Physics 7 Consevation of Momentum Intoduction Collisions occu all aound us and on many size scales. We obseve them in ou eveyday wold as ca accidents, battes hitting a baseball out of the ballpak, aindops pelting the hood of you ca duing a downpou, and butteflies landing gently on flowe petals. Collision expeiments at the atomic and sub-atomic levels have also pemitted scientists to pobe the stuctue of the atom and nucleus. Backgound Collisions ae simply inteactions of two o moe objects. The inteaction may be chaacteized by objects coming into diect contact with one anothe, like two billiad balls colliding in a pool game, o they may not eve physically touch, as with Eath-moon inteactions that aise fom thei gavitational attaction. In both cases, foces ae exeted on the objects duing the inteaction, and, as a esult, the motion of the objects is alteed. Newton s nd law expessed in the fom: F = m d x dt = m a descibes how the motion of an object changes when a foce is applied to it. This specific fomulation of the nd law assumes that the mass of the object is constant. Newton s nd law can be witten moe geneally as: F = d p dt whee p is a vecto quantity called the linea momentum, which is equal to the poduct of mass and velocity. Fo the special case of constant mass, this educes to the familia F = ma. F = d p dt = d ( mv ) = m d v dt dt = m a In the geneal fom, we can intepet the nd law in a new way - foces exeted on an object ove some time inteval cause changes in the momentum of the object.
Physics 7 Let s conside an example whee two billiad balls collide (Figue ). Duing the bief time inteval when the occus, Ball exets a foce on Ball, and Ball exets a foce on Ball. These two foces ae an action-eaction pai. Ball pushes on Ball just as much as Ball pushes on Ball. Newton s 3d law tells us that these foces ae equal in magnitude but opposite in diection F + F = F + (" F ) = 0 Figue : Foces at wok duing a Re-witing the foces in tems of changes in momentum, we find that dp dt + d dt p = d dt ( p + p ) = 0 If we teat the two balls as a system, the total momentum is constant. This is tue so long as the system is isolated. By isolated we mean that no net foces ae applied to any object in the system by objects that ae not a pat of the system. Foces exeted by objects outside a system ae efeed to as extenal foces while foces exeted on objects in a system by othe objects in the system ae called intenal foces. If we wee taking into consideation the gavitational pull that the Eath exets on both billiad balls in Figue, the gavitational foce would be an extenal because the Eath was not included in the definition of ou system. The foces illustated in Figue ae intenal foces, because they wee geneated by objects (i.e., the billiad balls) that belong to ou system unde study. The idea that the total momentum of an isolated system is constant is one of the most fundamental laws of physics known as consevation of momentum. Like consevation of enegy, no isolated systems have been found that violate consevation of momentum. Consevation of momentum is a vey poweful tool in analyzing s. If the objects paticipating in the expeience no net extenal foces, the total momentum of the system is the same and the. Fo ou colliding billiad balls in Figue, momentum consevation equies the following:
Physics 7 Total Momentum Befoe Collision = Total Momentum Afte Collision m { v + m v 3 = m { v " + m v 3 " Ball Befoe Ball Befoe Ball Afte Ball Afte whee the subscipt efes to popeties of Ball, the subscipt efes to popeties of Ball, the unpimed velocities coespond to values the takes place and the pimed velocities to those the occus. Caeful attention must be paid to both the magnitude and diection of each velocity in momentum consevation because, like velocity, momentum is also a vecto quantity. Collisions can be categoized based on the degee to which kinetic enegy is conseved. If all the kinetic enegy pesent pio to the goes into the kinetic enegy of the objects pesent the, kinetic enegy is conseved, and the is deemed elastic. On the othe hand, if kinetic enegy is lost duing the (it may be conveted to heat and dissipated, fo example), the is inelastic. A pefectly inelastic is one in which colliding objects move togethe as a single entity the. The expeiments pefomed in this lab ae designed to investigate both momentum and enegy consevation. You will devise a seies of s, both elastic and inelastic, fo two cats olling on a tack. Fom measuements of thei masses, initial velocities, and final velocities, you will compute the momentum and kinetic enegy of the two cat system both and the s to assess whethe momentum and kinetic enegy ae conseved in you expeiments. Momentum, Enegy and Collisions The of two cats on a tack can be descibed in tems of momentum consevation and, in some cases, enegy consevation. If thee is no net extenal foce expeienced by the system of two cats, then we expect the total momentum of the system to be conseved. This is tue egadless of the foce acting between the cats. In contast, enegy is only conseved when cetain types of foces ae exeted between the cats. Collisions ae classified as elastic (kinetic enegy is conseved), inelastic (kinetic enegy is lost) o completely inelastic (the objects stick togethe ). Sometimes s ae descibed as supe-elastic, if kinetic enegy is gained. In this expeiment you can obseve most of these types of s and test fo the consevation of momentum and enegy in each case. OBJECTIVES Obseve s between two cats, testing fo the consevation of momentum. Measue enegy changes duing diffeent types of s. Classify s as elastic, inelastic, o completely inelastic. 3
Physics 7 MATERIALS dynamics cat tack Venie compute inteface Logge Po two Motion Detectos two low-fiction dynamics cats with magnetic and Velco bumpes - 50 gam weights PRELIMINARY QUESTIONS. Conside a head-on between two billiad balls. One is initially at est and the othe moves towad it. Sketch a position vs. time gaph fo each ball, stating with time the and ending a shot time wad.. As you have dawn the gaph, is momentum conseved in this? Is kinetic enegy conseved? PROCEDURE. Measue the masses of you cats and ecod them in you data table. Label the cats as cat and cat.. Set up the tack so that it is hoizontal. Test this by eleasing a cat on the tack fom est. The cat should not move. 3. Pactice ceating gentle s by placing cat at est in the middle of the tack, and elease cat so it olls towad the fist cat, magnetic bumpe towad magnetic bumpe. The cats should smoothly epel one anothe without physically touching. 4. Place a Motion Detecto at each end of the tack, allowing fo the 0.5 m minimum distance between detecto and cat. Connect the Motion Detectos to the DIG/SONIC and DIG/SONIC channels of the inteface. If the Motion Detectos have switches, set them to Tack. 5. Open the file 8 Momentum Enegy Coll fom the Physics with Venie folde. 6. Click Collect to begin taking data. Repeat the you pacticed above and use the position gaphs to veify that the Motion Detectos can tack each cat popely thoughout the entie ange of motion. You may need to adjust the position of one o both of the Motion Detectos. 7. Place the two cats at est in the middle of the tack, with thei Velco bumpes towad one anothe and in contact. Keep you hands clea of the cats and click ZERO. Select both sensos and click OK. This pocedue will establish the same coodinate system fo both Motion Detectos. Veify that the zeoing was successful by clicking Collect, and allowing the still-linked cats to oll slowly acoss the tack. The gaphs fo each Motion Detecto should be nealy the same. If not, epeat the zeoing pocess. 4
Physics 7 Pat I: Magnetic Bumpes 8. Reposition the cats so the magnetic bumpes ae facing one anothe. Click Collect to begin taking data and epeat the you pacticed in Step 3. Make sue you keep you hands out of the way of the Motion Detectos you push the cat. 9. Fom the velocity gaphs you can detemine an aveage velocity and the fo each cat. To measue the aveage velocity duing a time inteval, dag the cuso acoss the inteval. Click the Statistics button to ead the aveage value. Measue the aveage velocity fo each cat, and, and ente the fou values in the data table. Delete the statistics box. 0. Repeat Step 9 as a second un with the magnetic bumpes, ecoding the velocities in the data table. Pat II: Velco Bumpes. Change the by tuning the cats so the Velco bumpes face one anothe. The cats should stick togethe. Pactice making the new, again stating with cat at est.. Click Collect to begin taking data and epeat the new. Using the pocedue in Step 9, measue and ecod the cat velocities in you data table. 3. Repeat the pevious step as a second un with the Velco bumpes. Pat III: Velco to Magnetic Bumpes 4. Face the Velco bumpe on one cat to the magnetic bumpe on the othe. The cats will not stick, but they will not smoothly bounce apat eithe. Pactice this, again stating with cat at est. 5. Click Collect to begin data collection and epeat the new. Using the pocedue in Step 9, measue and ecod the cat velocities in you data table. 6. Repeat the pevious step as a second un with the Velco to magnetic bumpes. 5
Physics 7 Momentum, Enegy and Collisions DATA TABLE Mass of cat (kg) Mass of cat (kg) Run numbe 3 4 5 6 Velocity of cat (m/s) Velocity of cat (m/s) Velocity of cat (m/s) Velocity of cat (m/s) Run numbe 3 4 5 6 Momentum of cat Momentum of cat Momentum of cat Momentum of cat Total momentum Total momentum Ratio of total momentum / Run numbe KE of cat KE of cat KE of cat KE of cat Total KE Total KE Ratio of total KE / 3 4 5 6 6
Physics 7 ANALYSIS. Detemine the momentum (mv) of each cat the, the, and the total momentum and the. Calculate the atio of the total momentum the to the total momentum the. Ente the values in you data table.. Detemine the kinetic enegy (½ mv ) fo each cat and the. Calculate the atio of the total kinetic enegy the to the total kinetic enegy the. Ente the values in you data table. 3. If the total momentum fo a system is the same and the, we say that momentum is conseved. If momentum wee conseved, what would be the atio of the total momentum the to the total momentum the? 4. If the total kinetic enegy fo a system is the same and the, we say that kinetic enegy is conseved. If kinetic wee conseved, what would be the atio of the total kinetic enegy the to the total kinetic enegy the? 5. Inspect the momentum atios. Even if momentum is conseved fo a given, the measued values may not be exactly the same and due to measuement uncetainty. The atio should be close to one, howeve. Is momentum conseved? 6. Repeat the peceding question fo the case of kinetic enegy. Is kinetic enegy conseved in the magnetic bumpe s? How about the Velco s? Is kinetic enegy consumed in the thid type of studies? Classify the thee types as elastic, inelastic, o completely inelastic. EXTENSIONS. Using a cat with a sping plunge, ceate a supe-elastic ; that is, a whee kinetic enegy inceases. The plunge sping should be compessed and locked the, but then eleased duing the. Measue momentum and the. Is momentum conseved in this case? Is enegy conseved?. Using the magnetic bumpes, conside othe combinations of cat mass by adding weight to one cat. Ae momentum o enegy conseved in these s? 3. Using the magnetic bumpes, conside othe combinations of initial velocities. Begin with having both cats moving towad one anothe initially. Ae momentum and enegy conseved in these s? 4. Pefom the momentum and enegy calculations fo the data tables using a speadsheet. 7
Concluding Questions When esponding to the questions/execises below, you esponses need to be complete and coheent. Full cedit will only be awaded fo coect answes that ae accompanied by an explanation and/o justification. Include enough of the question/execise in you esponse that it is clea to you teaching assistant to which poblem you ae esponding.. Could the linea momentum of a hummingbid be geate than that of a totoise? Explain you answe.. Conside a two cat on the tack simila to the ones you pefomed in this lab. Daw a fee body diagam fo each cat showing all the foces acting on each cat the instant when they collide. Identify which of these foces ae intenal and extenal to the two cat system. Explain why you can teat the two cats as an isolated system when extenal foces act on the system. 3. An astonaut is woking with some tools outside the spacecaft duing a mission. Due to a malfunction in his populsion equipment, he gets standed some distance fom the ship. How could the astonaut use the tools so that he could etun safely to the ship? Explain you easoning. 4. Two ice skates stand face to face, and then they push each othe away. If one skate weighs 75% of the othe, which skate has the geate speed? Explain you easoning.