# PRELAB: NEWTON S 3 RD LAW AND MOMENTUM CONSERVATION

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1 Newton s 3rd Law and Momentum Conservation, p./ PRELAB: NEWTON S 3 RD LAW AND MOMENTUM CONSERVATION Read over the lab and then answer the following questions about the procedures:. Write down the definition of momentum. 2. What is your Prediction -2? Does one car exert a larger force on the other or are both forces the same size? 3. In Activity -, why is the sign of probe reversed? 4. What is your Prediction -7 when the truck is accelerating? 5. What makes the collision in Activity 2- inelastic?

2 Newton s 3rd Law and Momentum Conservation, p.2/

4 Newton s 3rd Law and Momentum Conservation, p.4/ Investigation : Forces between Interacting Objects There are many situations where objects interact with each other, for example, during collisions. In this investigation we want to compare the forces exerted by the objects on each other. In a collision, both objects might have the same mass and be moving at the same speed, or one object might be much more massive, or they might be moving at very different speeds. What factors might determine the forces the objects exert on each other? Is there some general law that relates the forces the objects exert on each other? Is there some general law that relates the forces? Activity -: Collision Interaction Forces What can we say about the forces two objects exert on each other during a collision? Prediction -: Suppose two objects have the same mass are moving toward each other with the same speed so that m = m2 and v = v2. Predict the relative magnitudes of the forces between object and object 2 during the collision. Place a check next to your prediction: Object exerts a larger force on object 2. The objects exert the same size force on each other. Object 2 exerts a larger force on object. Prediction -2: Suppose the masses of two objects are the same and that object is moving toward object 2, but object 2 is at rest (i.e. m = m2 and vr 0, vr = 2 0 ). Predict the relative magnitudes of the forces between object and object 2 during the collision. Place a check next to your prediction: Object exerts a larger force on object 2. The objects exert the same size force on each other. Object 2 exerts a larger force on object. Prediction -3: Suppose the mass of object is greater than that of object 2, and that it is moving toward object 2, which is at rest (i.e. m > m2 and vr 0, vr = 0 2 ). Predict the relative magnitudes of the forces between object and object 2 during the collision. Place a check next to your prediction: Object exerts a larger force on object 2. The objects exert the same size force on each other. Object 2 exerts a larger force on object.

5 Newton s 3rd Law and Momentum Conservation, p.5/ Provide a summary of your predictions. What are the circumstances under which you predict that one object will exert a greater force on the other object? To test these predictions, you can study collisions between two force probes attached to carts. You can add masses to one of the carts so that it has significantly more mass than the other. If a compression spring is available you can also study an explosion between two carts by compressing the spring between the two carts and letting it go.. Set up the apparatus below. The force probes should be securely fastened to the carts. The hooks should be replaced by rubber stoppers, which should be carefully aligned so that they will collide head-on with each other. If the carts have friction pads, these should be raised so that they don t rub on the ramp. 2. Set up the software to collect data from the two force probes at the fastest possible sampling rate. Set pull positive for probe, push positive for probe 2. (This choice makes all forces to right positive). Set up axes like the ones below for force-time graphs for the two probes. The time axes of the graphs should be aligned. +0 force probe 2 (N) force probe (N) 0-0 time (s) 3. Use the probes to explore the various situations that correspond to the predictions you made about interaction forces. Your goal is to find out under what circumstances one cart exerts more force on the other. Try collisions (a)-(c) listed below. Zero the force probes before each collision. To protect the equipment, make sure the forces during the collision do not exceed 20 N. For each collision, use

7 Newton s 3rd Law and Momentum Conservation, p.7/ Prediction -4: Suppose the mass of object is greater than the mass of object 2 and the objects are moving toward each other at the same speed ( m > m2 and v = v2 ). Predict the relative magnitudes of the forces of interaction. Prediction -5: Suppose the mass of object is much greater than the mass of object 2 and that object 2 is moving in the same direction as object, but not as fast ( m >> m2 and v > v2 ). Predict the relative magnitudes of the forces of interaction. Prediction -6: Suppose the object is much greater than the mass of object 2 and that both objects are at rest until an explosion occurs ( m >> m2 and v = v2 = 0 ). Predict the relative magnitudes of the forces of interaction. Check your predictions -4, -5 and -6 and record your observations here:

9 Newton s 3rd Law and Momentum Conservation, p.9/ Q-5: Explain how cart 2 is able to accelerate. Use Newton s second law and analyze the combined (net) force exerted by all the forces acting on it. Is there a non-zero net force? Q-5b: Explain how cart is able to accelerate. Use Newton s second law and analyze the combined (net) force exerted by all the forces acting on it. Is there a non-zero net force? Extension -4: More Interactions Think of other physical situations with interaction forces between two objects that you can examine with the available equipment. Describe each physical situation completely. Draw a diagram. Predict the relative magnitudes of the two interaction forces. Then set up the apparatus and test your predictions. Describe your observations. Include any graphs you make. Compare your observations to your predictions. Investigation 2: 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 direction on a moment by moment basis for all the interactions you have studied. This is a testimonial to the seemingly universal applicability of Newton s third law to interactions between objects. As a consequence of the forces being equal and opposite at each moment, you should have seen that the impulses of the two forces were always equal in magnitude and opposite in direction. This observation, along with the impulse-momentum theorem, is the basis for the derivation of the conservation of momentum law, which you may have seen in lecture in or in your text. (The impulse-momentum theorem is mathematically equivalent to Newton s second law, since it can be derived mathematically from the second law). The argument is that the impulse J r acting on cart during the collision equals the change in momentum of cart, and the impulse J r 2 acting on cart 2 during the collision equals the change in momentum of cart 2: r v r v J = p J 2 = p2 But, as you have seen, if the only forces are the interaction forces between them, J = J 2. Thus, by simple algebra: v v v v p = p 2 or p + p2 = 0 That is, there is no change in the total momentum of the system (the two carts).

10 Newton s 3rd Law and Momentum Conservation, p.0/ If the momenta of the two carts before (initial subscript i) and after () the collision are represented in the diagram below, then p i = p f where r r = and p f = mv f + m2v2 f pi mv i + m2v2i In the next activity you will examine whether momentum is conserved in a simple inelastic collision between two carts of unequal mass. Activity 2-: Inelastic collision. Set up the carts, ramp and motion detector as shown below. Remove the force probe from the cart. Add masses to cart so that it is about twice as massive as cart Measure the masses of the carts. M (car) = M (car2) = (don t forget units) 3. Set up the motion detector to take velocity data at about 50 points per second. Set up axes to graph velocity-time like those below. +2 velocity (m/s) 0-2 time (s) Prediction 2-: You are going to give the more massive cart a push and collide it with cart 2, which is initially at rest. The carts will stick together after the collision. Suppose you measure the total momentum of cart and cart 2 before and after the collision. How do you think the total momentum after the collision will compare to the total momentum before the collision? Explain the basis for your prediction.

11 Newton s 3rd Law and Momentum Conservation, p./ 4. Test your prediction. Begin with cart at least 20 cm from the motion detector. 5. Use the software to measure the velocity of cart just before the collision and the velocity of both carts together just after the collision. (You will want to find the average velocities over the short time intervals just before and just after but not during the collision.) Record the values (with units) below. r r v i = v 2i = r r = = v f 6. Calculate the total momentum of carts and 2 before the collision and after the collision. Show the calculations below. Don t forget units for youesults. p r i p r f v 2 f = = Q2-: Was momentum conserved during the collision? Did youesults agree with your prediction? Explain. Q2-2: What are the difficulties in doing this experiment that might cause the momentum before the collision to be slightly different that the momentum after the collision? Explain. Q2-3: Momentum is conserved even when the carts do not stick together. Such collisions are called partially elastic collisions. This lab will not test whether momentum is conserved in partially elastic collisions because of equipment limitations. What additional equipment would be needed to test such a collision? Why is only one motion detectoequired to analyze the inelastic collision? Extension 2-2: Consider other collisions you can examine with the available apparatus. Describe each physical situation carefully. Draw a diagram. Predict how the total momentum after the collision will compare to the momentum before the collision. Then set up the apparatus and test your predictions. Describe your observations. Include copies of any graphs you make. Compare your observations to your predictions.

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