1 Name Date Day/Time of Lab Partner(s) Lab TA LAB 4: MOMENTUM AND COLLISIONS NEWTON S THIRD LAW OBJECTIVES To examine action-reaction force pairs To examine collisions and relate the law of conservation of momentum to colliding objects To differentiate between elastic and inelastic collisions and predict the elasticity of simple collisions INVESTIGATION 1: ACTIONS AND REACTIONS Of Newton s three laws, the third is perhaps the least intuitive in its application. We instinctively think that a more massive object, when it collides with a smaller one, exerts a much greater force than the smaller object exerts back. Newton s law states, however, that the forces each exerts on the other are precisely equal. We will test this law in the following experiments. You will need the following materials for this investigation: PASCO motion track with collision bracket two motion carts two force probes, one loaded with a spring, one with a rubber plug fan attachment Activity 1-1: Relative Forces in Collisions Between Carts of Equal Mass 1. Set up the experiment as shown in the diagram. Use the long thumb screws on the black Force Accessory Bracket to attach them to the carts, and use the two spring attachments, also from the bracket, on the ends of the force probes. Remove the hooks and screw the springs on.
2 2. Open the experiment file Collisions 1 from the Physics 131 folder. The experiment is set up to record force data at very high speed (1000 readings/second) during the collision, which takes place in a very short span of time. You can zoom in on the collision later using the cursor. 3. One of the force probes should have been set up in the software as push positive and one as pull positive. This is so that one direction of the track will be the positive direction and one negative. Determine which force probe is set up as which and decide which end of the track you will use as the positive end. Position the force probes and carts accordingly. 4. Make sure that when the carts collide, their only point of contact is the force probes. Prediction 1-1: Predict the relative forces between the two carts in the following situations. Make sure you are consistent in which cart is called what. a) Cart 1 and Cart 2 collide while moving toward each other at equal velocities: Cart 1 s force probe will register a greater force than Cart 2 s; The two force probes will register equal forces; Cart 2 s force probe will register a greater force than Cart 2 s. b) Cart 1 and Cart 2 collide, with Cart 1 moving significantly faster than Cart 2: Cart 1 s force probe will register a greater force than Cart 2 s; The two force probes will register equal forces; Cart 2 s force probe will register a greater force than Cart 2 s. c) Cart 1 collides with a stationary Cart 2: Cart 1 s force probe will register a greater force than Cart 2 s; The two force probes will register equal forces; Cart 2 s force probe will register a greater force than Cart 2 s. 5. Run the first scenario. First zero your force probes. Press Start, then push the carts so that they move together at approximately equal velocities. Make sure that the collision force will not exceed 50 N. 6. Analyze the data from the force probes. Keep a good run for later comparison. Question 1-1: What shape is your graph? Are the graphs of the two force probes the same shape? Question 1-2: Are the graphs of the two force probes mirror images? Why or why not?
3 Question 1-3: What is the average force exerted during the collision? (You can calculate this using the DataStudio Area function and dividing by the total time.) 7. Repeat the experiment for each of the scenarios. 8. Print out a copy of each scenario s graph to turn in at the end of lab. You may print them all on one sheet if it is convenient. Question 1-4: What similarities are there between the three scenarios? What differences are there? Question 1-5: Were your predictions correct? Why or why not? Activity 1-2: Relative Forces in Collisions Between a Moving Cart and a Fixed Obstacle We have seen what happens when a moving object collides with an object which is free to roll away. But what happens when the object is fixed in place? What is the relationship between the forces then? 9. Take one of the force probes and mount it on the collision bracket as shown. The same long thumb screw can be used to attach the force probe. Use the screws on the side of the bracket to attach it to the dynamics track, fitting the nuts on the back into the slot on the edge of the track. Force Probe Force Bracket Force Probe Cart Probe 10. Continue using the same Data Studio activity, keeping all your data so you can easily compare. Prediction 1-2: If you roll the cart into the collision bracket, what will the relation between the forces be? The cart s force probe will register a greater force; The two force probes will register equal forces; The bracket s force probe will register a greater force.
4 11. Test your prediction. Roll the cart toward the bracket, letting it collide and bounce off. 12. Analyze the force data as you did in Activity 1-1. Print out a copy of your graph to turn in at the end of lab. Question 1-7: Are the graphs from the two force probes the same shape? Are they mirror images? Why or why not? Should they be? Question 1-8: Was your prediction correct? Why or why not? INVESTIGATION 2: COLLISIONS AND MOMENTUM We will now move on to a more quantitative investigation of collisions by measuring the kinetic energy in a collision and the momentum of the colliding objects. The law of conservation of energy is often not helpful in collisions because internal forces can act to do work on the whole system. For example, if you throw a sticky blob at something, the chemical energy which makes the blob stick subtracts from the net kinetic energy of the system. Momentum is defined as p = mv Momentum is always conserved in a collision. A collision where both mechanical energy and momentum are conserved is called a perfectly elastic collision. Collisions range from the elastic to the inelastic (where the colliding objects stick together after impact, as in the sticky blob example above). Collisions need not be one or the other; they can fall anywhere in between the two extremes of elastic and inelastic. If there are no internal forces to do work on the system, it is a safe bet that a collision will be elastic (or very nearly so). In this Investigation, we will measure the momenta of objects in both elastic and inelastic collisions. You will need the following materials for this investigation: PASCO track with collision bracket two motion carts two motion sensors force probe Activity 2-1: Measuring Velocity and Momentum in Simple Collisions As the previous investigation should have shown, the forces exerted by one object on another in a collision are always precisely equal to those exerted back. This is a direct consequence of Newton s Third Law.
5 Because of this, we will only need one force probe for this investigation, because we will know exactly what any other force probe in the collision would read. 1. Set up the experiment as shown in the diagram. You can leave the force probe on the bracket. Force Probe Force Bracket 2. Open the experiment file Collisions 2. This experiment is set up much like the last one, except that this experiment has a much slower rate of data collection, only 50 readings/second. Make sure you graph the velocity measured by the motion sensor. You can get the velocity to be graphed by choosing Setup in Data Studio and clicking on the velocity button. Check to make sure you are getting 50 Hz data collection rate. Prediction 2-1: Will this collision be elastic or inelastic or somewhere in between? If the cart approaches the bracket with velocity x, so that the bracket imparts an average force of 15-25 N on the cart, what will the velocity of the cart be as it moves away after the collision? 3. Test your prediction. Press Start, then roll the cart down the track and collide it with the bracket. Repeat until you get a force of 15-25 N and constant velocities before and after the collision. 4. Print out a copy of your graphs to turn in at the end of lab. For comparison later, using the Setup menu, change the data acquisition rate on the Force Probe to 1000 Hz and record a good collision so that you can see the details of the forces. Use the Area function to calculate the area under the Force-time graph. Print the force data and this graph. You ll see why later. Question 2-1: Were your predictions correct? Why or why not? Activity 2-2: Elastic collision cart-cart 1. Select File > New Activity. Set up the experiment as shown. The motion sensors clip directly to the ends of the dynamics track, although you may want to keep the force bracket on the track.
6 Prediction 2-2: When the carts are rolled together, will there be any internal forces which will do work on the system? In other words, will this collision be elastic? 2. The mass of each cart is about 0.497kg. The mass of a force probe is 0.105kg. Enter the total masses below: m1 = m2 = 3. Practice rolling the carts so that neither motion detector sees a hand interfering with its detection of the cart. You may want to have one person handle each cart. 4. Press Start and set the carts in motion shortly after you hear the motion detector begin clicking. The carts should not be moving at the same speed. 5. Repeat until you get a graph which has constant velocities for both carts before and after the collision. 6. Save your data for the next Investigation. Print out a copy of your graphs to turn in at the end of lab. Question 2-2: Calculate each cart s momentum before and after the collision. Add the momenta and compare the total momentum of the system. (Remember to use the correct signs!) Question 2-3: Was the collision elastic (how can you tell?)? Did this agree with your prediction? INVESTIGATION 3: MOMENTUM AND IMPULSE IN PERFECTLY INELASTIC COLLISIONS We will now look at perfectly inelastic collisions. We said before that momentum was always conserved in collisions. However, we now must add the caveat that the system whose momentum is conserved is sometimes very large: in some cases, the whole planet! This will be the case in our first experiment in this investigation, when we will send a cart to impale a target with a dart, and in the process come to a complete stop, giving its momentum to the earth. However, in the second experiment, the two carts will form a complete system, as above. When we speak of the cart giving its momentum to the earth, what we are speaking of is the physical concept of impulse. Impulse is defined as J = Fdt which looks suspiciously like the definition for work. In fact, the relation between work and energy is
7 very much analogous to that between impulse and momentum. The external impulse is equal to the change in momentum that we measure: J = p Activity 3-1: Inelastic collision with a fixed obstacle We will use the same setup that we used in Activity 2-1, except that instead of a spring, the force probe will be loaded with a magnetic bracket. Use the magnetic bracket that is attached to the Force Accessory bracket, and attach this to the force probe instead of the spring. To get the force probe to stick to the Force bracket instead of bouncing off of it, take one of the track bumpers that have been placed at the ends of the dynamics track and mount it on top of the Force bracket using one of the holes on the side. This should put the magnets on the bumper at exactly the correct height to match the magnets on the force probe. Test to see that the cart will stick, i.e., that you haven t mounted the bumper backwards on the bracket. magnetic bracket. Remove and attach to Force Probe Prediction 3-1: Now when the cart hits the target it will come to rest. If the cart moves toward the target at the same velocity that it did in Activity 2-1, how much momentum will have to be transferred away? What should the impulse be? 1. Set up the experiment as described above. 2. Zero the force probe, then set the cart in motion with a velocity as close as possible to that which you used in Activity 2-1. Keep the data acquisition for the force probe set to take data at 1000 Hz. 3. Look closely at the force-time graph for the period of the collision. Use Data Studio s Area function to find the impulse during the collision. Question 3-1: How does the impulse compare to that which you observed in Activity 2-1? How do you explain this? 4. Print out a copy of your graph to turn in at the end of lab.
8 Activity 3-2: Inelastic Collision Between Two Carts For this activity you will use the same setup that you used in Activity 2-2. Turn the force probes on the carts sideways to allow the velcro on the end of each cart to stick to the other cart. 1. Measure the masses of the two carts you will be using. m1 = m2 = m1 + m2 = 2. Make sure that the carts will stick together without too much difficulty. 3. Start the experiment and set the carts rolling toward each other as you did before. You should move them at as close as possible a velocity to the one they each had before. 4. Once you get a good graph of velocity before and after the collision, print a copy to turn in at the end of lab. Question 3-2: Find the initial momentum of each of the carts and add to find the total initial momentum (be careful of the signs). p1 = p2 = p1 + p2 = ptotal = What is the momentum of the system once the two carts come together? Is the final momentum the same as the initial total? Why or why not? End-of-lab checklist: Make sure you turn in: your lab manual sheets graphs from Activities 1-1, 1-2, 1-3, 2-1, 2-2, 3-1, 3-2 Make sure you have filled in all relevant data and have answered all questions.