Lab - Collisions and Momentum - Newton s Third Law

Transcription

1 Lab 7 Collisions and Momentum-Newton s Third Law L7-1 Name Date Partners L07-1 Lab - Collisions and Momentum - LAB 7 - COLLISIONS AND MOMENTUM AND Newton s Third Law Name Date Partners NEWTON S THIRD LAW In any system of bodies which act on each or, action and reaction, estimated by momentum In any system gained of and bodies lost, which balance act on each each or or, according action and to reaction, laws of estimated by momentum gained and lost, balance each or according to laws equilibrium. Jean de la Rond D Alembert of equilibrium. OBJECTIVES Jean de la Rond D Alembert To understand definition of momentum and its vector nature as it applies to OBJECTIVES one-dimensional collisions. To develop concept of impulse to explain how forces act over time when an To object understand undergoes a definition collision. of momentum and its vector nature as it applies to onedimensional To study collisions. interaction forces between objects that undergo collisions. To develop examine concept relationship of impulse between to explain impulse how forces and momentum act over timexperimentally when an objectin undergoes both elastic a collision. (bouncy) and inelastic (sticky) collisions. To To study examine interaction consequences forces between of Newton s objects that third undergo law collisions. as applied to interaction forces between objects. To examine explore conservation relationshipof between momentum impulsein and one-dimensional momentum experimentally collisions. in both elastic (bouncy) and inelastic (sticky) collisions. OVERVIEW To examine consequences of Newton s third law as applied to interaction forces between In this lab we objects. explore forces of interaction between two objects and study changes in motion To explore that result conservation from se of momentum interactions. one-dimensional We are especially collisions. interested in studying collisions and explosions in which interactions take place in fractions of a second. Early investigators OVERVIEWspent a considerable amount of time trying to observe collisions and explosions, but y encountered difficulties. This is not surprising, since observation of In details this lab we of such explore phenomena forces of requires interaction between use of two instruments objects and study such as changes high-speed in motion that result from se interactions. We are especially interested in studying collisions and cameras that were not yet invented. explosions in which interactions take place in fractions of a second. Early investigators spent a However, considerable amount principles of time describing trying to observe outcomes collisions of collisions and explosions, were but well yunderstood encounteredby difficulties. late seventeenth This is not century surprising, when since several observation leading of European details of scientists, such phenomena including requires Isaac Newton, use of developed instruments such concepts as high-speed to describe cameras both that elastic were not collisions, yet invented. which objects bounce off each or, and inelastic collisions, in which objects stick toger.

2 L7-2 Lab 7 Collisions and Momentum-Newton s Third Law L07-2 However, principles describing outcomes Lab 7 of Collisions collisionsand were Momentum well understood Newton s bythird late Law seventeenth century when several leading European scientists, including Isaac Newton, developed concepts to describe both elastic collisions, in which objects bounce off each or, and We inelastic will begin collisions, our in study which of objects collisions stick by toger. exploring relationship between forces experienced by an object and its momentum change. It can be shown mamatically from We will Newton s begin our laws study and ofexperimentally collisions by exploring from our own relationship observations betweenthat forces change experi-ienced by anof object an object and itsis momentum equal to a change. quantity It can called be shown impulse. mamatically Impulse takes frominto Newton s account momentum both laws and applied experimentally force at from each our instant own observations in time and that time change interval momentum over which of an this object force is equal to a quantity called impulse. Impulse takes into account both applied force at each instant in time and time interval over which this force acts. The statement of equality between acts. The statement of equality between impulse and momentum change is known as impulse momentum orem. impulse and momentum change is known as impulse momentum orem. Since interactions like collisions and explosions never involve just one object, we turn Since interactions like collisions and explosions never involve just one object, we turn our attention to mutual forces of interaction between two or more objects. This will lead us to a very our attention to mutual forces of interaction between two or more objects. This will lead us to a very general law known as Newton s third law, which relates forces of general law known as Newton s third law, which relates forces of interaction exerted by two interaction objects on each exerted or. by This two will objects in turn on lead each us to or. one of This most will in important turn lead laws us of to interactions one of most between important objects, laws conservation of interactions of momentum between objects, law. conservation of momentum law. INVESTIGATION 1: MOMENTUM AND MOMENTUM CHANGE INVESTIGATION 1: Momentum and Momentum Change In this investigation we are going to develop concept of momentum to predict In this investigation we are going to develop concept of momentum to predict outcome outcome of collisions. But you don t officially know what momentum is because we of collisions. But you don t officially know what momentum is because we haven t defined it haven t defined it yet. We want to define momentum to help us describe collisions in yet. We want to define momentum to help us describe collisions in mamatical terms. mamatical terms. It s early Fall and you are driving along a two-lane highway in a rented moving van. It s full It s of early all of Fall your and possessions you are driving so along you and a two-lane loaded highway truck in weigh a rented 8,000 moving lb. van. You It s have full just of all of your possessions so you and loaded truck weigh 8,000 lb. You have just slowed down slowed down to 15 mph because you re in a school zone. It s a good thing you thought to to 15 mph because you re in a school zone. It s a good thing you thought to do that, because a do that, because a group of first graders are just starting to cross road. Just as you group of first graders are just starting to cross road. Just as you pass children you see a pass children you see a 2,000-lb sports car in or lane heading straight for 2,000-lb sports car in or lane heading straight for children at about 80 mph. children at about 80 mph. A desperate thought crosses your mind. You just have time to swing into or lane and A desperate thought crosses your mind. You just have time to swing into or lane speed up a bit before making a head-on collision with sports car. You want your truck and and speed sports up car a to bit crumple before into making a heap a head-on that sticks collision toger with and doesn t sports move. car. Can You you want save your truck children and or is this sports just car suicidal to crumple folly? into a heap that sticks toger and doesn t move. Can you save children or is this just suicidal folly? Prediction 1-1: How fast would you have to be going to completely stop sports car? Explain reasons for your prediction. University of of Virginia Physics Department PHYS 1429, Spring Modified from P. P. Laws, D. D. Sokoloff, R. R. Thornton

3 Lab 7 Collisions and Momentum-Newton s Third Law L7-3 To simulate this situation you can observe two carts of different mass set up to stick toger in trial collisions. You will need two low-friction carts with Velcro on one end four 1/2 kg masses to put on carts 2 m motion track level Activity 1-1: Can You Stop Car? 1. Verify that track is level. 2. Try some head-on collisions with carts of different mass to simulate event on a small scale. Don t collide m too hard - be sure that carts stick toger after collision. 3. Observe qualitatively what combinations of velocities cause two carts to be at rest after collision. Question 1-1: What happens when less massive cart is moving much faster than more massive cart? Much slower? Originally, Newton did not use concept of acceleration or velocity in his laws. Instead, he used term motion, which he defined as product of mass (m) and velocity (v). We now call that quantity momentum: p mv where symbol is used to designate defined as. NEWTON S FIRST TWO LAWS OF MOTION 1. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it. 2. The net force on an object can be calculated as product of its mass and its acceleration, where directions of force and of resulting acceleration are same. In or words: F net = ma = d p dt Now let s test your intuition about momentum and forces. You are sleeping in your sister s room while she is away at college. Your house is on fire and smoke is pouring into partially open

4 L7-4 Lab 7 Collisions and Momentum-Newton s Third Law bedroom door. To keep smoke from coming in, you must close door. The room is so messy that you cannot get to door. The only way to close door is to throw eir a blob of clay or a superball at door re isn t time to throw both. Prediction 1-2: Assuming that clay blob and superball have same mass, and that you throw m with same velocity, which would you throw to close door clay blob, which will stick to door, or superball, which will bounce back at almost same speed as it had before it collided with door? Give reasons for your choice using any notions you already have or any new concepts developed in physics, such as force, energy, momentum, or Newton s laws. If you think that re is no difference, justify your answer. It would be nice to be able to use Newton s formulation of second law of motion to find collision forces, but it is difficult to measure rate of change of momentum during a rapid collision without special instruments. However, measuring momenta of objects just before and just after a collision is usually not too difficult. This led scientists in seventeenth and eighteenth centuries to concentrate on overall changes in momentum that resulted from collisions. They n tried to relate changes in momentum to forces experienced by an object during a collision. In next activity you are going to explore mamatics of calculating momentum changes for two types of collisions elastic collision, where ball bounces off door, and inelastic collision, where ball sticks to door. Activity 1-2: Momentum Changes Momentum change is a vector given by p = p f p i where p i is initial momentum of object just before a collision and p f is its final momentum just after. [Remember, in one dimension, direction of a vector is indicated by its sign.] Prediction 1-3: Which object undergoes greater momentum change during collision with a door clay blob or superball? Explain your reasoning carefully. Just looking at maximum force exerted on ball does not tell whole story. You can see this from a simple experiment tossing raw eggs. We will do it as a thought experiment to avoid mess! Suppose somebody tosses you a raw egg and you catch it. [In physics jargon, one would say that egg and hand have undergone an inelastic collision.]

5 iment to avoid mess! Suppose somebody tosses you a raw egg and you catch it. ysics jargon, one would say that egg and hand have undergone an inelastic ion.] Lab 7 Collisions and Momentum-Newton s Third Law L7-5 tion 1-2: If you catch an egg of mass m that is heading toward hand at speed your v, hand what at speed magnitude v, what magnitude momentum momentum change change does it it go? [Hint: The undergo? egg is [Hint: at rest The after egg isyou at rest catch after you it.] catch it.] Question 1-2: If you catch an egg of mass m that is heading toward Question 1-3: Does total momentum change differ if you catch egg more slowly or is it same? tion 1-3: Does total momentum change differ if you catch g more slowly or is it same? In bringing an egg to rest, change in momentum is same wher you use a large force during a short time interval or a small force during a long time interval. [Of course, which one you choose makes a lot of difference in wher or not egg breaks!] L07-6 Lab 7 Collisions and Momentum Newton s Third Law A useful concept when analyzing collisions is called impulse. It combines applied force and time interval over which it acts. In one dimension, for a constant force F acting over a time A useful concept when analyzing collisions is called impulse. It combines applied force and time interval over which it acts. In one dimension, for a constant force F nging an egg to interval rest, t, aschange shown in in graph momentum below, is impulse same J is wher you use a large during a short time interval or a small force during a long time interval. [Of course, one you choose acting makes over a time lot interval of difference t, as shown in wher in graph or not below, egg impulse breaks!] J is J = F t (7.1) J = F t rsity of Virginia Physics Department 1429, Spring 2011 As you can see, a large force acting over a short time and a small force acting over a long time As you can can have see, a large same force impulse. acting over a short time and a small force acting over a long time can have same impulse. Note that F t is area of rectangle, that is, area under force vs. time curve. If Note that applied F t force is area is not of constant, rectangle, n that is, impulse area under can still force be calculated vs. time curve. as If area under applied force force is vs. not time constant, graph. n impulse can still be calculated as area under force vs. time graph. F In three dimensions we get: t

6 Note that F t is area of rectangle, that is, area under force vs. time curve. If L7-6 applied force is not constant, n Lab 7 Collisions impulse and can Momentum-Newton s still be calculated as Third Law area under force vs. time graph. F In three dimensions we get: In three dimensions we get: J =! F dt The Impulse-Momentum Theorem states J = that Fdt impulse is equal to change in momentum: The Impulse-momentum Theorem states that J = p impulse is equal to change in momentum: Lab 7 Collisions and Momentum Newton s Third J = Law p L07-7 Question 1-4: Suppose time you take to bring egg to a stop is t. Would you Question rar catch 1-4: egg Suppose in such a way time that you t take is small to bring or large? Explain. egg to a stop is t. Would you rar catch egg in such a way that t is small or large? Explain. t PHYS 1429, Spring 2011 On left boxer moves backwards during blow, which occurs during a relatively On left boxer moves backwards during blow, which occurs during a relatively long long time t, while on right boxer moves forward just as blow hits him. time t, while on right boxer moves forward just as blow hits him. Although t is Although t is shorter, force is greater on right. The greater forces on right shorter, force is greater on right. The greater forces on right side cause more damage side cause more damage to be done. to be done. INVESTIGATION 2: IMPULSE, MOMENTUM, AND COLLISIONS Let s first see qualitatively what an impulse curve might look like in a real collision in which forces change over time during collision. To explore this idea you will need! motion cart! 2 m motion track! dartboard target! rods, clamps, etc.! University force probe of Virginia Physics Department! Modified motion from detector P. Laws, D. Sokoloff, R. Thornton! level! spring and dart tips Activity 2-1: Observing Collision Forces That Change with Time

7 Lab 7 Collisions and Momentum-Newton s Third Law L7-7 INVESTIGATION 2: Impulse, Momentum, and Collisions Let s first see qualitatively what an impulse curve might look like in a real collision in which forces change over time during collision. To explore this idea you will need motion cart 2- m motion track dartboard target rods, clamps, etc. force probe motion detector level spring and dart tips Activity 2-1: Observing Collision Forces That Change with Time 1. Mount force probe on cart and screw in spring on end of force probe. 2. Use table clamps and or accessories to rigidly mount target to table so that spring on force probe will collide directly with target when cart is rolling down motion track. Ask your TA for help if this is not clear. 3. Gently start pushing cart about meter away from target, let cart coast and collide with target several times and observe what happens to spring. Note: Do not let spring bottom out. Question 2-1: If friction is negligible, what is net force exerted on cart just before it starts to collide?

8 Question L : When is magnitude Lab of 7 Collisions net force andon Momentum-Newton s cart maximum Third during Law collision? Question 2-2: When is magnitude of net force on cart maximum during collision? Question 2-3: Estimate roughly how long collision process takes? Half a second? Less Question time? 2-3: Several Estimate seconds? roughly how long collision process takes? Half a second? Less time? Several seconds? Prediction 2-1: 2-1: Draw aa rough rough sketch sketch below below of of shape of shape force of F w force spring F exerts w spring on cart as a function of time during collision. exerts on cart as a function of time during collision. F w During collision force is not constant. To measure impulse and compare it to During collision force is not constant. To measure impulse and compare it to change change in momentum in momentum of of cart, you cart, must you (1) must plot a force time (1) plot a force time graph and find graph area and under find it, area and under (2) measure it, and (2) velocity measure of cart velocity before and of after cart before collisionand withafter wall. collision Fortunately, with force probe, motion detector, and motion software will allow you to do this. PHYS The force 1429, probe Spring is2011 mounted on cart to measure force applied to cart. You will collide cart into target mounted near track. Activity 2-2: Examining Impulse-momentum Theorem in an Elastic Collision t In an elastic collision between a cart and fixed target, cart would recoil with same magnitude of momentum that it had before collision.

9 Lab 7 Collisions and Momentum-Newton s Third Law L Set up motion detector as shown. Be sure that ramp is level. 2. We will start with a heavy cart. Place two 1/2 kg masses on cart/force probe. Measure mass of cart, masses, and force probe combination. You may need to mass m separately and add masses. Total mass of cart: kg 3. Open experiment file called L Impulse and Momentum. This experiment has been set up to record force and motion data at 50 data points per second. Because positive direction is toward right in diagram above, software has been set up to record a push on force probe as a positive force, and velocity toward motion detector as positive. 4. Be sure that wire from force probe is out of way, so motion detector won t see it. 5. Practice pushing cart toward target and watching it bounce off. Find a way to push without putting your hand between motion detector and cart. 6. When you are ready, zero force probe and n start computer. As soon as you hear clicking of motion detector, give cart a push toward target, release it, and let it collide. Repeat until you get a good set of graphs. That is, a set in which motion detector saw relatively constant velocities of cart as it moved toward spring target and as it moved away, and that spring did not bottom out. We find that a maximum force of 8 N is about right so that spring does not bottom out. Question 2-4: Does shape of force time graph agree with your Prediction 2-1? In what way is it similar? In what way does it differ? 7. Use technique outlined in Example-4 of Appendix C to measure average velocity of cart as it approached target, and average velocity as it moved away from target. Don t forget to include a sign. Average velocity toward target: ± m/s Average velocity away from target: ± m/s Question 2-5: Calculate change in momentum of cart. Show your calculations including error of momentum change.

10 L7-10 Lab 7 Collisions and Momentum-Newton s Third Law p : ± kg m/s 8. Use area routine (statistics) in software to find area under force time graph impulse. (The area under a curve is same as integral of force vs. time.) In order to calculate error of impulse presume that our force probes (and thus area under force vs. distance curve) is known within 2%. J: ± N s 9. Print out one set of graphs for your group report. Question 2-6: Did calculated change in momentum of cart equal measured impulse applied to it by spring during nearly elastic collision? Discuss. Activity 2-3: A Smaller Momentum Change Suppose a less massive cart collided elastically with target. What would impulse be? You can take two 1/2 masses off cart and find out. Prediction 2-2: If cart had half mass and collided with target elastically moving at same velocity as in Activity 2-2, how large do you think impulse would be? The same as before? Larger? Smaller? Why? 1. Test your prediction. Take 1/2 kg masses off your cart to make total mass approximately half as large. It does not need to be exactly half. New mass of cart: kg 2. You can use same experiment file L Impulse and Momentum, as in Activity 2-2. Zero force probe, and n collide cart with target again. Try several times until you get initial velocity about same as in Activity 2-2. Find average velocities as in Activity 2-2 and calculate change in momentum. Average velocity (a vector) toward target: ± m/s Average velocity away from target: ± m/s p: ± kg m/s

11 L07-12 Lab 7 Collisions and Momentum Newton s Third Law Lab 7 Collisions and Momentum-Newton s Third Law L7-11 Question 2-7: Discuss how well this agrees with your prediction. 3. Find impulse as in Activity 2-2. J : ± N s 4. Print out one set of graphs for your group report. Question 2-7: Were impulse and change in momentum equal to each or? Discuss. Question 2-8: Were impulse and change in momentum equal to each or? Discuss. Activity 2-4: Impulse momentum Theorem in an Inelastic Collision It is also Activity possible2-4: to examine Impulse Momentum impulse momentum Theorem orem in in an ainelastic collision where Collision cart sticks to target and comes to rest after collision. This can be done by replacing spring with a dart It tipis atalso end possible of force to examine probe. impulse momentum orem in a collision where cart sticks to target and comes to rest after collision. This can be done by replacing spring with a dart tip at end of force probe. 1. Put extra mass on your cart so that its mass is same as in Activity 2-2. Attach 1. dartleave tip to force extra probe. mass Theon rest your of cart setup so is that as inits Activity mass is 2-2. same as in Activity 2-3. Attach dart tip to force probe. The rest of setup is as in Activity 2-2. Prediction 2-3: Now when cart cart hits hits target, target, it will it will come come to rest. to What rest. do What you do you predict about impulse? Will Will it beit be same, same, larger, larger, or smaller or smaller than inthan nearly in elastic nearly elastic collision? What do do you you predict predict now now about about impulse impulse and change and change in momentum? in momentum? Will Will y equal each or, or or will will one one be larger be larger than than or? or? 2. You can use same experiment file, L Impulse and Momentum, as in 2. Activity You 2-2. can use same experiment file, L Impulse and Momentum, as in Activity Zero force probe, and n collide cart with target. Try several times until you 3. get Zero initial velocity force probe, about and same n as collide in Activity cart 2-2. with target. Try several times until you get initial velocity about same as in Activity Find average velocity, as in Activity 2-2, and calculate change in momentum. University Average velocity of Virginia toward Physics Department target: Modified ± from P. Laws, D. m/ssokoloff, R. Thornton PHYS 1429, Spring 2011 p: ± kg m/s

12 Average velocity toward target: m/s L7-12 Lab 7 Collisions and Momentum-Newton s Third Law p = kg m/s 5. Find impulse as in Activity 2-2. Include area under rebound part of inelastic collision (ask your TA if you are not sure about this part). 5. Find impulse as in Activity 2-2. J: ± N s J 6. = Print out one set of graphs N s for your group report. 6. Print out one set of graphs for your group report. Question 2-8: Were impulse and change in momentum equal to each or for Question inelastic collision? 2-9: Were Explain impulse why you and think change results in momentum came out equal way to y each did. or for inelastic collision? Explain why you think results came out way y did. INVESTIGATION 3: Forces Between Interacting Objects INVESTIGATION There are many situations 3: FORCES where objects BETWEEN interact with INTERACTING each or, for example, OBJECTS during collisions. In this investigation we want to compare forces exerted by objects on each or. In a There collision, are both many objects situations might have where objects same mass interact and bewith moving each at or, samefor speed, example, or one object during collisions. might be much In this more investigation massive, or y we want mightto becompare moving at very forces different exerted speeds. by What objects factorson each might or. determine In a collision, forces both objects objects exertmight on eachhave or? Issame re some mass general and be law moving that relates same sespeed, forces? or one object might be much more massive, or y might be moving at very different speeds. What factors might determine forces objects exert on each Activity 3-1: Collision Interaction Forces or? Is re some general law that relates se forces? Activity 3-1: Collision Interaction Forces What can we say about forces two objects exert on each or during a collision? What Prediction can we 3-1: say about Suppose two forces objects two have objects exert sameon mass each andor are moving during toward a collision? each Prediction or at 3-1: same Suppose speed: two objects have same mass and are moving toward each or at same speed: m 1 = m 2 and v 1 = v m = m and v = 2 v Predict relative magnitudes of forces between object 1 and object 2 during collision. Place a check next to your prediction. Object 1 exerts a larger force on object 2. PHYS 1429, Spring 2011 The objects exert same size force on each or. Object 2 exerts a larger force on object 1. Prediction 3-2: Suppose masses of two objects are same and that object 1 is moving toward object 2, but object 2 is at rest: m 1 = m 2 and v 1 0,v 2 = 0

13 Prediction 3-2: Suppose masses of two objects are same and that object 1 is Prediction moving toward 3-2: object Suppose 2, but object masses 2 is of at rest: two objects are same and that object 1 is moving Lab 7 Collisions toward object and Momentum-Newton s 2, but object 2 is at Third rest: Law L7-13 m1 = m2 and v1 0, v 2 = 0 m = m and v 0, v = Predict relative magnitudes of forces between object 1 and object 2 during Predict collision. relative magnitudes of of forces forces between between object 1object and object 1 and 2 during object 2 during collision. collision. Object 1 Object exerts 1 exerts a larger a larger force force on object on object Object 1 exerts a larger force on object 2. The objects The objects exert exert same size sameforce size force on each on each or. or. The objects exert same size force on each or. Object 2 Object exerts 2 a exerts larger a larger force force on object on object Object 2 exerts a larger force on object 1. Prediction3-3: 3-3: Suppose mass of of object 1 is 1 is greater greater than than that that of object of object 2 and2 that and itthat is it is Prediction moving toward 3-3: object Suppose 2, 2, which mass is is at at rest: of rest: object 1 is greater than that of object 2 and that it is moving toward object 2, which is at rest: m1 > m 1 2> m 2 and v 1 v0,v 1 2 0, = v 02 = 0 m > m and v 0, v = Predict relative magnitudes of forces between object 1 and object 2 during Predict collision. relative magnitudes of forces between object 1 and object 2 during collision. Predict relative magnitudes of forces between object 1 and object 2 during collision. Object 1 exerts a larger force on object 2. Object 1 exerts a larger force on object 2. Object 1 exerts a larger force on object 2. The objects exert same size force on each or. The objects The objects exert exert same same size force size force on each on each or. or. Object 2 exerts a larger force on object 1. Object 2 Object exerts 2a exerts larger a force larger on force object on object To test predictions you made you can study gentle collisions between two force To probes test attached predictions to carts. you You made can add you masses can study to one gentle of collisions carts so between it has significantly two force probes To test more mass attached predictions than to carts. you or. You made can you add canmasses study gentle to one collisions of carts between so it two has force significantly probes more attached mass to than carts. You or. can add masses to one of carts so it has significantly more mass than or. University PHYS You will 1429, of need Spring Virginia 2011 Physics Department PHYS 1429, Spring 2011 two motion carts 2 m motion track level two force probes; one with a rubber stopper and one with a spring masses to place on one of carts to double and triple its mass 1. Set up apparatus as shown in following diagram. The force probes should be securely fastened to carts. The rubber stopper and spring should be carefully aligned so that y will collide head-on with each or.

14 L7-14 Lab 7 Collisions and Momentum-Newton s Third Law 2. Open experiment file called L Collisions. The software will be set up to measure forces applied to each probe with a very fast data collection rate of 2,000 points per second. (This allows you to see all of details of collision which takes place in a very short time interval.) The software will also be set up to be triggered, so that data collection will not start until carts actually collide. Make sure you keep force well below 50 N maximum. 3. The sign of Force in probe 1 should be reversed, because a push on it is negative (toward left). [This should already be done for you in experiment file.] 4. Use two carts to explore various situations that correspond to predictions you made about interaction forces. Your goal is to find out under what circumstances one cart exerts more force on or. Try collisions (a) (c) listed below. Be sure to zero force probes before each collision. Also be sure that forces during collisions do not exceed 50 N. 5. Print out one set of graphs for your group report. Be sure to label your graphs. 6. For each collision use area routine to find values of impulses exerted by each cart on or (i.e., areas under force-time graphs). Record se values in spaces below and carefully describe what you did and what you observed. (a) Two carts of same mass moving toward each or at about same speed. (b) Two carts of same mass, one at rest and or moving toward it. (c) One cart twice or three times as massive as or, moving toward or cart, which is at rest.

15 Lab 7 Collisions and Momentum-Newton s Third Law L7-15 Question 3-1: Did your observations agree with your predictions? conclude about forces of interaction during collisions? What can you Question 3-2: How does impulse due to cart 1 acting on cart 2 compare to impulse of cart 2 acting on cart 1 in each collision? Are y same in magnitude or different? Do y have same sign or different signs? INVESTIGATION 4: Newton s Laws and Momentum Conservation Your previous work should have shown that interaction forces between two objects are equal in magnitude and opposite in sign (direction) on a moment by moment basis for all interactions you might have studied. This is a testimonial to seemingly universal applicability of Newton s third law to interactions between objects. As a consequence of forces being equal and opposite at each moment, you should have seen that impulses of two forces were always equal in magnitude and opposite in direction. This observation, along with impulse momentum orem, is basis for derivation of conservation of momentum law. [The impulse momentum orem is really equivalent to Newton s second law since it can be derived mamatically from second law.] The argument is that impulse J 1 acting on cart 1 during collision equals change in momentum of cart 1, and impulse J 2 acting on cart 2 during collision equals change in momentum of cart 2: J 1 = p 1 J 2 = p 2 But, as you have seen, if only forces acting on carts are interaction forces between m, n J 1 = J 2. Thus, by simple algebra: p 1 = p 2 or p 2 + p 1 = 0 that is, re is no change in total momentum p total = p 1 + p 2 of system ( two carts). If momenta of two carts before (initial subscript i) and after (final subscript f ) collision are represented in diagrams above, n: where p f = p i p i = m 1 v 1i + m 2 v 2i and p f = m 1 v 1 f + m 2 v 2 f

16 L7-16 Lab 7 Collisions and Momentum-Newton s Third Law In next activity you will examine wher momentum is conserved in a simple inelastic collision between two carts of unequal mass. You will need following: two motion carts with Velcro ends 2 m motion track level motion detector masses to place on one of carts to double its mass Activity 4-1: Conservation of Momentum in an Inelastic Collision 1. Set up carts, ramp, and motion detector as shown below. If not already removed, remove force probes. Make sure that ends of carts will stick toger with Velcro after collision. Add masses to cart 1 so that it is about twice as massive as cart Measure masses of two carts. m 1 : kg m 2 : kg

17 Lab 7 Collisions and Momentum-Newton s Third Law L7-17 Prediction 4-1: You are going to give more massive cart 1 a push and collide it with cart 2, which is initially at rest. The carts will stick toger after collision. Suppose that you measure total momentum of cart 1 and cart 2 before and after collision. How do you think that total momentum after collision will compare to total momentum before collision? Explain basis for your prediction. Test your prediction. 3. Open experiment file called L Inelastic Collision. Begin with cart 1 at least 20 cm from motion detector. Begin graphing, and when you hear clicks of motion detector, give cart 1 a brisk push toward cart 2 and release it. Be sure that motion detector does not see your hand. 4. Repeat until you get a good run when carts stick and move toger after collision. 5. Print one copy of graph. 6. Again use technique outlined in Example-4 of Appendix C to measure velocity of cart 1 just before collision and velocity of two carts toger just after collision. [You will want to find average velocities over time intervals before and after but not during collision.] v 1i : ± m/s v 1 f = v 2 f : ± m/s 7. Calculate total momentum of carts 1 and 2 before collision and after collision. Show your calculations below. p i : ± kg m/s p f : ± kg m/s Question 4-1: Was momentum conserved during collision? Did your results agree with your prediction? Discuss.

18 L7-18 Lab 7 Collisions and Momentum-Newton s Third Law Question 4-2: Now look back at Activity 2-4(where cart collided inelastically with a fixed target). The cart clearly had momentum before collision, but was at rest afterwards. Using Newton s 2nd and 3rd laws, explain how this can be. Please clean up your lab area