1. Kinematics I: Position and Velocity

Transcription

1 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 eperimen you will generae and inerpre graphs of posiion vs. ime and velociy vs. ime. The graphs will be generaed by a car moving on an air rack and by a moving human, you or your parner. vs. graphs for consan velociy Velociy is disance over ime or v = Δ/Δ. The slope of a graph is rise over run; hence, if he graph is vs. hen he slope, rise over run, is Δ/Δ, or velociy. Graphs of vs. are skeched below, where is he posiion of he objec a =. v = Δ/Δ = /Δ = v = Δ/Δ = + cons. Δ Δ Δ v = Δ/Δ = - cons. Δ In mah books, graphs are ofen y vs., where y is ploed verically, is ploed horizonally, and he equaion of he sraigh line is y = b + m (1) where b is he verical inercep, he value of y a =, and m is he slope, he rise over run. For he above graphs of vs., he verical inercep is and he slope is v, hence he equaion of physics, analogous o he above mah equaion is: v vs. graphs for consan acceleraion = + v (2) Acceleraion, a, is change in velociy over ime, a = Δv/Δ, hence acceleraion is he slope of v vs. graphs, as shown below. v v a = Δv/Δ = /Δ = v v a = Δv/Δ = + cons. Δ Δv v v Δv a = Δv/Δ = - cons. Δ 15

2 The general equaion for v vs. graphs is v = v + a (3) where v, velociy a =, is he verical inercep and a, he acceleraion, is he slope. vs. graphs for consan acceleraion Posiion vs. ime graphs for consan acceleraion are shown below The insananeous velociy v a any ime is he slope of he angen line, he dashed lines in he graphs. For he lef graph angen lines are drawn a imes 1 and 2. Noe ha he slope is posiive, v >, and increasing wih ime, hus he objec is speeding up or acceleraing. For he righ graph he slope is negaive, v <, and decreasing, hence he objec is slowing down or deceleraing. Oucomes To learn how o carefully align and use a moion deecor. To eplore how various moions are represened on a posiion-ime graph. To eplore how various moions are represened on a velociy-ime graph. To discover he relaionship beween posiion-ime and velociy-ime graphs. Prelab Quesions d 1. Various vs. graphs are shown on he righ. Graph(s) indicaing consan velociy are. Graph(s) indicaing posiive velociy are. Graph(s) indicaing negaive b velociy are. Graph(s) indicaing changing velociy a c are. 2. For he vs. graph on he righ describe how you (m) 3 would walk o produce his graph. Your descripion 2 should include your velociy over ime inervals, e. g., 1 o 2 seconds (s) 16

3 3. A graph of posiion vs. ime for a dazed cyclis (m) 4 is shown. A wha ime(s) is he cyclis: (a) moving wih he greaes velociy? 2 (b) no moving, i.e., has zero velociy? (c) moving wih posiive velociy? (s) Seup and Alignmen Compuer Seup 1. Connec he Daa Sudio inerface o he compuer, urn on he inerface, and hen urn on he compuer. 2. Double click on he Daa Sudio icon. When he window opens click on Creae Eperimen. 3. Connec he moion sensor s plugs o Digial Channels 1 and 2 of he Daa Sudio inerface. Connec he yellow plug o Digial Channel 1 and he black one o Digial Channel In he Sensors panel on he lef, scroll down o Moion Sensor and double click. An icon for he moion sensor will appear in he righ panel. Double click on his icon and hen selec he Moion Sensor ab. Change he rigger rae o 4 Hz. Do no click OK. Alignmen of Moion Sensor and Flag 1. Wih he air rack blower urned off, bring he car and Moion Sensor close ogeher and raise or lower he Moion Sensor unil i is cenered on he flag. 2. Move he flag, wih he car aached of course, 2. m from he Moion Sensor. Noe he Curren Disance displayed on he screen. Adjus he direcion he Moion Sensor poins unil he Curren Disance reads 2. m wihin 1 %. Then place he flag 1. m from he Sensor. If he Curren Disance does no read 1. m wihin 1 %, hen adjus he Sensor direcion unil i does. Then go back and check ha he 2. m reading is sill OK. If he 2. m reading is no OK, hen re-adjus he Sensor, ec. 3. Posiion he flag a various disances, e.g.,.5, 1., 1.5, and 2. m, and hence verify ha he Curren Disance in each case is read o wihin 1 %. The sysem is ready o record moion. Now click OK. 4. Double click on Graph in he Display panel in he lower lef of he screen. Selec Posiion as he daa source. The Moion Sensor deecs moion by sending and receiving sound waves. The received waves for he moion of he car on he air rack are hose ha reflec off he flag on he car. Make sure objecs are no near he rack, which could ac as reflecors, e.g., your body. Flag Moion Compuer Bumper Bumper Sensor Air rack Inerface Digial Analog 17

4 Level Air Track 1. Begin by ensuring your air rack is level. Wih he air on place your car in he middle of he rack. If i begins o move, you need o adjus he black knobs on he fee of he rack o adjus he level. Again use your car o es for a level rack. Repea unil he car does no slide o one side. Recording Moion 2. Wih he car near he Moion Sensor end of rack, give i a shove. Afer he car makes a round rip and rebounds from he Sensor end of he rack, click he Sar buon a he op of he screen. Click he STOP buon jus before he car reaches he oher end of he rack. 3. Prin a copy of your graph for each member of your lab group. 4. Obain a Velociy vs. Time graph by again double clicking on Graph in he display panel and his ime selec velociy. Prin he graph. Quesion 1. From your Posiion vs. Time graph wha can you conclude abou he velociy? For eample, is he velociy consan and posiive? Consan and negaive? Eplain. Quesion 2. Does your Velociy vs. Time graph show he velociy is consan and posiive? Consan and negaive? Eplain. 5. Record boh a posiion vs. ime graph and a velociy vs. ime graph for he car ravelling down he rack, rebounding, and reurning o he Sensor end of he rack. Prin boh graphs. Quesion 3. Eplain how each graph indicaes posiive and negaive velociies. Curve Fiing Selec he porion of your vs. graph from (5) ha has a posiive slope by clicking and dragging he cursor o form a recangle enclosing his secion as shown on he righ. Click on he Fi buon above he graph and selec Linear Fi. In your noebook record he equaion of he curve as a physics equaion. The compuer will give you he slope and y- inercep of he generic equaion: b is he verical inercep m is he slope The equaion of physics is y = m + b = o + v i.e., b = o, unis of meers, and m = v, unis of m/s. 18

5 Quesion 4. Wha is he equaion of physics ha describes he moion of your car? You should wrie he above equaion wih values of o and v (wih unis) aken from he compuer curve fi analysis. How does he value of v derived from he vs. graph compare o he value you read off direcly from he v vs. graph? Walking o generae moion graphs Your walking moion will no be as smooh as he moion of he car on he air rack, hence, he graphs will have more dips and peaks han before. Use he cardboard as a reflecor in place of he flag on he car. Posiion vs. ime 1. Saring a he sensor, back slowly and seadily away. Sar he compuer by double clicking he Sar buon, when he person is abou.5 m from he sensor. Afer backing abou 3 m away, sop, and hen walk slowly and seadily oward he sensor. Click he STOP buon when he person is abou.5 m from he Sensor. Do no prin your graph, bu insead skech he observed graph in your lab noebook, smoohing ou he peaks and dips. Unis and scales are no required for he aes of your skech. 2. Repea he above ecep walk medium fas and seadily. (The compuer will auomaically plo a new graph.) Skech he vs. graph. Quesion 5. Eplain how he graphs indicae posiive and negaive velociies. How do hey show slow or fas speeds? 3. Briefly describe how you would walk o produce he graph on he righ. 4. Now walk o ry o reproduce he graph. Do he eperimen a few imes, if necessary, o obain a good reproducion. Skech he compuer generaed graph in your noebook. Commen, i.e., do he graphs agree? If no why do hey disagree? (m) (s) Velociy vs. ime Predicion 1. Wha would he v vs. graph would look like if you walked slowly and seadily oward he sensor for 4 seconds a.5 m/s, sopped for 2 s and hen walked away medium fas and seadily a 1 m/s. Make a skech wih unis and labeled ais. 1. Record he walk described above and skech he observed velociy vs. ime graph in your noebook. Does your graph agree wih your predicion? 19

6 2. Describe in words how you would walk o v(m/s) +1 produce he v vs. graph on he righ (s) 3. Now do he walk and skech he observed graph. Do he wo graphs agree? 2