Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion of how objecs move. Dynamics is he descripion of why objecs move. I is imporan o undersand how an objec moves before exploring why. Therefore, he firs labs in his course focus upon he sudy of kinemaics. In paricular, his sudy involves he relaionships beween he quaniies of posiion, disance, displacemen, speed, velociy, acceleraion, and ime. These relaionships are concepual, mahemaical, and graphical. Thorough undersanding of kinemaics requires knowledge of each of hese ypes of relaionships. Translaional moion is par of our everyday experiences. In addiion, i can also be a hrill. For example, much of he exciemen in riding a roller coaser arises from he high speeds and acceleraions experienced during he ride. The Seel Phanom a Kennywood Amusemen Park hp://www.kennywood.com/ Alhough moion ofen occurs in more han one dimension, i can be simplified by considering one dimension a a ime. Moion in one dimension is any moion ha occurs along a sraigh line. Noice ha one dimension has wo direcions. Therefore, posiive and negaive values of posiion, velociy, and acceleraion have paricular meaning. Several ypes of moion in one dimension occur commonly in a wide variey of physical circumsances: objecs a res, objecs in moion wih consan velociy, and objecs in moion wih an acceleraion ha is consan and parallel o he direcion of moion. Moion under he influence of graviy close o he earh's surface and moion under he influence of a consan force are he wo mos familiar examples of moion wih a consan acceleraion. Remember ha all moion is measured from a paricular origin or reference frame. Equaions and graphs are helpful when expressing relaionships beween moion quaniies. For example, when he acceleraion of an objec is consan, is velociy changes linearly wih ime: v v(0) v() = v(0) + a Eq. 1 v(0) is he velociy a =0 and a is he acceleraion. Noice ha he slope of he Velociy vs. Time graph (found by aking he derivaive) is he acceleraion. The area under he curve (found by aking he aniderivaive) represens he posiion of he objec. (Posiion can easily be used o deermine displacemen if he iniial posiion is known.) Noice, in his case, ha posiion changes quadraically wih ime:
x x () = x(0) + v(0) + 1 2 a 2 Eq. 2 x(0) x(0) is he posiion a ime =0. Therefore, if he Posiion vs. Time graph of an objec s moion is parabolic in shape, hen he objec mus be experiencing consan acceleraion.
Goals: Lab #2: Kinemaics in 1-Dimension Deermine he velociy of an objec from posiion and ime measuremens. Deermine he acceleraion of an objec from posiion and ime measuremens. Using Excel, creae graphs ha describe he moion of an objec. Draw relevan conclusions abou he moion of an objec based upon colleced daa. Equipmen Lis: 1.2 meer Air Track Dynamics Car Ulrasonic Moion Deecor Verical Sand and clamp Science Workshop Excel Angle Measuring Device NOTE: Open he emplae for Lab #1. Save his emplae as a Word documen before saring he lab. Always remember o save your emplae periodically hroughou he lab. Aciviy 1 : Uniform Velociy In his aciviy you will measure he moion of a car using an ulrasonic moion deecor. The daa colleced wih his deecor will be impored ino an Excel spreadshee for graphical analysis. 1. Configure he Science Workshop sofware in conjuncion wih he mo ion deecor o obain a able of posiion and ime daa for a car moving freely along he level rack. (Science Workshop can be found under he Sar Menu.) Before collecing daa, spend a few momens familiarizing yourself wih he feaures of Science Workshop. You may also view he uorial on configuring Science Workshop. 2. Record daa for a car moving freely along he rack. (Sar collecing daa before he car is pushed ino moion. I is imporan o be able o deermine which daa poins represen he desired moion. Undesired daa can be explained and/or ignored.) 3. Open an Excel spreadshee and impor he daa ha you colleced from he able in Science Workshop. You may wan o view he uorial on imporing daa if you are unfamiliar wih his procedure. 4. Use he funcion edior o generae wo addiional columns of values, he velociy of he car (beween wo adjacen ime values) and he corresponding median ime value. You may wan o view he uorial on wriing funcions ino Excel if you are unfamiliar wih his procedure. Use he following equaions: x V = ( n + 1) ( n + 1) x ( n) ( n) Eq. 3 = + 2 ( n + 1) ( n) Eq. 4 Your daa able should look somehing like his: Time (s) Posiion (m) Time (s) Velociy (m/s)
5. Use Excel o consruc a Posiion vs. Time graph and a Velociy vs. Time graph. Again, here is a uorial available if you have difficuly graphing daa in Excel. Copy he spreadshee and graphs ino he Templae. 6. Answer he following quesions relaed o he Posiion vs. Time graph: Wha ype of curve bes describes he Posiion vs. Time graph? Calculae he slope of he Posiion vs. Time graph using Excel. (Noe: Excel has a SLOPE funcion ha you can uilize.) Wha unis are associaed wih your slope? Wha does he slope represen on he laboraory seup ha you used o collec your daa? 7. Answer he following quesions relaed o he Velociy vs. Time graph: Wha ype of curve bes describes he Velociy vs. Time graph? Use your knowledge of he area of basic geomeric shapes o esimae he area beneah he curve. Wha are he unis associaed wih he area? Wha does he area represen on he laboraory seup ha you used o collec your daa? 8. Using your graphs, deermine he value of he acceleraion of he car. Explain how you arrived a your answer. Aciviy 2: Uniform Acceleraion Use he same procedure ha you employed above o analyze a moion ha is no a consan velociy. 1. Use he sand provided wih your apparaus o elevae one end of he rack o a paricular angle (provided o you by your TA). 2. Record he angle of your rack. 3. Use he Science Workshop sofware in conjuncion wih he moion deecor o obain posiion and ime daa in a able for a car released from REST a he elevaed end of he rack. (Place he moion deecor on he elevaed end of he rack so ha he car doesn run ino i.) 4. Impor he posiion and ime daa ino an Excel spreadshee. Use he funcion edior o generae wo addiional columns of values, he velociy of he car (beween wo adjacen ime values) and he corresponding median ime value. (Use equaions 3 and 4 as in Aciviy 1). 5. Use Excel o consruc a Posiion vs. Time graph and a Velociy vs. Time graph. Copy he spreadshee and graphs ino he Templae. 6. Answer he following quesions relaed o he Posiion vs. Time graph: Wha ype of curve bes describes he Posiion vs. Time graph? Wha happens o he slope of his graph as ime passes? Explain why his occurs. 7. Answer he following quesion relaed o he Velociy vs. Time graph: Wha ype of curve bes describes he Velociy vs. Time graph? Calculae he slope of he Velociy vs. Time graph using Excel. Include unis in your answer. (Noe: Excel has a SLOPE funcion ha you can uilize.)
Wha quaniy does he slope of he Velociy vs. Time graph represen? Use your knowledge of he area of basic geomeric shapes o esimae he area beneah he Velociy vs. Time graph (from he momen of release a res o he ime he car reaches he boom of he rack). Include unis in your answer. Wha does he area under he Velociy vs. Time graph represen? 8. Once he acceleraion of he objec has been deermined, pos he angle of he ramp and he car s corresponding acceleraion on he board. Copy he posed informaion from he oher lab groups for use in he Pos Lab.
Pos Lab #2: Kinemaics in 1-Dimension Name: Secion #: You have jus compleed a raher exensive lab in which you had he opporuniy o collec and analyze daa using various echniques. In his par of he lab, you are asked o exend your knowledge. Copy he acceleraion and corresponding ramp angles lised by each of he lab groups ino he able below. If more han one group used he same angle hen compue and use he average acceleraion value. Acceleraion (m/s 2 ) Angle (degrees) 9.8 90 o 1. Deermine a relaionship beween Acceleraion and he Angle of he Ramp Use Excel o creae a graph of Acceleraion vs. Ramp Angle. Wha kind of mahemaical relaionship does his graph sugges? If possible, sae your answer as a funcion. Use his relaionship o esimae he acceleraion ha should occur a an angle of 75 o. Clearly show how your deerminaion was made. Include any relevan graphs, daa ables, or oher informaion o suppor your deerminaion.