 5 and 3, ec. Do all of he calculaions for and y and place hese values in he char. Now, calculae v using v = y/. 3-5
Using he graph paper provided, make a plo v vs.. Make sure you use all ha you learned from he Graphical Analysis lab o graph properly. Use as much of he graph paper as possible. Compare he graph you ploed and he one you skeched in Quesion 12. Were he graphs he same? If no, hen wha error did you make in your reasoning? Using your ploed graph, calculae he acceleraion of he objec. Again, make sure you use all ha you learned from he Graphical Analysis lab. Using a percen error, compare your calculaed value for he acceleraion and is rue value. Quesion 13 Wha were he signs (+ or ) for your velociy and acceleraion of he objec according o our defined sysem? Quesion 14 Wha kind of moion did he objec have ( speeding up or slowing down )? Does his agree wih wha you learned from he Figure 6 Moion Char? Par 7 Back And Forh Moion Re-open he ACCELERATION file. Take he car and place i 170 cm away from he sensor wih he arrow poining away from he sensor. Turn on he fan, push COLLECT on he compuer, and give he car a push owards he sensor. Le he car move owards he sensor and hen back o is saring poin. Repea his unil he car urns around a jus abou 50 cm from he sensor AND you have a smooh graph while he car is freely moving. Make a skech of his graph in your lab repor. Quesion 15 Wha does he graph ell you abou he car s acceleraion a all imes? Make a char in your lab repor like he one in Figure 8. Fill in he char wih +,, or 0 for he v and a columns and hen he ype of moion in he moion column. Again, keep in mind you are no o ake ino accoun he acceleraion of he car due o you hand pushing i. Take ino accoun only he acceleraion due o he fan. FIGURE 8 - Moion char Duraion v a Moion of car Moving owards he sensor A he peak Moving away from he sensor Quesion 16 Does your a column have he same value for all hree rows? If so, explain why. If no, explain why. (Think abou wha he fan is doing during he enire moion.) Does your answer agree wih your answer from Quesion 15? Before moving on o he nex par, ask your TA o come over and check o make sure ha your moion char is correc. Par 8 Throwing a Bag Take he bean bag a your able and hrow i sraigh up ino he air and cach i a he same level ha you hrew i. Think abou wha kind of moion i has on is way up, a he peak, and back down. 3-6
Make a char in your lab repor like he one in Figure 9. Fill in he char wih +,, or 0 for he v and a columns and hen he ype of moion in he moion column. NOTE: Recall from before ha we are defining downwards as posiive. FIGURE 9 - Moion char Duraion v a Moion of ball Moving up ino he air A he peak Moving back down Quesion 17 Does your a column have he same value for all hree rows? If so, explain why. If no, explain why. (Think abou wha graviy is doing during he enire moion.) Compare he chars in Figures 8 and 9. They should be exacly he same. If hey aren hen you made a misake a some poin. A common misundersanding ha s made is ha when an objec reaches is peak is acceleraion is zero. This is no he case. Graviy does no urn off jus because he ball sops. I is on all of he ime, jus like he fan on he car was on all of he ime, even hough he car sopped briefly a is peak. Anoher misundersanding is ha he sign of he acceleraion is changing from when he ball moves up o when he ball moves back down. This is no he case eiher. Graviy always pulls down regardless of how he ball is moving. Did he fan on he car change direcions while he car was moving up and hen down? No, i did no. Graviy is no paying aenion o wha you or any objec is doing. Tha would be very egocenric. Ge over yourself. 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 chars ha you are asked o draw. Also, urn in he graph paper wih your plo from Par 6. 2008 by Michael J. Dubuque 3-7