Lab10 momentum215

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New Mexico State University *

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Dec 6, 2023

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Momentum Name Section Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 1 1. Introduction In the last lab, you were introduced to a conserved quantity, energy. Energy is a scalar quantity – it doesn’t depend on direction – and the amount of energy before or after some interaction or process is always conserved. That is, there is as much energy before any event as after, although this energy can change from one form to another (for example, from kinetic to potential). For processes, while the total amount of energy is conserved, some of this energy is transformed into forms that are harder to keep track of. For example, when a child travels down a slide, some of the initial potential energy is converted into kinetic energy, but because some is also converted into heat the final kinetic energy will not equal the initial potential energy. In this lab we will introduce a second conserved quantity, momentum. Momentum is a vector quantity and is equal to the product of an object’s mass and its velocity. During a colli sion, some or all of the momentum from one object may be transferred to another object, but the total of momentum vector will be unchanged or conserved. However, just as with energy, it is possible for momentum to be transferred from objects that we are paying attention to into objects that we are not (i.e., that are not part of our system). So while the total momentum is always conserved, it is possible for the momentum of a group of objects that we are focusing on to change if there is some interaction with objects that are not part of our system. 1.1: Lab Objectives. After completing this lab and the associated homework, you should be able to: 1. Describe the forces on two bodies as they collide. 2. Apply Newton’s third law to reason about the forces in a collis ion. 3. Calculate the momentum of an object, and predict the momentum of other objects based on the law of conservation of momentum. 4. Decide whether momentum is conserved for a system that we have defined. 1.2: Outline of Laboratory Approximate sequence of the lab and homework: 1. Verify Newton’s third law for interacting objects that are moving with varying speed. 2. Use Newton’s third law to make inferences about the change in momentum for colliding objects. 3. Apply momentum ideas to systems of colliding objects. 4. Use momentum ideas to predict velocities of carts after collisions.

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 2 2. Forces between interacting objects In this section, you will perform an analysis of the forces acting as two bodies move together. 2.1: For this experiment, you will be using two sliding carts (with attached force probes). We will call the cart on the left including two of the black 500-gram masses system A and the cart on the right with no added masses system B. Without turning on the data recording program, push the carts horizontally so that they speed up as they move to the right. Note that there is friction between the carts and the track. 2.2: Compare the net force (magnitude and direction) on system A to that on system B while they are speeding up. Explain how you arrived at your comparison. 2.3: Draw separate free- body diagrams for system A and system B. Label each of the forces in your diagrams by identifying: the type of force, the object on which the force is exerted, and the object exerting the force. 2.4: Would you expect the magnitude of the force exerted on system A by system B to be greater than, less than, or equal to the magnitude of the force exerted on system B by system A? Explain. Newton’s Third Law is an expression of the idea that force is an interaction – whenever object A exerts a force on object B, object B exerts a force on object A that has the same magnitude, but is opposite in direction to the force that A exerts on B. These two forces are of the same type (normal, gravitational, magnetic, etc.) and are known as a Newton’s third law force pair. Identify any Newton’s third law force pairs in your diagrams by placing one or more small “ ” symbols through each member of the pair (i.e., mark each member of the first pair as , each member of the second pair as , etc.). What feature of the labeling convention F on , by introduced in the Forces lab might be used to identify the force pair(s)? A B Track Free-body diagram for system A Free-body diagram for system B

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 3 3. Experimental analysis of interacting bodies In this section you will perform an experimental study of the situation that you considered above. With the data recording program running, push on both force probes so that you can identify which probe corresponds to each recording. Notice that a force to the right is recorded as a positive value for each probe – that is, if you push on the pad attached to probe A the force will be negative, but if you push on the pad attached to probe B, the force will be positive. 3.1: Zero the force probes. With the data recording program running, push horizontally so that the carts speed up as they move along the track to the right. Record the values for the measured forces. Which of the forces from your free-body diagrams on page 2 does the force recorded by probe A correspond to? Which of the forces from your free-body diagrams on page 2 does the force recorded by probe B correspond to? Are the values you obtained from the two force probes consistent with your predictions on page 2? If not, resolve the inconsistency. 3.3: Consider the following discussion between 3 students about a person in an elevator that is traveling upward. The elevator is slowing down: Alfonso: Newton’s third law tells us that the force on the person by the elevator is equal and opposite to the person’s weight. These forces are equal in magnitude and opposite in direction. Bettina: Not in this case. The person is not moving at a constant spe ed, so Newton’s third law does not apply. Carlota: Those two forces are not a Newton’s third law pair anyway, because they are acting on the same object, the person. Newton’s third law tells us about the force on the elevator by the person compared to the force on the person by the elevator. These would be equal, but only if the elevator was moving at a constant speed. None of these students is correct. Explain what part of each statement is incorrect, and then explain what (if anything) Newton’s third law tells us for this situation. Does Newton’s third law apply to two forces that act on the same object? A B Track

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Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 4 Does Newton’s third law apply to an object that is not moving at a constant speed?  Discuss your answers to sections 2 and 3 with your lab instructor before continuing. 4. Force and momentum 4.1: The drawing at right represents a photograph taken of the motion of a toy hovercraft. The hovercraft travels toward a wall at an angle, then strikes the wall and rebounds as shown. It is known that our attached blinkie emits light for 0.1 seconds (one-tenth of a second), and that the floor tiles that can be seen in the background are 10 cm on a side. Based on this drawing: A. Is the speed of the hovercraft at point A : greater than, less than, or equal to the speed of the hovercraft at point B? Explain. B. It is not correct to say that the velocity at point A is the same as the velocity at point B. Why not? C. In the space provided, use the technique of vector subtraction that you learned in a previous lab to find the direction of the change in velocity of the hovercraft during its collision with the wall . 4.2: The momentum p of an object is defined as the product of the object’s mass and its velocity: p m v . Momentum is a vector quantity with direction as well as magnitude. How does the direction of the momentum compare to the direction of the velocity? Hovercraft A B Wall Motion direction Motion direction 10 cm

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 5 In the space provided, draw vectors to show the direction and (approximate) magnitude of the initial and final momentum of the hovercraft from part 4.1. A conserved quantity is a quantity that does not change during some process. Is it accurate to say that the momentum of the hovercraft is conserved during its collision with the wall? Explain. Use vector subtraction to determine the direction of the change in momentum (i.e., the final momentum minus the initial momentum) of the hovercraft. 4.3: The impulse exerted on an object by a force is defined as that force times the amount of time that this force is acting, F t (assuming that the force is constant.) As you may have seen in lecture, the net impulse on an object is equal to the change in momentum of the object: F net t p m v . This equation is known as the impulse-momentum equation. Because this is a vector equation, the direction of the net force on the hovercraft during the time that it is colliding with the wall should be the same as the direction of the change in momentum. Is your result from 4.2 consistent with the direction of the force on the hovercraft by the wall? (What type of force is that?) 4.4: Consider two completely different collisions. In collision C, a hovercraft heads straight toward a wall and bounces straight back. In collision D, the hovercraft has the same initial speed, instead of a rubber bumper, this hovercraft’s surface is made of clay. This hovercraft sticks to the wall and stops completely. A. Before you do the calculation, what does your intuition tell you about the change in momentum of the hovercraft in collision D? Will it be bigger than, smaller than, or the same magnitude as the change in momentum from collision C?

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 6 B. In the space provided, construct the change in momentum vectors for the two collisions Is the magnitude of the change in momentum of the hovercraft in collision D greater than, less than, or equal to the change in momentum of the hovercraft in collision C? In the exercises above, you have seen that the momentum of the hovercraft is not conserved. You might wonder whether that contradicts what you have learned previously. Momentum is indeed a conserved quantity, but only if there is no net force acting on a system. In these examples, the wall exerts a force on the hovercraft, so momentum is not conserved. As we will see, using conservation of momentum requires that you look at a process where the only forces for a system are internal forces, or forces by one part of the system on another. Often one can choose a system that includes multiple objects in order to ensure that momentum is conserved, as we will in the next section. 5. Analyzing collisions 5.1: Imagine 3 balls made of different materials, but all with the same mass. Each ball is launched at the same initial speed v at three identical blocks, which we will call the targets. The targets all are at rest before the balls hit them. The first ball hits its target and sticks, s o we’ll call this ball “Sticker.” After the collision, Sticker and the target move to the right together. The second ball hits its target and stops completely, so we’ll call this ball “Stopper.” After the collision, Stopper comes to rest and its target moves to the right. The third ball hits its target and bounces back in the opposite direction. We’ll call this ball “Bouncer.” After the collision, Bouncer is moving to the left and its target moves to the right. A. Based on your intuition, how would you rank the speed of the three target blocks after the collision? B. For any of the collisions, how does the force on the ball by the target at an instant during the collision compare to the force on the target by the ball? Explain using your observations from sections 2 and 3. = 0 v v = 0 Before After : "Sticker" After : "Stopper" v = 0 After : "Bouncer"

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Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 7 Recall section 4 where we discussed the impulse, F t . Use your answer above to compare the impulse on the ball to the impulse on the target. (Hint: what must be true about the time that these forces act?) Recall the earlier discussion in which we used the fact that impulse equals the change in momentum ( F net t p m v ). Use this relationship and your answers above to compare the change in momentum vector for the ball to the change in momentum vector for the target. Consider both magnitude and direction. In a collision between two objects, if no net external forces act on the objects, the objects that collide will have change in momentum vectors that are equal and opposite. C. For each of the three collisions, what result is obtained if we add the change in momentum vectors for the target and the ball? That is, what is the change in momentum for the system consisting of the ball and the target? If the change in momentum vector for a system during a collision is zero, then the momentum of that system is the same before and after that collision. For which of the three collisions is the momentum of the ball + target system the same before and after the collision? In these cases, we say that the momentum of the system is conserved. D. Now use vector subtraction to analyze the three collisions. In each of the spaces provided, construct a vector that represents the change in momentum of one of the three balls: Sticker, Stopper, and Bouncer. Change in momentum: Sticker Change in momentum: Stopper Change in momentum: Bouncer You should find that the magnitudes of the change in momentum vectors are all different in magnitude. (The directions are all the same.) Rank the magnitudes of the change in momentum from largest to smallest. E. Based on your results, will the targets all have the same speed after the collision? Rank the speeds of the three targets after the collision from largest to smallest.

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 8 5.2: It may seem counterintuitive that the three collisions can have such different outcomes. However, the different types of balls lead to different types of collisions. For this reason, we classify collisions based on their outcomes. For example, a collision like the one between Sticker and its target, in which the colliding bodies move together as a unit after the collision, is known as perfectly inelastic. The classification of collisions depends on the extent to which the kinetic energy of the system is the same before and after the collision. If the kinetic energy is exactly the same before and after, the collision is perfectly elastic. In most collisions, some kinetic energy is lost (this energy is transformed to some other form of energy, like the internal thermal energy of one of the balls), and the collision is inelastic. Consider the collisions above, with Sticker, Stopper, Bouncer, and their respective targets. For each, state whether the momentum of the ball-target system is or is not conserved, and whether it’s possible that the kinetic energy of that system is the same before and after. Sticker and its target: Stopper and its target: Bouncer and its target: Discuss your answer with your instructor. 6. Measuring velocities before and after a collision In this section, you will perform an analysis of a collision between two bodies. You will analyze three cases where one cart, cart A , collides with another at rest, cart B . Using the principle of momentum conservation, you will predict and verify the final velocity of the carts after the collision compared to the initial velocity of cart A . For this experiment, you will be using two rolling carts whose velocity is monitored by the motion detector. We are no longer using the wooden sliding carts and force probes for this part of the experiment, therefore place these out of the way, so that they do not interfere with the rolling carts and motion detector. 6.1: Cart B is at rest on a track. Cart A collides with cart B and the two carts stick together. Derive an expression for the velocity of the two carts just after the collision in terms of the masses m A and m B of the two carts and the initial velocity v 0A of cart A. For the special case where the two carts have the same mass, what is the final velocity of the carts after the collision compared to the initial velocity of cart A?

Momentum Copyright 2009 by S. Kanim, M. Loverude, & L.Gomez 9 Now, use a triple-beam balance to verify the mass of the two carts. Record these mass values here. 6.2: Test your prediction above for two equal – mass carts colliding and sticking together. Turn each cart around so that the two velcro sides face each other. Use the motion detector to create a velocity versus time graph for cart A during the collision. 6.3: Now verify the equation you derived above for a situation where cart A has more mass than cart B. Increase the mass of cart A by placing one 500-gram black bar mass on it. Now with the increased mass of cart A , predict the speed of cart A after the collision in terms of its speed just before the collision. Test your prediction. 6.4: Finally, verify the equation above for a situation where cart B has more mass than cart A. Remove the 500-gram black bar mass from cart A, and increase the mass of cart B by placing the mass on it. Again, with the increased mass of cart B , predict the speed of cart A after the collision in terms of its speed before the collision, and test your prediction. Mass of cart A: Mass of cart B:

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