2. Activity-Based Questions choose a different analytic equation for your model. Are the values of the coefficients (A, B, etc.) that yield the best agreement different from what you estimated in part (d) List them here with appropriate units. 10 pts f) Explain how you can determine qy from the coefficients in your model that you found in part (e) or part (d). 10 pts Collect vertical data for the ride: To determine whether or not the gravitational acceleration of the cage in the Demon Drop is -9.8 m/s you'll analyze a video clip of the ride and then use an analytic mathematical modeling technique to determine whether you can find an "analytic equation that describes the motion of the falling cage. Open the Logger Pro Experiment file to obtain a video analysis setup. As you can see on the first frame of the movie, it has already been scaled based on the Cedar Point Park's claim that the Demon Drop cage falls 30 m by the time it reaches the level track. a) Take y vs. t data by clicking on the Add Point tool (6) near the top of the movie window. Then click on the same point on the cage in each frame. Logger Pro will then record the vertical position of the cage as a function of time. Hints: (1) To take data carefully, we suggest that you align the horizontal crosshair of the Add Point tool (6) with the lower edge of the cage and place the vertical line of the crosshair at the middle of the cage; and (2) If you mess up, start over by using the Clear All Data feature in the Data menu and then returning to the beginning of the movie. Fit your data with the appropriate equation. Make sure you have labeled the axis properly. g) After doing your video analysis and completing the questions above, pull down the Page menu and select Auto Arrange to display the y vs. t graph. Click on the graph and then copy and paste a copy of the graph with your curve fit here. Make sure your graph is labeled correctly. 20 pts b) Which equation will model your data? Call up the Model feature in the Logger Pro Analyze menu and choose the most appropriate general equation" to model the data (Proportional, Linear, Quadratic, Cubic, and so on.). Write down the algebraic equation that you will use to develop your model and explain why you chose it. Hint: Look at the answers you gave in section 1! 10 pts 3. Reflections on Your Findings a) Comment on how well the results of this experiment agree with the prediction of Newton's theory of Universal Gravitation, ay = -9.8 m/s2 Note: Small uncertainties in your measurements can lead to some variation in your results. 5 pts c) What do the coefficients (A, B, etc.) represent physically? The equation that you chose as your model in Logger Pro, after thinking about the kinematic equation you listed in 10. contains several coefficients (A. B, etc.). Please summarize how these coefficients are related to the physical quantities that describe the motion of the Demon Drop cage: its vertical acceleration (Qy), initial velocity (voy), and initial position (vo). 15 pts b) Compare the value of the cage's initial vertical velocity component voy from part 2 (e) to the value you estimated for the cage's initial velocity in question 2 (d). Could you have made a better estimate in 2 (d)? Explain. 5 pts c) In some experiments, you measure a quantity and compare it to an accepted or known value. In other experiments, you make an assumption and check whether or not it is consistent with the data. What did you do in this experiment? 5 pts d) Estimate the numerical values of the coefficients: You can use the prediction for the acceleration of the falling cage, Qy, and the data for the location of the bottom of the cage, yo, shown in the first frame of the movie for to = 0.00 s to calculate the expected values of some of the coefficients. Another fact you can use is that the cage had already fallen about 1 m in about 0.4 s before the first frame of your movie was recorded. Show your calculations and explain the reasoning used for estimating the values of A, B, etc. Then summarize your values for these coefficients along with units in the space below. Hints: (1) You may want to refer to the data table for initial position information; and (2) Logger Pro is set up with a conventional coordinate system where upward is the positive y-axis, so the predicted y-component of the acceleration is ay = -9.8 m/s 10 pts e) Check the model: Enter your estimated coefficients into the Logger Pro Modeling (i.e., Manual Fit) screen. Does the "model" line match the data? If not, think about the estimates you made in part (d). Start by adjusting the coefficients most likely to be off, such as the ones related to voy and yo. Make sure you have used minus signs in appropriate places, etc. If it is impossible to get good agreement, then you may need to 2. Activity-Based Questions choose a different analytic equation for your model. Are the values of the coefficients (A, B, etc.) that yield the best agreement different from what you estimated in part (d) List them here with appropriate units. 10 pts f) Explain how you can determine qy from the coefficients in your model that you found in part (e) or part (d). 10 pts Collect vertical data for the ride: To determine whether or not the gravitational acceleration of the cage in the Demon Drop is -9.8 m/s you'll analyze a video clip of the ride and then use an analytic mathematical modeling technique to determine whether you can find an "analytic equation that describes the motion of the falling cage. Open the Logger Pro Experiment file to obtain a video analysis setup. As you can see on the first frame of the movie, it has already been scaled based on the Cedar Point Park's claim that the Demon Drop cage falls 30 m by the time it reaches the level track. a) Take y vs. t data by clicking on the Add Point tool (6) near the top of the movie window. Then click on the same point on the cage in each frame. Logger Pro will then record the vertical position of the cage as a function of time. Hints: (1) To take data carefully, we suggest that you align the horizontal crosshair of the Add Point tool (6) with the lower edge of the cage and place the vertical line of the crosshair at the middle of the cage; and (2) If you mess up, start over by using the Clear All Data feature in the Data menu and then returning to the beginning of the movie. Fit your data with the appropriate equation. Make sure you have labeled the axis properly. g) After doing your video analysis and completing the questions above, pull down the Page menu and select Auto Arrange to display the y vs. t graph. Click on the graph and then copy and paste a copy of the graph with your curve fit here. Make sure your graph is labeled correctly. 20 pts b) Which equation will model your data? Call up the Model feature in the Logger Pro Analyze menu and choose the most appropriate general equation" to model the data (Proportional, Linear, Quadratic, Cubic, and so on.). Write down the algebraic equation that you will use to develop your model and explain why you chose it. Hint: Look at the answers you gave in section 1! 10 pts 3. Reflections on Your Findings a) Comment on how well the results of this experiment agree with the prediction of Newton's theory of Universal Gravitation, ay = -9.8 m/s2 Note: Small uncertainties in your measurements can lead to some variation in your results. 5 pts c) What do the coefficients (A, B, etc.) represent physically? The equation that you chose as your model in Logger Pro, after thinking about the kinematic equation you listed in 10. contains several coefficients (A. B, etc.). Please summarize how these coefficients are related to the physical quantities that describe the motion of the Demon Drop cage: its vertical acceleration (Qy), initial velocity (voy), and initial position (vo). 15 pts b) Compare the value of the cage's initial vertical velocity component voy from part 2 (e) to the value you estimated for the cage's initial velocity in question 2 (d). Could you have made a better estimate in 2 (d)? Explain. 5 pts c) In some experiments, you measure a quantity and compare it to an accepted or known value. In other experiments, you make an assumption and check whether or not it is consistent with the data. What did you do in this experiment? 5 pts d) Estimate the numerical values of the coefficients: You can use the prediction for the acceleration of the falling cage, Qy, and the data for the location of the bottom of the cage, yo, shown in the first frame of the movie for to = 0.00 s to calculate the expected values of some of the coefficients. Another fact you can use is that the cage had already fallen about 1 m in about 0.4 s before the first frame of your movie was recorded. Show your calculations and explain the reasoning used for estimating the values of A, B, etc. Then summarize your values for these coefficients along with units in the space below. Hints: (1) You may want to refer to the data table for initial position information; and (2) Logger Pro is set up with a conventional coordinate system where upward is the positive y-axis, so the predicted y-component of the acceleration is ay = -9.8 m/s 10 pts e) Check the model: Enter your estimated coefficients into the Logger Pro Modeling (i.e., Manual Fit) screen. Does the "model" line match the data? If not, think about the estimates you made in part (d). Start by adjusting the coefficients most likely to be off, such as the ones related to voy and yo. Make sure you have used minus signs in appropriate places, etc. If it is impossible to get good agreement, then you may need to