THE PHYSICS 23 LAB BOOK 23 Lab 03: Conservation of Linear Momentum

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1 6/4/03 23lab3.cd THE PHYSICS 23 LAB BOOK 23 Lab 03: Conservaton of Lnear Moentu SS2003 ds Nae: Lab Instructor: Objectve:.To easure the oentu before and after collsons between artrack glders. 2.To calculate the ntal and fnal oentu for the syste of colldng glders. 3. To copare the theoretcal value for fnal veloctes for collsons between objects of ass M and M2. 4. To assess the elastc nature of the collson as deterned fro the analyss of the echancal energy of the projectle glder before and after the collson. MD2 Sprng MD M2 M Key Words: Moentu Change of Moentu elastc collson nelastc collson 9:06 AM

2 6/4/03 23lab3.cd Readng: :???????? Introducton: The su of externally appled forces s equal to the te rate of change of the lnear oentu of an object. d F = P d t Ths s the general stateent of Newton's Second Law. The (vector) change n lnear oentu (the pulse) can be expressed as the ntegral over te of the external (vector) te dependent force. Ths s the Ipulse Theore. In the absence of net external force on the syste, all coponents of lnear oentu are conserved. Lnear oentu s approxately conserved n these collsons along a horzontal ar track. The two glders observed n ths experent collde on a (nearly) frctonless, (nearly) horzontal artrack resultng n no (apprecable, or sensble) external force n the drecton of oton. The oentu along the track s expected to be (nearly) conserved n accord wth the prncple of Conservaton of Lnear Moentu. Recall that lnear oentu s conserved for each drecton along whch the net force s zero. The target glder s at rest before the collson. The projectle glder s reproducbly launched fro dentcal copressons of a soft elastc sprng. The collson s ade nearly elastc by the placeent of peranent agnets or elastc bupers at the ends of the glders. The collson s separately ade totally nelastc through the use of stcky wax. The observed fnal oentu and knetc energy of the projectle and target are copared wth the theoretcal values for each collson. Apparatus: The apparatus provded for ths experent conssts of the followng: ) Horzontal ar track wth two glders of varable ass, bupers and wax. 2) Two Moton Sensors, coputer, and software (Scence Workshop: 23lab3.sws) 9:06 AM 2

3 6/4/03 23lab3.cd Procedure: Please copose paragraphs detalng the procedures lsted below, along wth any I have left out. Recall that you can nsert lnes usng CTRL-F9, delete lnes usng CTRL-F0. ds Moton Detector Calbraton: Move X c, read screen dsplaceent fro both Moton Sensors, ultply veloctes easured by Moton Sensor by relevant fxt factor R. Generate a square wave wth three tops and three bottos by ovng the glder between known postons. Fnd average values of three peaks and three bottos. Calbrate both Moton Detectors, Placeent of M2 wth respect to the ond oton detector: Such that collson occurs at least 30 c fro ond detector to allow deternaton of fnal velocty of M2. Use earlest possble velocty value to nze effects of frcton. Copresson of sprng and release to reproducbly launch M: As per Work Energy lab. Fndng the Intal Velocty of launched glder: Slope of x(t) for M Fndng the Fnal Velocty of launched glder: Slope of x(t) for M after collson. Fnal velocty of target glder: Slope of x(t) for M2 after collson. Apply calbraton factors R and R2 to velocty easured for M, and for M2: Why so? Wll the calbraton factor affect the concluson concernng conservaton of oentu? How about conservaton of energy? Fndng P for the syste: Should be zero. Is oentu conserved? Check sgns! Dscuss analyss procedure.. Fndng E for the syste: Calculate ntal and fnal knetc energes and take the dfference. Be sure to apply the calbraton factors R and R2 correctly. Data: Glder Masses: Projectle glder Two Masses M := Epty g Four Masses 9:06 AM 3

4 6/4/03 23lab3.cd Target glder := g := g Moton Detector Calbraton Factors: k := Move glder by XX c near Moton Detector to record calbraton data. (Or other ethod of your choce.) Near := Far := k k XX := c XX R = ean( Far) ean( Near) Near2 := Far2 := k k XX2 := c R2 = XX2 ean( Far2) ean( Near2) Elastc Collson Data: Values of the ntal and fnal velocty coponents recorded for the projectle glder for three launches each under the followng launch condtons wth the target glder ntally at rest and the bupers n place to provde elastc collsons: Observaton Index: Intal Velocty: := Fnal Velocty: VeI := VeF := V2eF := M2 := M > : =0,,2 M < : = 3,4,5 9:06 AM 4

5 6/4/03 23lab3.cd Inelastc Collson Data: Values are to be recorded for the ntal and fnal velocty coponents for the projectle glder for three launches each under the followng launch condtons wth the target glder ntally at rest and the needle/wax n place to provde nelastc collsons: Observaton Index: := Intal Velocty: Fnal Velocty: VI := VF := V2F := M2 := M > : =0,,2 M < : = 3,4,5 9:06 AM 5

6 6/4/03 23lab3.cd Analyss: Moentu: Experental Values of Moentu: Soe of these veloctes need to be ultpled by R! Elastc Inelastc Intal Moentu: PIe := PI := Fnal Moentu: PFe := PF := Theoretcal (Elastc Collson) Values for Fnal Veloctes wth zero ntal velocty for the target glder and VI for the projectle glder: M M2 V f = V M + M2 2 M V2 f = V M + M2 (0-8) (0-9) You ust forat the correct equatons here. Reeber that x[ s the keystroke sequence to put the nteger ndex on the eleents of the vector x. For the elastc collsons: Fnal theoretcal velocty of the projectle: M M2 VeFT := VeI M + M2 Fnal theoretcal velocty of the target: V2eFT := 2 M VeI M + M2 For the nelastc collsons: Fnal theoretcal velocty of the cobned projectle and target: VFT := M VI M + M2 9:06 AM 6

7 6/4/03 23lab3.cd Coparson of the predcted (T) fnal veloctes wth the observed fnal veloctes: Elastc collsons: VFe := ( ) 00 V2Fe := ( ) 00 Inelastc collsons: V2F := ( ) 00 Percent change n fnal oentu wth respect to ntal oentu. Energy Conservaton: Elastc collsons: EeI := 2 M ( )2 EeF := 2 M ( )2 + 2 M2 ( ) 2 Inelastc collsons: EI := 2 M ( )2 EF := 2 ( ) ( )2 9:06 AM 7

8 6/4/03 23lab3.cd Percent change n fnal energy wth respect to ntal energy. Concluson: You are to wrte your own concluson to go wth your objectves, procedures, and analyses. Be sure to address whether your outcoe confrs the conservaton of oentu for both elastc and nelastc collsons, wthn experental uncertanty. If the data does not show conservaton of oentu for the supposed elastc collson, what can be expected fro a calculaton of the conservaton of energy? I a eager to assess the developent of your skll wth respect to an acceptble style of laboratory work and reportng. ds The general for of Physcs Lab reports s: ) the Objectve: What s to be done 2) the Key Words: What vocabulary words are needed or encountered 3) the Readng: What ateral s prerequste or helpful 4) the Introducton: What s known of ths experent (see Readng) 5) the Procedure: What was constant, what vared, what easured 6) the Apparatus: What equpent was used 7) the Data: What are the knowns, the data sets (flenaes) to analyze 8) the Analyss: What are the values of the unknowns, or how well was the objectve et? 9) the Concluson: a) Restate the Objectve b) Rend the reader of the Procedure used c) Redee the Objectve: The theory fts the data. 9:06 AM 8