Lab07-Crash Lab-Capstone

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Pennsylvania State University *

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211

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Physics

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Dec 6, 2023

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1 Physics 211R: Lab – Crash Lab Physics 211R: Lab Crash Lab (Impulse, Momentum & Energy) You are just started your job as a research assistant in the Crash Lab, which studies what happens to vehicles and their occupants during crashes and thus how to design cars so that crashes are less likely to seriously injure passengers. (There is such a lab like this at Penn State, the Larson Institute Crash Safety Research Facility – check out their website sometime at http://www.larson.psu.edu/crashSafety ). Before they let you crash real vehicles, you need to prove that you can analyze a crash on a scale model, which is what you will be doing today. In particular, you have been charged with answering these specific questions from actual crash data that you will collect: I. Is an individual vehicle’s linear momentum ( p = m v ) conserved during a collision? II. Is the total linear momentum ( P = p 1 + p 2 ) of the system of two vehicles conserved during a collision? III. Is the total mechanical energy ( E = K + U ) of the system of two vehicles conserved during a collision? (Is it the same before & after the collision?) What about just K? IV. Does the type of collision – that is, whether the vehicles bounce off one another or whether the vehicles stick together – affect what happens to the momentum and the mechanical energy? V. In a collision between a stationary vehicle and a moving vehicle, which vehicle experiences the larger change in momentum? VI. In a collision between a more massive vehicle and a less massive vehicle, which vehicle experiences the larger change in momentum? Warm-up: As you prepare for your test, you review in your mind some basic relationships among the quantities involved: kinetic energy ( K ), velocity ( v ), momentum ( p ), and average net force ( F avg ). Label the relationships on your printed sheet (the last page of this file) . K v p F avg You also refresh in your mind a useful tool for visualizing what happens to the momentum of an object or system during a collision or some other interaction. For example, the diagram to the right shows the momentum graph for a car moving in the positive x- direction brakes momentary (interacting with the road through friction) before continuing to coast. On your printed sheet (the last page of this file), draw the p x (t) graphs asked for http://www.carbuyingtips.com/disaster.htm p x t

2 Physics 211R: Lab – Crash Lab Crash Lab (Impulse, Momentum & Energy) Reading: HRW: Chapter 9, Sections 4-10 Knight: Chapter 11, Sections 1-4; Conceptual Understanding Goals: By the end of this laboratory, you should be able to: (1) Determine the impulse exerted on an object from its mass and change in velocity. (2) Determine the average force on an object during a collision given its impulse and the duration of the collision. (3) Determine whether momentum is conserved in a collision. (4) Determine whether kinetic energy is conserved in a collision. (5) Articulate the conditions for momentum and/or energy to be conserved in a collision. Laboratory Skill Goals: By the end of this laboratory, you should be able to: (1) Use the calculator feature of Capstone to graph momentum and kinetic energy as a function of time. (2) Design an experiment to explore conservation of momentum and kinetic energy. (3) Draw reasonable conclusions about momentum and kinetic energy conservation based upon experimental data. Equipment List: Computer with Capstone™ and Pasco® 550 Universal Interface Ultrasonic Motion Detectors Dynamics collision cart Extra mass (500 g) 2-meter long low-friction track (shared between two adjacent groups) Sharing Data: You will be sharing equipment with a neighboring group for this lab. You will gather data as a group of 6 students on one computer and then share the data, which will then be opened on another computer for analysis. The analysis portions of the lab will be completed in the usual groups of 3 students. To share data: 1) finish gathering your data on the 1 st computer, 2) click ‘File’, then ‘Save Experiment As…’, 3) save a .cap file to a known location, 4) email the .cap file to a member of the other group, 5) download the .cap file to a known location on a 2 nd computer, 6) launch the Capstone software on the 2 nd computer, 7) open the .cap file on the 2 nd computer. 8) Each group completes the lab individually. Place a Motion Sensor on one side of the track and a blue Motion Sensor on the other side. The Motion Sensor plug into the PasPort1 and PasPort2 ports of the same 550 Interface. You can set up your motion sensors, settings within Calculator and graphs without the sensors being plugged in and unplugging the motion sensors does not mess up your settings or data already collected.

3 Physics 211R: Lab – Crash Lab Motion Sensor setting: Since collisions occur over a very short period of time, set the sample rate to 50 Hz. Your vehicles: You have two vehicles that look identical but there is one important difference. One vehicle is labeled (“attract” and “repel”) and whichever end is pointed at the other vehicle indicates how the two will act towards one another (there are magnets in the carts to exert attractive or repulsive forces on each other). This is useful if you want to create collisions in which the vehicles bounce (even without touching!) or stick together. In addition, you can make one vehicle more massive than the other by adding the black bar (about 500 g) to the top of one of the vehicles. ( Generally, run collision experiments with cars of different masses .) In designing your experiments to answer the questions that have been posed to you, you will want to consider:  What will be your coordinate system? Will both your motion sensors use that coordinate system by default (and if not, how can you handle that)?  What variables (in the Capstone “Calculator”) will you want to define? What will those definitions (equations) be?  What kind of graphs will you want to view?  While these are low-friction carts, they are not zero-friction carts, so how will you account for friction in interpreting your graphs? (For example, if the kinetic energy is decreasing over time, how will you separate any change in kinetic energy due to the collision with the change in kinetic energy that would have occurred during that time just due to friction?) Here are some important tips to make your life easier as you do your experiments:  Subscripts on quantities are vital for an experiment with both multiple objects and “initial” (before collision) and “final” (after collision) times. If the reviewer of your work can’t tell what quantities you are referring to, it’s quite unlikely that it will pass muster and you’ll be allowed to experiment on the “big toys”.  Use relatively low speeds so that when set up for “repel,” the cars don’t make contact; and when set up for “attract,” they don’t hit very hard (it will damage them and may have them “derail,” significantly increasing the friction acting on the car.  Use a blank Word file in which you record your raw data (e.g., masses of each car and whether the cars were set to attract or repel), your graphs for that run, and any comments or observations you have made about that run. Then pull from the file to answer the questions your have been tasked with answering experimentally.  When graphing any quantity to see if it is conserved, have the lowest value (or highest value if the quantity is negative) of the graph 0.  When determining p or K of a cart or the system before and after the collision, notice what is happening to the p or K before the collisions and decide what the best value for the momentum or kinetic energy “right before ” and “ right after” the collision will be.  If you want to compare a quantity before the collision with a quantity after the collision, you can calculate the % difference between the two values using the following equation (written for momentum, but if can be used for any quantity):

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4 Physics 211R: Lab – Crash Lab  If you change any mass, remember to update the Calculator with the new mass of your cart. If you do change a calculation, it will change all your past runs’ calculations, too.

5 Physics 211R: Lab – Crash Lab Physics 211R: Lab Report Template Crash Lab (Impulse, Momentum & Energy) (Type in this document and print these pages at the end of the laboratory) NOTE: Remember to SAVE this template as a Word document before starting the lab. Always remember to save your template periodically throughout the lab.  A maximum of three students will be allowed per group without prior instructor permission.  All the members of the group must participate in the activity. If a student is not participating (even when present) s/he may receive a score of zero in the activity. Students arriving 10 minutes or more past start will not be admitted.  This activity must be returned at the end of the lab period. All the students completing the activity must be present when handing this to the laboratory instructor; a student not present at this time may not get credit for the activity. Writing the name of a person not present is not permissible and may result in a potential academic integrity violation being processed.  After you receive the graded report back, you should make a copy of the front page (this page) and keep it for you records. This will serve as evidence of your grade for this activity.  You are responsible for checking your grade (in the course website) and report any mistakes to your laboratory instructor within two weeks after the activity. Date: ________________ Enter your name as it appears in your PSU registration, no nicknames please. Name: Section # Name: Section # Name: Section # Clean Up Check: After you finish working and completing the lab report, you need to clean and organize your working area. Then call one of your laboratory instructors who will check your area, initialize below and take the lab report. All the members of the group must be present at that time. If you leave the lab before your laboratory instructor performs the check up, you will be deducted 5 points from your score for this lab report. Laboratory Instructor Initials: _______ Score: _______

6 Physics 211R: Lab – Crash Lab Before you begin collecting any data, you will want to think about the physics of your situation. ( Do the Warm-Up on your printed sheet , the last page of this file, now if you haven’t done that already. ) Q1. Write an analytic expression for the total linear momentum of the system of the two cars (mass m 1 and m 2 ), with velocities v 1 and v 2 . Q2. Write an analytic expression for the kinetic energy of the system of the two cars (mass m 1 and m 2 ), with velocities v 1 and v 2 . Q3. For conservation of momentum to be satisfied, a system has to be isolated – that is, it has no interactions with other objects that result in a net force acting on the system. How could one of these cars be considered “isolated” even though it has both a gravitational force from the Earth and the normal force from the track acting on it? (Why would the track need to be level for the car to be “isolated”?) Q4. If the change in momentum is J =  p = F net  t , why might conservation of momentum be a reasonable approximate model for a system during a very brief collision, even if the system is not isolated? That is, the net force on the system , F net , isn’t zero – e.g., there is some friction with the road. Now here’s some nitty-gritty details to think about for setting up your experiment to collect data: Q5. While these are low -friction carts, they are not zero -friction carts, so how will you account for friction in interpreting your graphs? For example, if the kinetic energy is decreasing smoothly over time due to friction, how will you separate any change in kinetic energy due to the collision with the change in kinetic energy that would have occurred during that time just due to friction? Q6. On your printed sheet (the last page of this file): What will be your coordinate system for this experiment? ( Sketch your track, your motion sensors, and draw your coordinate system on this sketch ). Will both your motion sensors use that coordinate system by default (and if not, how can you handle that)?

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7 Physics 211R: Lab – Crash Lab Q7. What quantities will you want to graph in order to answer questions I – VI on page 2? [Hint: the graphs are not position, velocity, or acceleration! You will need a minimum of 4 graphs and all are of calculated quantities.] Q8. What variables (in the Capstone “Calculator”) will you want to define? [hint: Anything you graph, you probably want to define!] What will those definitions (equations) be? Now you are ready to do some experimenting! This is a good time to review the information on pages 3 (at bottom) & 4. Make sure to leave at least 30 minutes at the end to write your responses to the questions! Remember to save your plots and other data in a blank file so you can pull from that file when you need to refer to data in your responses to the questions posed to you. A couple tips: (1) Center your experiment on the track (2) Start data collection immediately after pushing the car(s) (3) There are two types of collisions (stick together or bounce) – be sure to test out both Q9. First, be sure to measure all your masses ( record these values on your printed sheet, the last page of this file ). Q10. TEST RUN: Do one data run with your calculations and plots set up in Capstone. Take the time to thoroughly review your data, calculations and graphs for this run to make sure everything is set up correctly before collecting any further data. Print the relevant graphs for this data run (e.g., use PrintScreen to print the screen so you get all the graphs on the same page) and annotate the graphs by hand to indicate what information you about able to extract from them . Check with an instructor at this point! Once you are sure that your setup and calculations are correct, collect additional data needed to answer all the questions that have been posed to you . The more data you have to make your case the better, but plan to spend at least 30 minutes answering these questions after you have collected your data.

8 Physics 211R: Lab – Crash Lab Q11. Now it’s time for you to marshal your data and make your report about your conclusions. For each question, provide a reasoned argument based on your data and show appropriate graphs and/or tables to support your arguments. Remember that a single experiment or data point is often not enough to be convincing. In addition, you need clearly explain how you accounted for friction. Just showing a graph is not sufficient since you must explain what the graph shows; in addition, think carefully about how you present your graph. I. Is the magnitude of an individual vehicle’s linear momentum (p = mv) conserved during a collision? (Explain why, including any necessary graphs.) II. In a collision between a stationary vehicle and a moving vehicle, how do their changes of momentum compare? (Explain, including any necessary graphs.) III. In a collision between a more massive vehicle and a less massive vehicle, how do their changes of momentum compare? (Explain, including any necessary graphs.) IV. Is the sum of the magnitudes of the cart’s linear momenta ( | 𝒑 𝟏 | ൅ | 𝒑 𝟐 | ) of the system of two vehicles conserved during a collision? (Explain why, including any necessary graphs.) V. Is the total mechanical energy ( E = K + U ) of the system of two vehicles conserved during a collision? (Is it the same before & after the collision?) What about just the kinetic energy? (Is there a dip in the kinetic energy during the collision when the cars are set to repel? Where might the system’s energy be during this time?) If E=K+U is not conserved, does that mean the law of conservation of energy has been violated? (Explain why, including any necessary graphs.) VI. Does the type of collision – where the vehicles bounce off one another or where the vehicles stick together – affect what happens to the momentum and the mechanical energy? (Explain why, including any necessary graphs.) Have fun doing crash tests on real cars now that you’ve proved yourself with the scale model cars!

9 Physics 211R: Lab – Crash Lab Physics 211R: Lab Report Template Crash Lab (Impulse, Momentum & Energy) PRINT THIS PAGE (p. 1) WHEN YOU BEGIN AND INCLUDE IN YOUR REPORT Warm-Up: As you prepare for your test, you review in your mind some basic relationships among the quantities involved: kinetic energy ( K ), velocity ( v ), momentum ( p ), and average net force ( F avg ). K v p F avg On the left, draw the momentum-time p x ( t ) graph for a block moving to the right that hits a wall and then bounces back with half the speed it originally had (assume no friction). On the right, draw the diagram if friction were present. Q6. What will be your coordinate system? ( Sketch the axes on this photo below ). Will both your motion sensors use that coordinate system by default (and if not, how can you handle that)? Q9. Measure all your masses (using the scale at the back of the room): Vehicle 1 (no labels): m 1 = __________________ Vehicle 2 (as in “2-faced”): m 2 = _________________ Black bar: m bb = _______________________ While the vehicles have different masses, when we want to compare a more and a less massive cart, we will put bars into one of the carts. p x t p x t

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