Position, Velocity, and Acceleration
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1 rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME Car ME Fan Accessory ME Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose of his aciviy is o sudy some of he basic behaviors of a mass ha is being uniformly acceleraed, ha meaning experiencing a consan acceleraion. Theory Displacemen is defined o be he sraigh line lengh measured from wha is aken o be he iniial posiion, and he final posiion. x = x x o The average velociy is defined o be he ime rae of change of posiion, herefore i is he displacemen divided by he ime inerval he displacemen ook place over. v avg = x = x x o The average acceleraion is defined as he ime rae of change of velociy, herefore i is he average velociy divided by he ime inerval he change in velociy ook place over. a avg = v avg = v v o For a mass o be acceleraion uniformly he value of he acceleraion mus be consan, meaning i always has he same value, and herefore is such a case we can drop he avg subscrip for he acceleraion in he above equaion. a = v v o When he acceleraion a mass is experiencing is consan we say ha ha mass is being uniformly acceleraed. Since acceleraion is he ime rae of change of velociy hen for a mass being uniformly acceleraed is velociy will be changing a a consan rae such ha is average velociy will also be given by he following equaion. 1
2 v avg = v + v o 2 This equaion ells us ha for a mass being uniformly acceleraed is average velociy is jus he average value beween is iniial and final velociies. Keep in mind ha his equaion is only rue for masses experiencing uniform acceleraion! Jus using hese definiions, and wih he assumpion of uniform acceleraion we can easily consruc he Linear Kinemaic Equaions of Moion. Some of he equaions we can consruc are he following Uniformly Acceleraed Moion a = a o (consan value) v = v o + a x = x o + v o a2 Ploing hese hree equaions ou as funcions of ime will wield graphs similar o he following; A concep ha is rarely discussed in freshman physics classes is he jerk. The average jerk is defined o be he ime rae change of he acceleraion, herefore i is he change in acceleraion divided by he ime inerval he change in acceleraion ook place over. J avg = a a o In his exercise will be ignoring whaever lile jerk here migh be. 2
3 Seup 1. Lay he rack fla on he able. 2. Aach he moion sensor o he end of he rack closes o he PASCO 850 Inerface. Don jus place he moion sensor nex o he end of he rack. I is designed o be physically aached o he end of he rack. Plug he moion sensor ino Digial Inpus Ch(1), and Ch(2) of he PASCO 850 Inerface. Yellow goes ino Ch(1), black ino Ch(2). Using he nob on he side of he Moion Sensor make sure he sensor is aimed horizonally down he lengh of he rack. 3. Aach he fan accessory o he car. 4. Place he car ono he rack wih he fan poining a he moion sensor There needs o be 15 cm beween he back of he car and he moion sensor. 5. A he oher end of he rack aach he barrier o preven he car from falling of he rack when preforming he experimen. 6. Make sure he PASCO 850 inerface is urned on. 7. Double Click he Capsone icon o open he Capsone sofware. 8. In he Tool Bar, on he lef hand side of he screen, click on he Hardware Seup icon o open he Hardware Seup window. In he Hardware Seup window here should be an image of he PASCO 850 Inerface, if here is skip o sep 9. If here isn click on Choose Inerface o open he Choose Inerface window. In he Choose Inerface window chose PASPORT, Auomaically Selec, hen click OK. 9. On he image of he 850 PASCO Inerface click on Digial Inpus Ch(1). This will open a sensor lis. Scroll down, and selecion Moion Sensor II. A he boom of he screen se he sample rae o 20 Hz. 10. In he Tool Bar click on he Daa Summary icon, his will open up he Daa Summary window. Nex o where he Moion Sensor II is lised in he Daa Summary window click on he whie riangle o open up he measuremens lis for he Moion Sensor. 3
4 Click on he word Acceleraion his should cause a propery icon o appear o is righ, click on i, and he properies window for he acceleraion measuremens should open. Click on Numerical forma, and se Number of Decimal Places o 3, and hen click Ok. 11. Close he Tool Bar. 12. In he Display Bar, on he righ side of he screen, click-drag ou-and release he graph icon hree imes. For one of hem for he y-axis click on Selec Measuremen, and hen selec Posiion (m). For anoher for he y-axis click on Selecion Measuremen, and hen selec Velociy (m/s). For he y-axis of he hird click on Selecion Measuremen, and hen selec Acceleraion (m/s 2 ). The compuer will auomaically se he x-axis o Time (s) for all of hem. Procedure 1. Place a finger righ in fron of he car o hold i in place, and hen urn on he fan accessory. 2. A he boom lef of he screen click on he big red circle o sar recording daa, and quickly removed your finger allowing he car o be acceleraed down he rack. 3. When he car bumps ino he barrier a he opposie end of he rack click on he big red square a he boom lef side of he screen o sop recording daa. 4. Turn off he fan accessory. 5. For each graph click on Scale Axes icon so you can see you daa much more clearly. I is he far lef icon a he op of each graph. 6. For he Posiion vs. Time graph click on he Highligh range icon a he op of he graph o make he highligh box appear in he Posiion vs. Time graph. Move he box around by lef-click-and-dragging, and srech he box such ha all he daa poins from when he car sared moving ill he car hi he barrier are highlighed. Click on he down arrow nex o he Apply Seleced Curve Fi icon o open he bes fi line lis. Selec boh he linear fi, and he Quadraic fi. For he linear fi record he m, and b values in he posiion able, ignoring he error bars. For he quadraic fi record he A, B, and C values in he posiion able, ignoring he error bars. Click on he Add a Coordinae Tool icon, and use i o find he coordinae values for he wo daa poins ha are righ in he middle of he highlighed region of he posiion graph. Record he values of hese wo coordinaes in he posiion able wih unis. Then calculae he slope, wih unis, beween hese wo poins. 7. For he Velociy vs. Time graph click on he Highligh Range icon a he op of he graph o make he highligh box appear in he Velociy vs. Time graph. Move he box around by lef-click-and-dragging, and srech he box such ha all he daa poins from when he car sared moving ill he car hi he barrier are highlighed. 4
5 Click on he down arrow nex o he Apply Seleced Curve Fi icon o open he bes fi line lis. Selec he linear fi. Record he values for m, and b values in he Velociy Table, ignoring he error bars. Click on he Add a Coordinae Tool icon, and use i o find he coordinae values of he firs daa poin, and he las daa poin ha is highlighed in he velociy graph, and record hese values, wih unis, in he able for he velociy graph. Then using hese wo values o find he average value of he velociy and record i in he velociy able. Use he Coordinae Tool o find he ime when your calculaed average velociy occurred and record i in he velociy able wih unis. 8. For he Acceleraion vs. Time graph click on he Highligh Range icon a he op of he graph o make he highligh box appear in he acceleraion vs. Time graph. Move he box around by lef-click-and-dragging, and srech he box such ha all he daa poins from when he car sared moving ill he car hi he barrier are highlighed. Click on he down arrow nex o he Apply Seleced Curve Fi icon o open he bes fi line lis. Selec he linear fi. Record he values for m, and b values in he Acceleraion Table, ignoring he error bars. Click on he down arrow nex o he Display Seleced Sas icon o open he sas lis. Make sure Mean is seleced, hen click on he down arrow again o close lis. Click on he Display Seleced Sas so he value of he Mean will appear on he Acceleraion vs. Time graph, and record he value of he Mean in he Acceleraion Table. 5
6 Analysis Table (16 poins) Posiion vs Time Linear Fi m B y = mx + b Quadraic Fi A B C y = Ax 2 + Bx + C (x1, y1) (x2, y2) Slope Velociy vs. Time m b y = mx + b (x1, y1) (x2, y2) vavg vavg ime Acceleraion vs. Time m b y = mx + b The mean Value Value Value 6
7 1. Wha are he appropriae unis for he slope of he: (a) Posiion vs Time graph? (2 poins) (b) Velociy vs Time graph? (2 poins) (c) Acceleraion vs Time graph? (2 poins) 2. For Posiion vs Time daa: (a) Did your quadraic fi of his graph provide iniial posiion? If yes, wha is is value? (b) Did your quadraic fi of his graph provide iniial velociy? If yes, wha is is value? (c) Did your quadraic fi of his graph provide acceleraion? If yes, wha is is value? (d) Wha specific physical quaniy does he slope of he wo middle poins from he Posiion vs. Time graph represen? 3. For Velociy vs Time daa: (a) Did your linear fi of his graph provide iniial posiion? If yes, wha is is value? (b) Did your linear fi of his graph provide iniial velociy? If yes, wha is is value? (c) Did your linear fi of his graph provide acceleraion? If yes, wha is is value? 7
8 (d) How does he ime your calculaed average velociy occurred a compare o he imes of he wo middle poins from he posiion vs. ime graph? (3 poins) (e) How does he ime your calculaed average velociy value occurred a relae o he ime values of he firs and las good daa poins in he Velociy vs. Time graph? (3 poins) 4. For Acceleraion vs Time daa: (a) Did your linear fi of his graph provide iniial posiion? If yes, wha is is value? (b) Did your linear fi of his graph provide iniial velociy? If yes, wha is is value? (c) Did your linear fi of his graph provide acceleraion? If yes, wha is is value? (d) Which mehod, he mean or he linear fi, gives an acceleraion value ha in beer agreemen wih he values of acceleraion given by he posiion and velociy daa? (2 poins) (e) Did your linear fi of his graph yield Jerk? If yes, wha is is value? (f) If Jerk was observed, was is value small enough o be negleced, ie, close o zero? (g) Wha are he SI unis of he Jerk? (2 poins) 8
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