PHYSICS LAB DUE 30TH

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Apr 3, 2024

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One-Dimensional Collisions - 7 Data and Work Sheets - Print or bring it on an electronic device One-Dimensional Collisions - Physics 1201A 2022-2023 Please circle the appropriate values Course 1101A 1201A 1401A 1501A Lab Section 002 003 004 005 006 007 008 009 010 013 014 Lab Subsection A B C D Name First: Last: Student # Lab Partner First: Last: Lab Station # Date Demonstrator Disclaimer: Please note that some but not all questions in this lab writeup will be graded. PART I: INVESTIGATIONS OF ELASTIC AND INELASTIC COLLISIONS EXPERIMENT 1: PRELIMINARY ADJUSTMENTS OF THE TRACK, CARTS AND THE MOTION SENSORS Figure 5: Linear track with collision carts. Linear Track The experiments in this lab utilize a smooth linear metal track.

One-Dimensional Collisions - 8 Levelling the Track Center a bubble level on the track at the 60 cm mark. Use the adjustable levelling feet on the linear track (see Figure 5) to center the air bubble in the bubble level. Turn the bubble level 90 degrees to level the track in the perpendicular direction to travel. When the track is level a cart centered at the 60 cm mark should remain stationary. Collision Carts This lab uses two carts with low-friction ball bearing wheels that allow the carts to roll down the track with minimal resistance caused by friction. One end of each cart is labeled ‘ elastic ’ and is used when performing elastic collision experiments. Magnets are mounted underneath the ‘ elastic ’ ends of the carts in order to facilitate elastic collisions. The other end of the cart is not labeled but can be identified from the mounted velcro tabs, which are used to facilitate inelastic collisions. Each cart is labeled either A or B. Cart B contains a spring-loaded plunger held in place by a ‘plunger lock’. The plunger is used to facilitate the ‘explosion’ in Experiment 4. Check that you have one of each type of cart as in Figure 5 . Figure 6: Connecting Motion Sensor A to port A on the PowerLink hub. Motion Sensors Each experiment requires a measurement of the velocity of the carts before and after a collision. For this pur- pose you will use motion sensors mounted to the ends of the linear track as in Figure 7. The motion sensors emit pulses of ultrasound that reflect off ends of the carts and return to the motion sensors where they are detected and used to measure the position of the carts as a function of time. The position vs time information is sent to the com- puter where it is recorded and converted to velocity vs time data. The motion sensors have a switch on top with ‘ person ’ or ‘ cart ’ selections. Each motion sensor will produce smoother data in either one or the other mode, you should adjust your own sensors for best results. The motion sensors are labeled A, B or C, as shown in Figure 6. The ports on the PowerLink hub are also la- beled A, B or C. Ensure that each motion sensor is connected to the correct port on the PowerLink hub. The collision carts should be placed in each experiment such that they are closest to their matching motion sensor at the beginning of the experiment. In each experiment the motion sensors will begin collecting data when the velocity of one of the carts goes above v = 0.200 m/s. This helps to ensure good quality data with less noise in each experiment. If you see a message indicating that the initial conditions was not reached, try taking data again.

One-Dimensional Collisions - 9 Sign Convention The velocity data produced by the motion sensors is given a sign based on whether the object under investigation is moving in the positive or negative x direction as shown in Figure 7. Carts moving to the right will be given a positive velocity while carts moving to the left will be given a negative velocity. Figure 7: The experimental setup Experiment 1(a) showing the direction of motion that produces a positive velocity. Note: Ensure that your experimental setup is the same as shown in Figure 7, i.e. Motion Sensor A on the left side of the track, and Motion Sensor B on the right hand side of the track. EXPERIMENT 1(a): MOTION SENSOR ALIGNMENT APPARATUS Linear track, two motion sensors, one collision cart, computer with PASCO Cap- stone software. The alignment procedure is described as below. Use the bubble leveler to make sure that the truck is perfectly horizontal. Make use of the adjustable legs if needed. Use the bubble leveler first along the track and subsequently perpendicular to the track. Position your eye, level with the track, at the 50 cm mark. Your cheek should be almost touching the track with your eyes directed to motion sensor A. Adjust the tilt of the motion sensor so that you can see your reflection in the motion sensors reflective face. Follow the same procedure for motion sensor B. This procedure is crucial to the rest of the experiment turning out well. Get help from your TA with this part if you need it!

One-Dimensional Collisions - 10 EXPERIMENT 1(b): HOW TO TAKE MEASUREMENTS Open ”1D Collisions.cap”. Different pages will be available in this file. You can toggle among the pages by clicking on the heading names. The first page by default shows the experiment’s outline. Click on the page video ”Instruction 1” to learn how to use the PASCO Capstone graph interface and how to take measurements from a graph. Click the on the video to have it started. You can re-click on the video to pause the video as well. During the course of this video, the initial and final velocities of Cart A, from the data on the graph will be measured. Record the values given in the video below in Table 1. Table 1: Velocities measured in the instructional video Data Run Results Run #1 Initial Velocity = Final Velocity = EXPERIMENT 1(c): ELASTIC COLLISIONS Figure 8: An elastic collision between two carts. Showing (a) before the collision: cart A has initial velocity v iA , and cart B is at rest, v iB = 0; (b) after the collision: cart A has final velocity v fA , and cart B has final velocity v fB . 0 297 M/s 0 077 m/s

One-Dimensional Collisions - 11 OBSERVATION: ELASTIC COLLISION BETWEEN CARTS WITH EQUAL MASS APPARATUS Linear track, two motion sensors, two collision carts, computer with PASCO Cap- stone software. METHOD (1) Watch the collision videos in the page heading ”Collisions Video” - A Simple Experiment. Click I to start a video. (2) Make a prediction as to which video best represents an elastic collision between two carts of equal mass where one cart is initially at rest. Circle your prediction below. Prediction: (A) (B) (C) Note: you will not lose marks if your prediction is wrong, but you will if you don’t make a predic- tion! (3) With the track satisfactorily levelled, place both collision carts on the track so that the sides of the carts labelled ‘ elastic ’ are facing each other. With one cart stationary, give the other cart a gentle push so that it rolls towards the other at constant velocity. Watch how the velocities of each cart change after they collide. Was your prediction correct? (Yes) (No) (4) Now, roll one cart slowly, and the other at least twice as fast, towards each other so that they collide. Observe again how the velocities of the carts change after they collide. Question: Carts of equal mass collide in an elastic collision, where cart A has an initial mo- mentum p A and cart B has an initial momentum p B . What would you expect the final momenta of cart A and cart B to be? Cart A will have a final momentum that is equal to the initial momentum of cart B because [Pf = EPi . This means that PfB = PiA -

One-Dimensional Collisions - 12 EXPERIMENT 2: INVESTIGATION OF AN ELASTIC COLLISION USING PASCO CAPSTONE SOFTWARE APPARATUS Linear track, two motion sensors, two collision carts, metal bar, electric balance, computer with PASCO Capstone software. INTRODUCTION To study the law of conservation of momentum for an elastic collision, you will perform a series of experiments to investigate how the initial velocity and mass of each cart involved in a collision affects the final velocities of the carts after a collision, thus we will study METHOD Click on the ”Elastic Collision Page” . Measure the mass of each cart and the metal bar using the electronic balance and record your results in the section Data before Table 2. The mass of the carts are very similar and you will place the metal bar on cart A to increase its mass. In this experiment, PASCO Capstone will provide graphs of the total momentum vs time and total kinetic energy vs time . In order for PASCO Capstone to provide these graphs, you must register the mass of each cart in PASCO Capstone . To register the masses of the carts in PASCO Capstone , click the Calculator button on the PASCO Capstone left side of the screen under Tools. A window will pop up. Select and double- click M 1 from the list. Enter your measured value for the total mass of cart A (cart + metal bar) in kg. This will be the mass of cart A in the experiment. Select and double-click M 2 . Enter the mass of cart B and then click the accept button . Be sure not to click the delete button by mistake . Center Cart B at around the 70 cm mark on the linear track with it’s ‘elastic’ end facing motion sensor A. With cart B stationary, hit the PASCO Capstone record button and give cart A a push towards cart B to begin collecting data (as in Figure 8). The computer screen will display the veloc- ity vs time , total momentum vs time and total kinetic energy vs time graphs for both cars. Measure the initial velocity v iA of cart A, the final velocities v fA and v fB of carts A and B respectively. Also measure the total initial momentum p i , total final momentum p f , total initial kinetic energy K i and total final kinetic energy K f for carts A and B. Record the measured values in Table 2. Repeat the experiment two more times. To delete previously taken plots, go to ‘Experiment’ menu. Note, in PASCO Capstone , if the entire plot area (3 plots) is not fully visible within the screen area, click on the graph and press the scale axes button to rescale your screen resolution. DATA Mass of cart A Mass of the metal bar Total mass of cart A = mass of cart A + metal bar Mass of cart B 498 29 498 29 996 49 498 39

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