Conservation of Linear Momentum PHYS 244

Transcription

1 Conseraton o Lnear Moentu PHYS 44 Ths laboratory wll be perored n the dscoery orat. Ths handout s proded as a gude to the equpent and possble easureents but students are encouraged to deelop ther own technques or explorng the phenoena and presentng results. Introducton In ths lab, you wll be obserng the conseraton o oentu under three derent condtons. In Part I, you wll obsere the elastc collson o two dynacs carts wth agnets that repel one another. In Part II, you wll obsere the perectly nelastc collson o two dynacs carts wth Velcro ends that attach on contact. In Part III, you wll place two carts together and obsere conseraton o oentu as a sprng propels the two n opposte drectons ro rest. Materals All Parts: Dynacs track, Data Studo, Moton Sensor, Excel Part I: two dynacs carts wth agnet ends Part II: two dynacs carts wth elcro ends Part III: one dynacs cart wth sprng-loaded plunger Reerence Gancol, Physcs 6th Edton: Chapter 7, sectons:,,4,5,6 Theory The conseraton o lnear oentu (p = ) s an portant concept n physcs. In a closed syste, wheneer oentu s consered the ntal and nal total oentu are equal. By a "closed syste" we ean that there are no outsde orces actng on the syste. For ths lab, we wll assue that there are no sgncant outsde orces--such as rcton--present durng the collsons. Ths wll not lterally be the case but the collson s short n duraton, t s reasonable to ake ths assupton because the rcton s sall and the duraton oer whch t acts s short. Thereore, p = p. We wll exane oton o two carts n only one denson so the ntal and nal oentu equatons are: Intal: p = + Fnal: And nally, conseraton o oentu p = + p = p ges = + + ()

2 Part I: An elastc collson s one n whch knetc energy s consered, oentu: ( ) = + and = + ( ) = as well as Fgure I there are no external orces actng on the objects n a collson (such as rcton) the oentu s consered, but the collson s not necessarly perectly elastc. Knetc energy ust also be consered n order to dene the collson as elastc. Knetc energy s oten dsspated through bratons o each object upon collson. For ths reason, we use slar poles o agnets (whch repel one another) to preent physcal contact between the two carts durng the elastc collson. Part II: Collsons where < are reerred to as nelastc collsons and the energy dsspated s Δ =. A collson where the two objects stck together s reerred to as a perectly nelastc collson because the axu possble energy s dsspated (typcally n the or o heat). Moentu, howeer, s stll consered. You wll obsere ths n the case o two carts whch becoe attached upon collson by the elcro abrc on ther ends. Part III: You wll also study conseraton o oentu or two carts pushng away ro each other through the orce exerted by a coled sprng launcher on one o the carts. Because the syste s ntally at rest and oentu s consered, the nal oentu o each o the two carts ust be equal n agntude and opposte n drecton. The resultng total oentu o the syste s equal to zero, the ntal total oentu. We hae = and thus =. ()

3 The total energy o the syste s consered but knetc energy s not because the total energy stored n the two cart syste begns as elastc potental energy n the coled sprng. Ater the ntal pulse when the sprng s released, the energy s shared by the two carts n the or o knetc energy. The knetc energy s dstrbuted between the two carts such that oentu s consered. They wll NOT hae the sae knetc energes unless the asses are equal. Usng the aboe equaton and the equaton or knetc energy, = = = (3). We nd = (4) Procedure All three experents wll be conducted usng the dynacs track wth a oton sensor at each end. Steps -5 o Part I apply to all three parts o the lab. Part I: Elastc collsons. Attach the two oton sensors to the Data Studo nterace. Double-clck on each oton sensor con and set the trgger rate to 5 Hz. Set the swtch on each oton sensor to the shortrange settng.. The gure below shows typcal elocty s. te data or a collson where s ntally at rest. Snce the oton sensor or s on the opposte end o the track and orented the opposte drecton, you wll need to reerse the sgn o n order to get the approprate elocty relate to the syste. (In ths graph, both alues are recorded as negate and one should be ade poste.) Ths can be done n Data Studo but t s easer to reerse the sgn anually by ultplyng results by - when you record the nto Excel.

4 Fgure. Velocty o the two carts easured throughout the collson. The sgn o the elocty o Cart s reersed. Note: snce there s actually soe rcton actng on the carts (as shown by the slght downward slope o the otherwse horzontal lnes), t s portant to deterne the elocty ro the graph edately beore and ater the collson. (Ths way, the te oer whch rcton has acted s nal and thereore ts eect on the conseraton o oentu wll be nal.) 3. Orent the dynacs carts wth the agnets toward each other. Snce the agnets are strong you should keep your watch and any loppy dsks away ro the. 4. Create a table n Excel lke the one below or your data on elastc collsons. In all cases s the ncdent cart and s statonary or ong slowly you wsh. (I you choose to hae t ong slowly, ake sure that you record ts ntal elocty under. Reeber that the sgn o the elocty or has to be reersed. M C M C 0 M C +0.5 kg 0 M C M C +.0kg 0 M C +0.5 kg M C 0 M C +.0 kg M C 0 P P % ΔP Δ % Δ 5. Measure the ass o the cart and record t nto the table. The asses labeled as +0.5 kg are shorthand or you to add 0.5 kg to the cart and put the total ass o the cart plus 0.5 kg n the spreadsheet cell. 6. Run the trals lsted n the table and graph the usng DataStudo. (Press Start, accelerate the carts towards each other, record the collson, let the separate and press Stop.) Note: the agnets produce a collson that s approxately elastc when the carts are repelled solely by the agnetc repulse orce. Thereore, your results wll be ost accurate you aod pushng the carts so hard that they physcally ht each other.

5 7. Fnd the alues or the ntal and nal eloctes o both carts and record the n your Excel table. Use those alues to calculate the alues n the rest o the table. 8. Estate the uncertanty n the ntal and nal oentu. 9. Deterne oentu s consered. I the ntal and nal alues o oentu are not equal, exane the change n oentu as a percent o the agntude o the aerage ΔP oentu based on the ntal and nal alues calculated. ΔP = P P ; % ΔP = 00 p 0. For each tral, use the alue o Δ you calculated to deterne the collson s elastc. I Δ s not close to 0, look at ts agntude as a percentage o the agntude o the aerage Δ knetc energy based on the ntal and nal alues calculated. ( % Δ = 00 ) Part II: Perectly Inelastc Collsons. Orent the two carts wth ther elcro ends are towards each other so that the carts wll stck together n a collson.. Repeat the procedure ro Part I usng trals, and 4 ro the table. Add the data ro Part II to the table below the data ro Part I. Make t clear whch data belongs to whch experent. Dscuss the results. 3. Is oentu consered? Look at the percent change n the oentu not. 4. Is Δ larger than or the nelastc collsons o Part I? What s the percent change? Part III: Conseraton o Moentu or Two Carts Pushng Away ro Each Other. Place the two carts aganst each other wth the plunger o the dynacs cart copletely retracted and latched n ts axu poston.. Press Start n Data Studo and then gently tap the plunger release button on the top o the cart so that the carts push each other apart. 3. Press Stop ater the carts hae reached the end o the track. 4. Record the nal elocty o each o the carts and coplete the rst row o the table below. Snce both the carts are ntally at rest, only nal elocty alues are ncluded n the table. P P M C M C M C M C +0.5 kg M C M C +.0 kg

6 5. Repeat the process or each o the derent asses shown n the table aboe. Dscuss the results. 6. Is oentu consered? 7. Is knetc energy shared accordng to the rato o the asses as predcted by the theory? (See Equaton (4)). For your Lab Report Include saple calculatons o the ntal and nal oenta ro Part I, tral. Estate the uncertanty or the ass and elocty easureents and nclude these n your calculaton. Copare your results wth uncertantes to see oentu was consered.