In addition to reading this assignment, also read Appendices A and B.

Transcription

1 1 Kinematics I Introduction In addition to reading this assignment, also read Appendices A and B. We will be using a motion detector to track the positions of objects with time in several lab exercises this semester. We will use a program called Logger Pro to control a LabPro interface connected to the USB port of your laptop to collect data from the motion detector and from other sensors. Your technical task in this first lab meeting is to install Logger Pro on your laptop, and collect some data. Your physics tasks are to measure your average walking speed and the average walking speed of your lab section, calculate the statistical variations in these results, and consider the following question: Is your walking speed above or below average? We will start with a theoretical model based on the assumption that your natural walking speed is constant. The position of an object moving in one dimension with constant speed v is described as a function of time t by x 2 = x 1 +v t (1) where t = t 2 t 1, and x 1 is the position of the object at t 1. This is a linear model. That is, it describes a position vs. time graph that is a straight line with slope v and intercept x 1. You will also investigate the motions required to produce nonlinear position vs. time graphs. Experiments Logger Pro Place the installation CD in the CDROMdrive of your Laptop. Runthe.exe file on the CD. Use the password written on the CD. Choose the standard installation options by clicking Next several times and then Finish. There should now be a Vernier Software tab on the Start -> Programs menu containing one item called Logger Pro. Average Walking Speed The motion detector can measure positions within a range of approximately meters from its front face. The ultrasonic pulses it emits spread out into a cone with a pitch of approximately 20. The detector tracks the loudest echo it receives, so it is important that the object of interest be the best reflector of sound within this cone. Chairs, lab tables, walls, and lab partners within the cone can lead to ambiguous results.

2 Although lab group members should help each other, each group member should complete the following steps with his/her own laptop to iron out any hardware or software problems. In future labs, one member of each lab group will collect data for the group. 1. Connect the LabPro interface to the USB port of your laptop with the cable provided. (No special driver or hardware configuration is required.) 2. Run Logger Pro. The software should automatically detect the LabPro interface and themotiondetector. Ifitdoes, youwillseeacollectbutton a blank data table, distance vs. time, and velocity vs. time graphs. inthetoolbar, 3. Place your motion detector on the counter along the wall so that it faces across the room. If you clear the area of people and chairs, there should a clear walking lane in front of the detector over 5 meters in length. 4. Press the Collect button to start data collection, and walk either directly toward or away from the detector. Try to walk at a steady, natural pace. You should see a graph of your distance from the detector vs. time in the Graph Window and a table of time and distance data in the Table Window, generated in real time. Somewhere in the neighborhood of 5-6 m, the detector will lose you in reflections from objects on the far side of the room. This is a good place to turn around and walk back toward the detector. 5. By default, Logger Pro collects data for 5 seconds at a sampling rate of 30 points per second. You can adjust these parameters using the Data Collection... button. The sampling rate is fine, but you may want to adjust the experiment length. 6. Use the motion detector and Logger Pro to measure your position vs. time as you walk toward or away from the detector at your normal walking speed. Gather at least 5 measurements covering as great a total displacement as possible. Click Experiment -> Store Latest Run to save the measurements you want to keep. A typical run may contain two or more intervals of walking separated by junk collected when the detector lost you or while you were turning around. This is not a problem, as the software allows you to select segments of a run for analysis. Graph Matching Match the shape of each of the distance vs. time graphs shown in Fig. 1 by moving either your body, or some object like a book, in front of the motion detector. Use Experiment -> Store Latest Run to save your graphs.

3 (a) (b) (c) (d) Analysis Average Walking Speed Figure 1: Some simple non-linear distance vs. time graphs. The slope of a graph of distance vs. time is velocity. You will use the linear regression function of Logger Pro to extract slopes and uncertainties from your measurements. 1. Drag with the cursor in the graph window to select a region on the graph that you would like to analyze. This should be a time interval during which you were walking at a steady pace. (How should a steady pace look on the graph?) If you have several stored runs, and would like to see only one displayed in the graph window, use Data -> Hide Data Set to hide the distractions. Use Data -> Show Data Set to bring back hidden runs. 2. Click the Curve Fit... button. If you have several runs stored, select the one you d like to fit. Choose the equation of a straight line (mx + b). Then click Try Fit

4 and Ok. 3. The best fit line should be shown on the graph along with a box describing the fit. This includes the slope (m) and intercept (b) values with uncertainties (standard deviations), along with the root mean square error (RMSE) and the correlation coefficient (Correlation). If you are unfamiliar with these quantities, see Appendix B. 4. Fit all of your walking measurements, and record each walking speed and its uncertainty. 5. Use File -> Save to save your entire Logger Pro session as an experiment file. All of your stored runs, the configuration of the motion detector, and any fits displayed on your graphs will be saved. 6. Enter your walking speed measurements into a column in a spreadsheet, and use the average() function to calculate a best value of your walking speed. Calculate the standard deviation using the spreadsheet function stdev(). The uncertainty in your best value is the standard deviation of the mean (the standard deviation divided by N). Write your result along with its uncertainty on the white board at the front of the lab. 7. Enter all of the individual average walking speeds from your lab section (on the white board) into another column of your spreadsheet. Calculate the average walking speed of your lab section and the associated standard deviation and standard deviation of the mean. Graph Matching Write a brief description of the motions you made to reproduce the distance vs. time graphs in Fig. 1. Keep sketches of the graphs and your descriptions with your class notes. This is a warm-up for our work with velocity and acceleration. Questions Go over your answers to these questions with your instructor before you leave lab. 1. Explain why 30 points per second is an acceptable sampling rate by giving examples of sampling rates that are too fast and too slow, and explaining why in each case. 2. Explain the different meanings of (a) the standard deviation of the slope reported by the fitting routine for each average walking speed measurement, the standard deviation and the standard deviation of the mean of (b) the set of walking speed measurements of a single student and (c) the set of walking speed measurements collected by the entire lab section. 3. Based on your observations, how consistent is the walking speed of a typical Ursinus student (a) during a single short walk and (b) from walk to walk? Use quantitative results from your analysis in your responses.

5 4. On the basis of your analysis of the available data, compare your personal average walking speed with that of a typical Ursinus student. Can you conclude that your walking speed is above average, or below average? (Assume here that your lab section is a representative sample of all Ursinus students.) 5. Go over your graphs and descriptions from the graph matching exercise.