Lab7_activity

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Physics

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Dec 6, 2023

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Physics 211 v1.0 Lab 7 Activity In today’s experiment you will explore how forces are exerted over the duration of a collision. Objectives for Lab 7: • Plot the evolution of forces acting on the IOLab during its collision with the rubber band • Discuss the time evolution of each force and compare it to the theoretical model • Write a report of your observation experiment. Preparation for today’s experiments: Before you do today’s experiments, you will need to 1. Check the calibration of your force probe [see Prelab 3 if you need a refresher]. If everything looks good, you do not need to recalibrate; If your calibration check gives a weird result you should recalibrate the force probe. 2. Attach the screw with the flat push plate to your force probe 3. Set up a board with two machine screws, two wing nuts and a rubber band, as shown. The rubber band should be suspended at a height such that the IOLab’s push plate will collide with the rubber band when the IOLab rolls into it. Figure 1. Board setup with screws and rubber band for Lab 7 experiment

Physics 211 v1.0 Plotting the evolution of the collision When we talk about collisions in Physics 211 we tend to focus on what happens before and after the collision, without looking much at what happens in the middle. You did something similar in Lab 6 where you measured change in momentum and impulse from the rubber band. Today we will return to the Lab 6 setup, but will focus on figuring out what is actually happening while the collision occurs. Your task today is to measure (directly or indirectly) the forces acting on the IOLab during the time that it is colliding with the rubber band and plot the evolution of the forces over time. Your investigation should span the time of the entire collision, starting with when the IOLab first contacts the rubber band and ending when the IOLab ends contact with the rubber band. To accomplish today’s task you will need to determine how to measure: 1. Force of the rubber band acting on the IOLab as a function of time 2. Force of friction in the wheels as a function of time 3. Net force of the IOLab as a function of time Using Excel, Google Sheets, Desmos, or the spreadsheet software of your choice , plot the time evolution of the three measurements above. Your plot should include axis labels and a legend, like that shown in Figure 2. A template Google Sheets file is available to help you get started. You may find it helpful to export IOLab data (See Appendix ). After you have made your plot , discuss the friction and rubber band force graphs with your group, comparing them to the theoretical plot shown in Figure 2. Based on your observations and your knowledge about friction and springs, decide whether this collision is closer to being inelastic or elastic and justify your answer in your report. Figure 2. An example of the kind of plot you should include in your report. This is the time-evolution plot of an ideal collision with a spring with a simple model of kinetic friction. A title, axis labels, and a legend have been included. Your own plot may be different than this theoretical example.

Physics 211 v1.0 Theoretical model of the collision: During the collision, your IOLab feels a force from the rubber band and from the friction of the device’s wheels rubbing on their axles. In Lab 2 you discovered that the friction in the wheels is large enough to impact your acceleration measurements on a ramp. The rubber band in this collision is like gravity in Lab 2 because it causes the IOLab to slow down, turn around, and speed away. Friction in the wheels is still present during this process. Friction in the wheels: So far in the lab we have modeled friction between the wheels as if the IOLab were feeling kinetic friction from sliding on the table. Under this model, friction is constant if the IOLab is moving, at a force around 0.05 N that opposes the velocity of the device. Force of the rubber band: Our theoretical model for this situation will model the rubber band as an ideal spring that follows 𝐹𝐹 = −𝑘𝑘𝑘𝑘 where 𝑘𝑘 is the displacement of the spring from its equilibrium position. The force of stretching or compressing of an ideal spring as a function of time is described by the equation 𝐹𝐹 ( 𝑡𝑡 ) = 𝐹𝐹 𝑚𝑚𝑚𝑚𝑚𝑚 sin( 2𝜋𝜋 𝑇𝑇 𝑡𝑡 ) where T is the time for the spring to undergo its full range of motion back and forth. The collision we are exploring only shows half of the full oscillation, after which the IOLab disconnects from the rubber band and the force becomes zero. Combining the forces to make our model : Figure 2 shows the modeled spring force (in yellow), the modeled friction force (in red), and the sum of the two forces together. The plot is not actual data – it is just a prediction based on how we have chosen to model the forces present in the collision.

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Physics 211 v1.0 Your report Write a report of your experiment containing the following sections: Introduction, Methods, Results, Analysis, Discussion, Conclusions. The structure below provides some general guidance for what belongs in your report. You should aim to write at a level that another student in Physics 211 could understand your report and have enough information to evaluate your work, including your measurement techniques. Refer to the Lab 7 rubric for further guidance, or feel free to ask your TA or LA for assistance. 1. Introduction: Give your reader a summary of the report that they will read, including any background information they may need to understand the report. 2. Methods: Describe how your experiment was carried out and why you decided to do it this way. Make sure your description is complete enough that another group could repeat your experiment just by reading the methods section. 3. Results: Use this section to show qualitative and/or quantitative results from your experiment, including the results of calculations, where relevant. Always include graphs of raw IOLab data. 4. Discussion: Point out interesting information from your results and explain the meaning of your results to your best ability. You should not introduce any new results in this section. 5. Conclusion : Summarize what you learned from this experiment (i.e., what your reader should have learned from reading your report) and any implications your results might have for future investigations.

Physics 211 v1.0 Appendix: Exporting raw IOLab data Your IOLab software can export spreadsheets showing the measurements taken at each time. This is useful when you want to manipulate and plot time-dependent data in external software. To export data from a sensor: Click the tool bar icon ( )under the sensor with the data you want to export. Figure 3. Force probe data in the IOLab software. The tool bar icon for the force probe is under the graph. Figure 4. Expanded tool bar The tool bar will expand (Figure 4). Click Export to CSV to save the data to your computer. Your data has been saved in your computer’s Documents folder. From the Documents folder, click IOLab- WorkFiles , then click export . You will see your files labeled with the export data and the sensor name. Figure 5. Raw data from the wheel sensor The data that will be most useful to you are in the columns labeled ‘ time ’ and ‘cal ,’ the calibrated measurement made by the sensor at that specific time. When you use the force probe, you will only see one ‘raw’ column and one ‘cal’ column. For the wheel sensor you will see three, which correspond to the following measurements: Position: raw[0] Velocity: raw[1] Acceleration: raw[2]

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