Conservation of Momentum. The purpose of this experiment is to verify the conservation of momentum in two dimensions.

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Mervyn Melton
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1 Conseraion of Moenu Purose The urose of his exerien is o erify he conseraion of oenu in wo diensions. Inroducion and Theory The oenu of a body ( ) is defined as he roduc of is ass () and elociy ( ): When wo objecs collide, if he exernal forces are negligible relaie o he inernal forces, he oenu of he syse is consered before and he collision, or syse, We will le a shere srike a shere, find he oenu of he 2-shere syse before and he collision, and coare he wo oenus o erify he conseraion. Unlike oher labs, we are going o analyze he daa grahically. Aaraus Draw a labelled diagra as Figure 1 and lis all oher equien you will use, along wih any idenifying nubers. (No need o draw Figure 2 on your reor.) shere shere Ra # _ suoring screw Side View, noe ha he wo sheres are a he sae heigh Poin A y Poin B Figure 1 To View Figure Conseraion of Moenu - 1 Saed: Ocober 17, 2018

2 Daa and Analysis Measure and record he asses of he sheres, and wih a 4-bea balance. Seu he aaraus as in Figure 1 and lace a shee of newsrin on he floor beneah he ra. Do soe rial runs by releasing he shere fro he nail osiion and hae i collide off-cenred wih he shere a he boo of he ra (see Figure 2). Then reoe he shere and le he shere roll down alone. Adjus he orienaion of he suoring screw and he osiion of he aer so ha (1) he shere will hi he shere, bu no he suoring screw; (2) he saring osiions of boh sheres fall on he big aer; (3) he collision, boh he shere and he shere land on he big aer; (4) wihou he collision, he shere lands on he big aer. Also check ha he wo sheres are a he sae heigh when colliding. (The boo of he rack is a he sae heigh as he o of he suoring screw.) If no, consul he insrucor. You are no suosed o adjus he heigh of he suoring screw yourself. Once you achiee he condiions aboe, kee he screw and he aer in osiion and do no oe he. You ay secure he osiion of he big aer wih asses fro he ass box. Now, creae 5 oins on he big aer (Figure 3): he saring osiions of boh sheres (oins A and C), he landing osiions of boh sheres hey collide (oins D and E), and he landing osiion of he shere wihou he collision (oin B). Use a lub bob o ark oins A and C. Poins B, D and E are arked by coering he big aer wih carbon aers, and allowing he sheres o land on he carbon aers. To ge an idea of uncerainy, ark oin B (landing of he shere alone) a few ies. Afer finishing he daa aking, your big aer should look like Figure 3, where oin B is a grou of oins. Poin D Poin B Poin E Poin A Seel ball saring osiion Poin B Seel ball landing so wihou collision Poin C Glass ball saring osiion Poin D Seel ball landing so wih collision Poin C Poin A Figure 3 Poin E Glass ball landing so wih collision 1125 Conseraion of Moenu - 2 Saed: Ocober 17, 2018

3 Now you can reoe he big aer fro he floor and analyse i. Our goal o find ou he oenu of he syse before and he collision, which are he ecor su of he oenu of each shere:,before,before and syse,,, There are wo ways o add ecors: The firs is adding by coonens, he second is adding grahically using he ail-o-head ehod. We will use he second ehod oday, so all quaniies are ecors on he big aer. >>Before he collision The shere is saionary, so all he oenu coes fro he shere: Vecor AB >>Afer he collision is associaed wih he syse oenu before he collision (wih a coefficien AB ). Boh sheres are oing and hae heir own oenu:, AD, and, The syse oenu is he su of he wo: syse, AD Le s exaine hese wo ecors: he ie is he sae for boh sheres, and i is he sae as he oenu before he collision. (Think of he reason yourself). Howeer, he wo asses are clearly differen, so he ecors AD and do no reflec he relaie oenus: The ecor is long on he aer, bu ha shows a big elociy insead of a big oenu. We need o scale down his ecor by he ass raio so ha i reflecs he oenu. To achiee ha, we creae a new ecor lengh of in c, calculae he lengh : On your big aer, easure and record he, and hen locae oin E on he aer. In ers of his new ecor, he syse oenu he collision is: syse, AD AD AD ' ( AD ') 1125 Conseraion of Moenu - 3 Saed: Ocober 17, 2018

4 Nex se is o add he ecors AD and riangle ehod ). To do so, oe he ecor oin say oin F. Vecor AF = AD DF AD. syse, ( AD ' ) So, ecor AF on he aer by he ail-o-head ehod (also called he so ha is ail is a oin D and is head lands a a is associaed wih he syse oenu he collision (wih he sae coefficien as he syse oenu before he collision). Once you locae oin F, you hae on he big aer he oenu of he syse boh before and he collision, so ha is all for he daa analysis! Adding ecors grahically is no hard, bu you us be careful when oing ecor o DF : boh he agniude and he direcion hae o say unchanged! Using a eer sick and a righ riangle, you can oe a ecor wihou losing is direcion, bu you should double check ha for a arallelogra. >>Wriing reor ' FD Since he daa analysis is osly done on he big aer, oday s lab reor has a slighly differen srucure. Cobine Daa, Calculaions and Uncerainy Analysis ino one Daa and Analysis secion. In his secion, firs record he asses of boh sheres (reeber he uncerainy). Then exlain in your own words how o find he oenu of he syse before and he collision. Draw a rough skech of he big aer o hel your exlanaion. Make sure you exlain how you ge he locaions of all oins, esecially for oins E and F. Conclusions Firs, sae once ore which wo ecors reresen he oenu of he syse before and he collision. Then, o coare he wo ecors, sae he relaie osiion of oin F and he uncerainy circle of B. The ideal siuaion is ha oin F falls inside he circle of B, which eans wo ecors AF and AB are non-disinguishable. Howeer, if oin F falls jus ouside he circle B, you ay argue ha oin F hae a siilar aoun of uncerainy oin B, and draw a circle of a siilar size around F. If he wo circles oerla, you can say ha he wo ecors agree. Finally, sae wheher he conseraion of oenu is erified by your exerien. Discussions Did you ignore any uncerainies in your analysis? Are here oher hysical facors ha could hae affeced your resuls? Do you hink hey are significan? AF 1125 Conseraion of Moenu - 4 Saed: Ocober 17, 2018

5 Checklis For he big aer: Measureen of he lengh ; Calculaions of he lengh Poins A B C D E E and F; ; A descriie ile, your desk nuber and boh arner s naes. For he Daa and Analysis on your reor: The asses of boh sheres, ogeher wih he uncerainy; A rough skech of he aer, wih all oins arked and exlained? Don forge o exlain how you locae oin E and F. Exlanaions of how you ge he oenu of he syse boh before and he collision. You ay wan o se u a 3x2 able o lis 6 oenu ecors. (of he, of he, of he syse; before collision, collision.) 1125 Conseraion of Moenu - 5 Saed: Ocober 17, 2018

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3 A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew: