{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# Objects in Flight"],"metadata":{"id":"YhH6aukqPlIc"}},{"cell_type":"markdown","source":["In this lab, we'll be testing different models to describe the motion of objects in vertical flight (up and down).\n","\n","**By the end of this session, you will present to your TA your claim and evidence about the extent to which several objects can be described by different models of vertical flight.**\n","\n","## **Learning goals**\n","By the end of this unit, you should be able to:\n","\n","* Use physical models to make predictions and check to what extent results agree or disagree with predictions.\n","* Conduct follow-up experiments to explain why results disagree with predictions or to further probe a model when results agree with predictions.\n"],"metadata":{"id":"g6vn80J4NBxk"}},{"cell_type":"markdown","source":["## **Setup the Notebook**\n","Run the code cell below to mount your Google Drive and load the ``utilities.ipynb`` file as in previous weeks.\n"],"metadata":{"id":"74FZXs0RrqVy"}},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive')\n","\n","#Fill in the appropriate directory info in the ``...``\n","%run \"/content/drive/My Drive/.../utilities.ipynb\""],"metadata":{"id":"JvhLSlvRrqVz"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["\n","## **A. Exploring the models**\n","\n","We'll start by testing two simplified models about the forces that act on the objects in vertical flight:\n","\n","**Model 1:**  The only force on the object is due to gravity.\n","\n","**Model 2:** The only forces on the object are due to gravity and air drag.\n","\n","*Note: By averaging several sources, we estimate that $g_{Ithaca} = 9.80296 \\pm 0.00011$ m/s$^2$, although a change in altitude of $10$ m may change the value by $0.00003$ m/s$^2$.*\n","\n","**By the end of today's lab, you will present to your TA your claim and evidence and which, if either, of these two models best describes the motion of objects in vertical flight.**\n","\n"],"metadata":{"id":"G37Zgq6zrmM5"}},{"cell_type":"markdown","source":["To design our experiment, we're going to consider what evidence might help us distinguish whether one, the other, or neither of these two models are accurate representations of objects in vertical flight.\n","\n","**Q.** In a brief sentence, what basic physical properties characterize the air drag force?"],"metadata":{"id":"C0lAARzTJWXV"}},{"cell_type":"markdown","source":["**[Your answer here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"wC3mWPtuJfOa"}},{"cell_type":"markdown","source":["**Q.** Draw a free-body diagram for each of the models when the object is on the way up and on the way down (i.e. four free-body diagrams). Assume the drag force is smaller in magnitude than the weight of the object. (You can do this on a whiteboard, piece of paper, chalkboard -- whatever!)\n","\n","---"],"metadata":{"id":"xmqNGgt6Jhve"}},{"cell_type":"markdown","source":["**Q.** For each of the four free-body diagrams, predict how the object's acceleration should compare with the acceleration due to gravity alone (e.g., is the magnitude equal to/less than/greater than and in the same/opposite direction?).\n","\n","You should generate four predictions: one for each model on the way up and one for each model on the way down."],"metadata":{"id":"jB5Y_gYBJ9Zy"}},{"cell_type":"markdown","source":["**[Your FOUR predictions here]**\n","\n","Model 1 Up:\n","\n","Model 1 Down:\n","\n","Model 2 Up:\n","\n","Model 2 Down:\n","\n","\n","---\n","\n"],"metadata":{"id":"CIUgbHtYKTH-"}},{"cell_type":"markdown","source":["**Q.** Discuss your free-body diagrams and predictions with another group."],"metadata":{"id":"tVw6v1jqsQzi"}},{"cell_type":"markdown","source":["**[Compare your FBDs and predictions to those of another group]**\n","\n","---"],"metadata":{"id":"rnHyfm2tJsp0"}},{"cell_type":"markdown","source":["## **B. Designing an experimental plan**\n","\n","Next, we'll design an experiment to test which model better describes your data.\n","\n","To collect data, you can use the sonic rangers connected to the lab computers to monitor and graph positions and velocities as functions of time.\n","\n","Try out the apparatus to see what it can do and how the software works. After playing around, talking to other groups, and talking to the TA, start your experimental design by answering the following questions."],"metadata":{"id":"pUluI9f7KquP"}},{"cell_type":"markdown","source":["**Q.** In a few sentences, what does the sonic ranger do and how can you use it to measure acceleration of an object in vertical flight?"],"metadata":{"id":"snT7C43cLKRa"}},{"cell_type":"markdown","source":["**[Your answer here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"uvH5EXPvLnDD"}},{"cell_type":"markdown","source":["There are multiple ways to measure acceleration from the sonic ranger data. One way is to ask LoggerPro to plot the acceleration as a function of time. Another way is to ask it to plot the velocity as a function of time and then find the slope of your region of interest. **Make sure you figure out how to perform the measurement both ways**. Ask your TA for help if you need to.\n","\n","*Note:* To get the acceleration from the velocity data, select your region of interest **(be thoughtful when making this selection)** -> click on the Linear Fit button on the toolbar at the top of the screen. A box should pop up over your selected region that gives you the slope with an estimated uncertainty value. If the uncertainty values are not visible, double-click the box. A menu should appear that allows you to toggle on uncertainties.\n","\n","**Q.** Why might it be better to estimate the acceleration from measures of velocity rather than from the software's estimate of the acceleration?"],"metadata":{"id":"YWam1_V7LpiS"}},{"cell_type":"markdown","source":["**[Your answer here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"uIMTmsPhLxqM"}},{"cell_type":"markdown","source":["**Q.** What are your main sources of uncertainty in estimating the acceleration and how will you quantify them? As you respond, consider the following:\n","*   if the uncertainty measure from Logger Pro sufficiently captures your sources of uncertainty,\n","*   if there are more systematic (rather than random) differences between trials, and\n","*   whether you necessarily need to conduct repeated trials for each object."],"metadata":{"id":"U_nBjqvELzgd"}},{"cell_type":"markdown","source":["**[Your answer here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"Ra0zHXcoMBkS"}},{"cell_type":"markdown","source":["**Q.** Where along the object's path will you measure acceleration and at how many positions along the trajectory?\n","\n","Consider, for example, the benefits and drawbacks of averaging measurements across a range of the object's trajectory. Justify your decision, referring also to your free-body diagrams and their predictions."],"metadata":{"id":"8zIfFI5vMGmy"}},{"cell_type":"markdown","source":["**[Your answer here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"QR01L8HOMjaG"}},{"cell_type":"markdown","source":["## **C. Data and analysis**\n","\n","Use the code cells below to record and analyze your data. Some code that may be of use to you is given below and you are welcome to copy over code from last week, write your own, etc. Be sure to comment your code so it's clear what data the analyses and outputs correspond to. You can also create separate code cells to run different analyses separately."],"metadata":{"id":"HL9sUeqSN2vw"}},{"cell_type":"markdown","source":["**[Brief (2-3 sentences) description of your experimental method, including the object you choose to use and how you are getting data.]**\n","\n","\n","\n","\n","\n","\n","---\n","\n"],"metadata":{"id":"RsmOsYODVS6W"}},{"cell_type":"code","source":["# Object 1 data\n","## Measurements of acceleration on the way up and down (# of Trials = ... , Other details = ...)\n","O1_acc_up_data = np.array([...])\n","O1_acc_down_data = np.array([...])\n","\n","## Estimate of the accleration on the way up and down (e.g., mean if # Trials > 1)\n","O1_acc_up_est = ...\n","O1_acc_down_est = ...\n","\n","## Uncertainty in the estimate of acceleration on the way up and down (e.g., SU if # Trails > 1)\n","O1_acc_up_unc = ...\n","O1_acc_down_unc = ..."],"metadata":{"id":"iPIWWsgGPEnj"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["The code cell below is set up with **one way** (there are others!) to compare your measurements to values predicted by Model 1."],"metadata":{"id":"Jg_65xvXtQw5"}},{"cell_type":"code","source":["# Comparing measurements to predictions from Model 1\n","\n","## Predictions\n","M1_acc_up_pred = ...\n","M1_acc_up_unc =\n","\n","M1_acc_down_pred = ...\n","M1_acc_down_unc =\n","\n","\n","## Compare data to Model 1\n","t_M1_O1_up = t_prime(M1_acc_up_pred, M1_acc_up_unc, O1_acc_up_est, O1_acc_up_unc)\n","\n","t_M1_O1_down = ...\n","\n","print(\"Way up: Acceleration = \" + str(\"%.2f\" % O1_acc_up_est) + \" m/s^2 +/- \" + str(\"%.2f\" % O1_acc_up_unc) + \" m/s^2\")\n","\n","print(\"t-prime (compared to Model 1 prediction) = \" + str(\"%.2f\" % t_M1_O1_up))\n","\n","print(\"Way down: Acceleration = \" + str(\"%.2f\" % O1_acc_down_est) + \" m/s^2 +/- \" + str(\"%.2f\" % O1_acc_down_unc) + \" m/s^2\")\n","\n","print(\"t-prime (compared to Model 1 prediction) = \" + str(\"%.2f\" % ...))\n"],"metadata":{"id":"SLWMay2xRpsv"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["**Q.** Based on this output, what is your tentative claim about the extent to which your data are modeled by Model 1?"],"metadata":{"id":"9ok5xvGmGMcx"}},{"cell_type":"markdown","source":["**[Your claim and evidence here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"UgQbd2pQGU0N"}},{"cell_type":"markdown","source":["Set up the next code cell to compare your measurements to values predicted by Model 2. **Be aware that you do not need to test Model 2 in the exact same way you tested Model 1.**"],"metadata":{"id":"j17yI2FztXcp"}},{"cell_type":"code","source":["# Comparing measurements to predictions from Model 2\n","# (You don't need to copy the exact analysis you did above -- think critically about how you'll test Model 2)\n","\n","..."],"metadata":{"id":"yZrUO4-4VgUr"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["**Q.** Based on this output, what is your tentative claim about the extent to which your data are modeled by Model 2?"],"metadata":{"id":"ge-tzgyKtdMY"}},{"cell_type":"markdown","source":["**[Your claim and evidence here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"4sPh2scktdMY"}},{"cell_type":"markdown","source":["## **D. Iterating and extending**\n","\n","Based on your results, design and conduct a follow up investigation, such as:\n","* If your data are described by BOTH models, work with your group to design an improved procedure to better distinguish them.  \n","* If your data reject one of the models, repeat your procedure with another object to test the generalizability of this finding.\n","* If your data are not described by EITHER model, check your predictions, repeat your procedure with another object and/or construct a new model that is consistent with your data and design a new experiment to test the new model.\n","\n","***Notes about philosophy of science:***\n","A Popperian \"falsification\" view of science is one where models can only be proven to be false -- they cannot be proven true. Thus, evidence in support of a model does not prove the model is true -- it only adds weight to the evidence in favor of the model. Evidence that refutes a model, however, does mean the model is false (or limited). Further, evidence that rejects one model does not necessarily mean that the other model is correct.\n"],"metadata":{"id":"b738AzJYTgd2"}},{"cell_type":"markdown","source":["**[Your follow-up design here, including justification that draws on the items above. Please be thorough in describing and justifying your experimental procdeure.]**\n","\n","\n","\n","---\n","\n"],"metadata":{"id":"A8LB0Vi-T3sE"}},{"cell_type":"code","source":["## Your follow-up data and analysis here, copying code starters from above"],"metadata":{"id":"d41Je9xNUZpN"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["\n","*Note:* You should not remove anything above to replace it with \"good\" experiments or data. There is no single correct experiment here and each experiment should necessarily inform the next. Showing your evolving process will be graded more highly than just documenting a single \"good\" experiment."],"metadata":{"id":"eB2TQFasJoyM"}},{"cell_type":"markdown","source":["**[Your ongoing claims and evidence here]**\n","\n","\n","---\n","\n","\n"],"metadata":{"id":"AroDQJ-jUgjE"}},{"cell_type":"markdown","source":["Continue exploring your objects in flight, iteratively proposing modified methods and models to explain your results. Continue to document your methods, results, and interpretations by adding Text and Code cells below.\n","\n","---\n"],"metadata":{"id":"wx8Q6b2NIs-L"}},{"cell_type":"markdown","source":["## Lab Checkout\n","\n","By the end of the lab session, document below a claim about **the extent to which various models best describes the motion of different objects in vertical flight** and briefly summarize your evidence that supports your claim. Present your claim to your TA or (if you are out of time), they will look over these notes to evaluate your claim.\n","\n","In the checkout, they will be looking for:\n","* Whether the claim is supported by evidence,\n","* Whether that evidence is sufficient, and\n","* Whether it is clear that you collected the data."],"metadata":{"id":"NZVszqMKnipN"}},{"cell_type":"markdown","source":["**[Your response here]**\n","\n","\n","---\n","\n"],"metadata":{"id":"kQwO7eQVoMfr"}}]}