phys172_lab12_jkain

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Ivy Tech Community College, Indianapolis *

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Dec 6, 2023

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4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 1/9 LAB 12: Translational Motion vs Rotational Motion Double-Click (or Edit) to provide the information below First Name: Joseph Last Name: Kain Lab Group: 26 Lab Section: Thursday 9:30 Learning Goals iterate through your solution to the CPE problem, estimate the angular momentum of a spinning object. Welcome to Lab 12! This week, we continue our work on C omputational P hysics E ssay ( CPE ). Please take your time to elaborate on the ideas generated in the previous labs. An example of CPE is provided for further guidance. In addition, there is an activity with heavy rotating objects presented in this lab. Let's get started. Pre-lab Notes Run the following Code cell to enable the programs provided in this lab to work properly. import numpy as np #for handling numbers and vectors import pandas as pd #for handling data and building tables import matplotlib.pyplot as plt #for plotting graphs Part 1: Computational Physics Essay 1.1. A New CPE Example Here another example CPE is presented to you. This is intended only for reference and inspiration. You don't have to repeat after it. Note its structure: introduction, body, conclusion. Just like in a standard essay. However, it is not a polished report where everything works out. Note the progression involved. For CPE, you need to tell a story of how you arrived at your conclusions and provide all necessary details along the way. Source: adopted from The University of Oslo Introduction

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 2/9 In volleyball, the goal is to make the ball hit the ±oor on the opponent side of the net. To get the ball into play, you serve the ball from behind the court, over to your opponents side, where they try to catch it. The strategy then is to make their initial catch of the ball as di²cult as possible, either by making the serve fast or unpredictable. A fast serve means that the ball spends the least amount of time in the air before making a potential contact with the ±oor, giving the opponent shorter time to react. A predictable serve means that it travels with some spin which results in a slightly curved trajectory of the ball. In this essay, we are interested in making the serve fast not unpredictable. Thus, the effects due to spin will be neglected. Note: expand this section to view it, then collapse before submitting the ±le. [ ] ↳ 15 cells hidden First Model Note: expand this section to view it, then collapse before submitting the ±le. [ ] ↳ 7 cells hidden Final Model Conclusion The total time it takes the ball to reach the ±oor will depend on the angle we provide. Of course, we cannot increase the angle inde³nitely because eventually the ball will start ±ying beyond the court. So, the trend is clear: the lowest allowed angle leads to the fastest serve . In our case, it was about deg with the horizontal. By changing the initial speed of the ball and height this value will change correspondingly. The actual e²ciency of such a serve is up for discussion, as where the ball lands in relation to the defenders plays a big role. 1.2. Your Work For this week, ±rst re±ne and review your problem statement. Address the following points in your group discussion. Brie±y outline your problem statement. State clearly: the client and stakeholders; criteria and constraints; explain the choice of any metrics (numerical values) stated Describe the design aspect of your problem. State which of the three principles - momentum, energy, angular momentum - you will apply to your problem solution. Explain brie±y how you intend to use the stated principles. To capture the richness of your discussion, please record your conversation (using a cell phone) and save it. Start your discussion by stating “This is Group # _ in PHYS Rm. __ on (day) at _ time" . EVERYONE in the Group MUST contribute to the audio-recorded discussion. The audio recording should be AT LEAST 4 MINUTES long. THE AUDIO RECORDING MUST BE CLEARLY AUDIBLE. If there are long pauses, you can pause the recording for a while and then resume it. However, make sure that you upload a SINGLE audio ³le at the end. Discussion Audio Recording

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 3/9 ONE PERSON per GROUP, please be sure to UPLOAD your AUDIO ±le in the link provided in Brightspace in the COMPUTATIONAL PHYSICS ESSAY folder. Failure to do so will result in loss of 10 points for your GROUP. Next, continue with your solution to the problem. Address new elements from the Rubric or elaborate on those already present. You can copy and paste any relevant sections from Labs 09-10 here. Provide relevant information from online resources or your own estimates. Edit your CPE draft in the Template if you have started it already. Problem Statement: Sports have a signi³cant relationship with physics, since nearly all of them involve exerting forces either on an object or even on another person for entertainment. One classic type of sport is called cue sports, more speci³cally billiards or pool. Billiards is a game that is often played on a table which involves a cue stick striking balls against each other or against the wall in order to sink them into the pockets around the edge of the table. Billiards, and other cue sports, is a game of skill in which a billiards player must precisely calibrate the correct amount of force and the correct approach angle in order to hit the ball perfectly so it doesn't ±y into the air or send the other ball in the wrong direction. In the case of a game of billiards, the player must understand how to correctly strike the cue ball to not only avoid hitting his opponent's balls but also precisley land his ball into the edge pockets. This essay will investigate the following questions: What is the ³nal velocity and distance of the second ball? How much time was the second ball in motion? The Rubric Elements DESIGN THINKING Stakeholders: The clients in this problem are people who want to learn about the spors (viewers, offcials, etc.)speci³cally poeple that require basic knowledge of how to play the game. Meanwhile, the users are the players, who require the knowledge and skills to prefrom their best in order to beat their opponent (they value the criteria of our problem). Finally, the stakeholders include everyone involves with the sport including manufacturers, broacasters, viewers, and players. Constraints: We are presented with multiple constraints with our problem including the dimenions of the board, the sizes of the ball, the masses of each ball, the frictional force acting on the ball, the inital force, how fast the ball is moving, the angle of approach. Criteria: Along with constraints, we are also presented with criteria for our problem. We must be able to determine the maximum velocity, the distance traveled, and total time of movement of the second ball. While determining a solution, we must acknowledge that both balls must remain on the table over the entire duration of time. Finally, we will need to understand the work done on the ball by the table in terms of friction. Assumptions: When calculating our solution we must mke some assumptions about the game of billiards, treating it as a series of elastic collisions. We must assume that a constant force of friction will act on the balls, while we can neglect the presence of air resistance. We are also assuming that the cue balls are perfectly smooth and circular, and equipment sustains (does not vary in e³cacy). This solution will be determined in stable and constant environmental conditions. Approximations: In addition, we have approximated the acceleration due to gravity is everywhere and friction is constant. Trade-offs: neglect some important variations in friction and environment to get our predicted calculations, which is necessary to make a simpli³ed baseline prediction Iterations: We will complete many tests with different starting scenarios such as varying initial velocities and varying masses. SCIENCE THINKING We will utulize the following scienti³c ideas: Momentum Principle Energy Principle Rotational kinetic energy Translational kinetic energy System: Both balls and the earth Surroundings: Table The momentum principle and energy principle will be used to help solve this problem. The system that we are using consists of both balls and the earth, while the surroundings that we will consider include the table and the forces from the cue stick. The system allows use to use momentum and energy princples to determine the ³nal velocity and distance of the second ball? The system also helps us determine how much time was the second ball in motion? When calculating an appropiate solution, we are able to consider both point particle and extended models.

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4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 4/9 MAHEMATICAL THINKING Momentum Conservation Principle: Energy Principle: ) CODING Codes are in the following boxes: g = 9.8# Gravitational Acceleration Constant m/s^2 R = 0.0285# Radius of Pool Balls m = 0.165# Mass of Pool Balls I = 2/5 *m*R**2 # Intertia of Sphere pi = 3.14159265 # pi constant w = 0 # Angular Velocity Vi1 = 1.9 # m/s of First Ball Vi2 = 0 # m/s of Second Ball Vf2 = Vi1 # Final Velocity of the Second Ball after the Collision Ktrans = 1/2 * m * Vf2**2 # Translational Kinetic Energy of Second Ball after the Collision w = 1.9 / R # Angular Velocity of the Second Ball after Collision Krot = 1/2 * I * W**2 # Rotational Kinetic Energy of the Second Ball after Collision print(f'w = {w}') print(f'Ktrans = {Ktrans}') print(f"Krot = {Krot}") w = 66.66666666666666 Ktrans = 0.297825 Krot = 0.11912999999999999 M = 0.165 # Mass of each pool ball R = 0.057 # Radius of each pool ball I = (2/5) * (M) * (R)**2 This concludes Part 1 of the lab. Part 2. The Conservation of Angular Momentum The effects of moving heavy rotating objects can often be counter-intuitive so it is important to be careful! Only sit on the rotating chair. Do not stand on it. When extending your arms, make sure there is no obstacle blocking them. Be alert for strong forces and sharp movements in unexpected directions. Keep the spinning bicycle wheel in the vertical plane when not collecting any data. Only use the wooden block to stop the bicycle wheel spinning. Do not use your hands. Tuck away all loose clothing, jewelry, and hair to avoid getting it tangled in the bicycle wheel. Keep plenty of free elbowroom. 2.1. Rotating Dumbells Measure the mass of one dumbell in kg, type it in the following Code cell and run the cell. EDIT CELL(S) BELOW

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 5/9 m_d = 2.26796 EDIT CELL(S) ABOVE Follow these setup instructions: Sit securely on the rotating chair with your center of mass approximately over the axis of rotation. Hold the two dumbbells at full arm’s length. One of your teammates should rotate the chair, not too fast since you will spin faster when you pull your arms in. Rotate for 1 to 2 revolutions, and then pull your arms in close to your body for 1 to 2 revolutions, and then re-extend your arms so that you won't get too dizzy! Another teammate should measure the time it takes for one revolution with the dumbbells out and again the time it takes for one revolution with the dumbbells in. For the person in your group who is willing to sit on the rotating chair and perform the experiment: Measure the distance, (m) between a dumbbell and the axis of rotation when arms are extended, Measure the initial rotational time period (s) when the dumbells are out and the ³nal period (s) when they are in, Calculate the corresponding initial angular speed (rad/s) and ³nal angular speed (rad/s) of rotation. EDIT CELL(S) BELOW #Type the distance between one dumbell and the center r_d = 0.78 #Type the initial period of rotation T_i = 2.56 #Type the final period of rotation T_f = 1.38 #The number pi is defined pi = 3.1416 #Type the initial angular speed omega_i = 2 * 3.1416 / (T_i) #Type the final angular speed omega_f = 2*3.1416 / (T_f) EDIT CELL(S) ABOVE FOR THE QUESTIONS Q01 - Q08 BELOW PLEASE FOLLOW THE GUIDANCE OF YOUR TA. Consider the rotation only AFTER the teammate(s) gave the push to the person on the chair. Q01: Choose (the person + rotating chair + dumbbells) as the system . What objects are in the surroundings ? The surroundings are the earth and the person applying a force to the chair. Q02: What is the total initial moment of inertia of the system ?

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 6/9 Write an expression for the moment of inertia of the dumbbells alone about the axis of rotation when the arms are extended. Use previously de³ned and . Assume that each dumbbell is a point mass. Denote the moment of inertia of the person + chair about the axis of rotation by . Assume that arms contribute negligibly compared to the whole body. You do not need to ³nd this quantity now. Since the moment of inertia is an additive quantity, combine and into . Q03: What is the total initial angular momentum of the system ? Assume the Z axis is pointing vertically upward. Express it in terms of , , , and . DO NOT PLUG IN ANY NUMBERS YET, KEEP THIS AS AN EXPRESSION IN SYMBOLS. Q04: What is the total ±nal moment of inertia of the system ? Estimate the moment of inertia of the dumbbells alone (about the axis of rotation) when they were brought in, close to the axis of rotation (i.e. ³nal position)? Assume that the distance between the dumbbells and the axis of rotation in that position is negligible compared to the length of an extended arm. Following this logic, does the moment of inertia of the rest of the system change? The intertia of the dumbells should be zero since the radius is considered to be zero between their center of mass and the axis of rotation. does not change due to the fact that the mass and radius of the chair remain constant Q05: What is the total ±nal angular momentum of the system ? Assume the Z axis is pointing vertically upward. Express it in terms of and . Q06: What is the net torque exerted by the surroundings on the system? Explain. The net torque is equal to zero becasue the mass is even on both sides of the pivot point and the only force acting after the push is gravity. Q07: What is the change of the angular momentum of the system from initial to ³nal states ? The Angular Momentum Principle dictates that (where is the duration of the impact of the torque), You do not need to know the exact value of . The angular momentum is conserved due to the fact that the torque value is equal to zero. Q08: Based on your answer to the previous question, obtain an expression for in terms of , , and . Use the relation with your expressions for and . DO NOT PLUG IN ANY NUMBERS YET, KEEP THIS AS AN EXPRESSION IN SYMBOLS .

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4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 7/9 Using the expression you derived above, calculate (kg*m^2) in the following Code cell using the expression you obtained above. #Type your expression for the moment of inertia I_o #Use m_d, r_d, omega_i, and omega_f defined ealier I_o = ( 2* m_d * r_d**2 * omega_i) / (omega_f - omega_i) print(f'The moment of inertia of (body + chair): {I_o} kg*m^2') The moment of inertia of (body + chair): 3.2273916479999993 kg*m^2 2.2. Spinning Wheel There are PASCO bicycle wheels (aka Gyroscope) in the room. To spin the bicycle wheel there is a motor station. Place the wheel against the hub on the motor and step on the foot switch. Be careful as you move about the room. Make sure you have no loose items (scarves, ties, necklaces, etc.) that could get caught in the wheel’s spokes. Do not tip the bicycle wheel until you have plenty of elbowroom. DO NOT try to stop the spinning wheel with your hand or other body part – have your teammate ±rmly hold the wooden block with two hands and use it to slow the wheel. Follow these setup instructions below. One PERSON should: Sit on the stool without rotating initially. Not touch the ±oor so it can rotate freely. Another PERSON should: Use the motor to spin up the bicycle wheel. Orient the spinning wheel in the horizontal plane so that the wheel is spinning counterclockwise when viewed from above. Hand the spinning wheel to the teammate sitting on the stool. Invert the wheel by 180 deg. You will notice that the chair starts rotating. Measure the time it takes for the person on the stool to complete 1-2 revolutions. Stop the chair before getting dizzy. Then stop the wheel. NOTE: The person on the chair should be the same person who volunteered for the previous section. Otherwise, measure again. Type the number of rotations you have measured and the time it took in the Code cell below and run it. It will calculate the period and the angular speed of rotation. #Type the number of revolutions recorded n = 1 #Type the time of the recorded revolutions in s t = 3.88 pi = 3.1416 T = t / n #the period of rotation in s omega = 2 * pi / T #the angular speed in rad/s print(f'The period of rotation was: {T} s') The period of rotation was: 3.88 s

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 8/9 De³ne the system as (the person + rotating chair + the wheel) and everything else in the surroundings. Assume, for simplicity, that the wheel’s axis coincides with the rotating chair’s axis. FOR THE QUESTIONS Q09 - Q15 BELOW PLEASE FOLLOW THE GUIDANCE OF YOUR TA. Q09: Suppose that the angular momentum of the spinning wheel is in the +Z, write an expression for the angular momentum of the system BEFORE the wheel is ±ipped in terms of . Q10: What is the angular momentum of the bicycle wheel AFTER it was ±ipped over? [ Hint: Think about how the direction of rotational axis has changed.] Q11: Now consider the angular momentum of the rest of the system (body + chair) AFTER the wheel was ±ipped over. Assume its moment of inertia is the same as from Section 2.1. Denote the angular speed calculated earlier as simply . Express in terms of and and combine it with your expression for to ³nd the ±nal angular momentum of the system . Your answer should be an expression in terms of , , and . # This is formatted as code Q12: What is the net torque exerted by the surroundings on the system? Explain. The net torque is zero because the only forces acting ont he object is gravity and it is acting downwards. Q13: What is the change of the angular momentum of the system from initial to ³nal states ? The Angular Momentum Principle dictates that (where is the duration of the impact of the torque), You do not need to know the exact value of . Δ L = 0 Q14: Based your answer above, obtain an expression for in terms of and . Use the relation with your expressions for and . DO NOT PLUG IN ANY NUMBERS YET, KEEP THIS AS AN EXPRESSION IN SYMBOLS. Q15: Calculate (kg*m^2/s) in the following Code cell using the expression you obtained. #Type your expression for the moment of inertia L_w #Use I_o found in Section 2.1 and omega found earlier L_w = I_o * omega_f/2 print(f'The angular momentum of the wheel (magnitude): {L_w} kg*m^2/s') The angular momentum of the wheel (magnitude): 7.347227247359998 kg*m^2/s This concludes Part 2 of the lab.

4/6/23, 12:48 PM phys172_lab12_jkain.ipynb - Colaboratory https://colab.research.google.com/drive/1PCQT5BCekYTsSqsKeeL6__AdxIau_fkJ#scrollTo=vJ4nKMXncCQw&printMode=true 9/9  0s completed at 12:46 PM Post-lab Notes Please follow the directions on Brightspace for uploading this Notebook in both IPYNB and PDF format . Please make sure to expand ALL the cells with your work so that it's visible to your TA for grading. If some part(s) of your Notebook is cut off when printed as PDF, then try using a Jupyter Notebook to PDF converter online.

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