1 One Dimensional Horizontal Motion Position vs. time


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1 PHY115 Experiment 1 One Dimensional Horizontal Motion Position vs. time One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration vs. time. From such a graphical representation, it is possible to determine in what direction an object is going, how fast it is moving, how far it traveled, and whether it is speeding up or slowing down. In this experiment, you will use a Motion Detector to determine this information by plotting a real time graph of your motion as you move across the classroom. The Motion Detector measures the time it takes for a high frequency sound pulse to travel from the detector to an object and back. Using this roundtrip time and the speed of sound, you can determine the distance to the object; that is, its position. Logger Pro will perform this calculation for you. It can then use the change in position to calculate the object s velocity and acceleration. All of this information can be displayed either as a table or a graph. A qualitative analysis of the graphs of your motion will help you develop an understanding of the concepts of kinematics. walk back and forth in front of Motion Detector OBJECTIVES Analyze the motion of a student walking across the room. Predict, sketch, and test distance vs. time kinematics graphs. Predict, sketch, and test velocity vs. time kinematics graphs. MATERIALS Power Macintosh or Windows PC LabPro or Universal Lab Interface Logger Pro Vernier Motion Detector meter stick masking tape Physics with Computers 11
2 Experiment 1 PRELIMINARY QUESTIONS 1. Use a coordinate system with the origin at far left and positive distances increasing to the right. Sketch the distance vs. time graph for each of the following situations: An object at rest An object moving in the positive direction with a constant speed An object moving in the negative direction with a constant speed 2. Have me come by and initial your sketches. You will need to include this sheet with your report. PROCEDURE Part l Preliminary Experiments 1. Connect the Motion Detector to DIG/SONIC 2 of the interface. 2. Place the Motion Detector so that it points toward an open space at least 4 m long. Use meter sticks to mark the 1 m, 2 m, and 3 m distances from the Motion Detector. 3. Inside the Physics with Vernier folder, open the experiment file 01a Graph Matching. One graph will appear on the screen. The vertical axis has distance scaled from 0 to 4 meters. The horizontal axis has time scaled from 0 to 10 seconds. 4. Using Logger Pro, produce a graph of your motion when you walk away from the detector with constant velocity. To do this, stand about 1 m from the Motion Detector and have your lab partner click Collect. Walk slowly away from the Motion Detector when you hear it begin to click. 5. Try to match the shape of the distance vs. time graphs that you sketched in the Preliminary Questions section by walking in front of the Motion Detector. Do they match? 6. You do not need to save any of this data. When you are satisfied that the equipment is working properly, move on to part II. Part Il Distance vs. Time Graph Matching 7. Open the experiment file 01b Graph Matching. The distance vs. time graph shown will appear. 12 Physics with Computers
3 Graph Matching 8. Before you start, think about how you would walk to produce this target graph. Analyze each type of motion separately, for example, for the previous graph you have the following intervals to analyze: [0 to 1 s], [1 s to 3 s], [3 s to 6 s], [6 s to 7.5 s] (approximately), and [7.5 s to 10 s]. All these intervals of time represent different types of motion. For each of these intervals, you must know the distance covered and what was the average velocity in that interval of time. 9. To test your prediction, choose a starting position and stand at that point. Start data collection by clicking Collect. When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the computer screen. 10. If you were not successful, repeat the process until your motion closely matches the graph on the screen. Save your best attempt on your floppy disk, or a memory stick. You will need to include a printout with your report. A good strategy is to save each reasonable attempt; you can always delete the bad files later. 11. Open the experiment file 01c Graph Matching and repeat Steps 8 10, using a new target graph. 12. These questions need to be answered in your lab report: Interval (a) Describe how you walked to match each graph by completing the following table: Initial time t 1 (s) Final time t 2 (s) t (s) Initial position x 1 (m) Final position x 2 (m) x (m) Velocity v (m/s) You will need to be very organized and specific with regards to time intervals, positions, velocities, and directions! Divide the plots in time intervals first. Each time interval should refer to a type of motion, until that motion was changed. Therefore, time intervals are not necessarily equal to 1 s or 2 s, etc, it depends on how long a certain type of motion lasted. (b) What type of motion is occurring when the slope of a distance vs. time graph is zero? (c) What type of motion is occurring when the slope of a distance vs. time graph is constant? (d) What type of motion is occurring when the slope of a distance vs. time graph is 3 m/s? (e) What type of motion is occurring when the slope of a distance vs. time graph is +5 m/s? Physics with Computers 13
4 Experiment 1 REPORT For this experiment, your report should include the following, in this precise order: 1) Cover sheet with title of the experiment, number of the experiment, date, your name, instructor s name, course number, section number. 2) Attach the preliminary sketches initialed by me. 3) Printouts of your best attempt at matching the graphs 01b and 01c (choose only ONE example for each!). LABEL your printouts, i.e., give them a title. Every time you refer to your two printouts, refer to their title. Every graph or printout should always have a title/label. 4) Answer the questions in step 12. Question 12a needs to be answered for graphs 01b and 01c. 5) Attach the exercise page with all that is asked (a graph plotted manually). 14 Physics with Computers
5 Graph Matching Exercise Distance (m) Distance vs. Time t s A properly executed graph must contain all the following elements: 1) title; 2) labeled axis; 3) units on both axes; 4) a sensible choice of scale on the axes that makes FULL use of the graph paper. The slope is defined as the change in the vertical axis (generally called y, but for the graph shown it corresponds to s) divided by the change in the horizontal axis (generally called x, but for the graph shown it corresponds to t). In the graph shown, slope = s/ t. Data Set: Time (s) A car is observed to be moving in a straight line. The following positions are recorded at the time shown. Assume the position can be observed with an uncertainty of ± 10 m, and the time measurement uncertainty is ± 0.5 sec. Time (sec) Position (m) Plot a position vs. time graph, including vertical and horizontal error bars on each data point. Find the "best fit straight line" through the data using a ruler. When you draw the line of best fit it does NOT mean you will connect the dots!! You actually do not need to go through the real data points. Find the line that best represents the average behavior of your data points. Calculate the slope of the line of best fit. Use positions that lie exactly on the line of best fit. If none of the data points passes exactly through the line of best fit, extrapolate a new data point by reading the axes of your graph. Slope = (remember to write the UNITS) What is the physical significance of the slope in this case, i.e., what physical quantity does it represent? Physics with Computers 15
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