Motion 1 Equipment: DataStudio, motion sensor mounted about 25 cm above lab bench, Data studio files mot1.ds and mot2.ds. Lab Report: Describe procedures not given in the write up. Submit data graphs where asked. Label your work with the section numbers of this write up. 1 Introduction In part 1 of this lab you will set up DataStudio for the motion sensor and digits display. The motion of a notebook that you move with your arms will be examined as will various aspects of the digits display. As this is the first lab using DataStudio the instructions will be more detailed than they will be in future labs. Please remember the procedures for configuring the motion sensor calibration window, digits display set up window, input menu, and any other relevant operations. In Part 2 of this lab a curve of position vs time and a curve of speed vs time will be presented on the computer screen. The position and speed will be that of a notebook that you move in front of the motion sensor. The motion sensor will record the position or the speed of the notebook as you move it, and the data will also be presented on the computer screen. Your task is to move the notebook so that your data follows the presented curves as closely as possible. IMPORTANT: Before doing the experiments, look at the curves and infer what motion you must impart to the notebook so that your data most closely matches the curves! 2 The Motion Sensor The motion sensor uses sound waves to detect the distance of an object. Sound is a pressure wave that travels with a certain speed, depending on the type and temperature of the gas it is traveling in. For air at 20 deg C the speed is 344 m/s. Like all wave phenomena, sound can be reflected (echos). The motion sensor not only sends out the pulses but also detects the reflections. The motion sensor emits short sound pulses, each traveling at the speed of sound. The pulses are equally spaced in time, and the number of pulses emitted per unit time is called the sample rate. The sample rate gives the number of positions measured per second. The sample rate can be varied from 1 per second to 250 per second. The unit of per second is called a Hertz, or Hz for short. The default sample rate is 10 Hz. The pulses are ultrasonic (you cannot hear them), but you can hear a click. The motion sensor also detects the reflected pulses and measures the time between the emission and reflection of a given pulse using the Motion Timer. Keep in mind it measures the round trip time. The DataStudio digits display used can be programmed to give the round trip time of the pulses, distance from the motion sensor, velocity, and acceleration. What is measured is the round trip pulse time. The other quantities are calculated by DataStudio. The motion sensor is a 2 plug digital sensor. The yellow plug carries the transmitted signal and is inserted into channel 1 of the interface. The black plug detects the echo and is inserted into channel 2. The maximum distance that can be measured depends on the sample rate. Some of the motion sensors have a switch which allows you to choose between a pulse emitted in a narrow or somewhat broader cone. Choose the switch position that gives the best results. 1
3 Part 1 3.1 Programming DataStudio To program DataStudio for the motion sensor, open DataStudio by double clicking on it from the desktop then, choose Create Experiment. If you decide to close the Welcome to DataStudio window then go to top left corner and click setup, next choose interface and select science workshop 750, then click on Channel 1 and choose motion sensor from the scroll down menu. Under the measurements tab be sure to check Motion Timer, Position, Velocity, and Acceleration. Click the Motion Sensor tab to access the calibration window and then calibrate the sensor by putting a notebook 1 m from the grill of the sensor and clicking the set sensor distance button. Set the sensor distance equal to standard distance. What is the speed of sound? Can you think of why it might vary from day to day? In the experiment setup window the default sample rate of 10 Hz is shown. Change the sample rate to 100 Hz and observe the message dialog window that pops up. Next increase the sample rate to 200 Hz and again observe what the maximum distance the motion sensor can measure. Can you think of why the maximum distance depends on the sample rate? Set the sample rate to 20 Hz. Open a digits display by clicking Digits located in the Displays menu and select Position, Ch 1&2. (The m in parentheses means the units are meters.) Note that Position, Ch 1&2 will appear in the title bar of the digits display window. Now try the following. 2
Move the digits display window by dragging the title bar. See if you can enlarge the digits display window by dragging an edge or a corner. You should be able to enlarge the display and this will be useful. In order to add different digits displays to the same window, click and drag Digits 1 to the other measurements at the top. First try adding a Velocity Digits display by dragging it to where it says Velocity, Ch 1&2. Repeat for other items in the Data Menu and when you re done, close all displays except Position by right clicking on the display and selecting Remove Selected Data. 3.2 Measuring Position Move the motion sensor so that it is on one side of the lab bench and about 25 cm above the bench. Then sit across the lab bench from this sensor. Place a meter stick on the bench with one end in the plane of the sensor grill, and hold a notebook in your hands. Have your partner click the start button in the left experiment set up window and examine the digits display and meter stick while you move the notebook in the acoustic beam of the sensor. Click the STOP button when finished. Run # 1 appears in the data box. The digits display shows the last value measured. Do you think the number of digits to the right of the decimal point is sufficient? If not, increase the number to a reasonable value (Drag the right side of the window enough to the right so that all digits are displayed and then click the arrow of the 3.14 button in the box and select Increase Precision until it is at the desired precision. See next page for illustration) and justify that value. Take another run and see how close you can get the notebook to the sensor and get reliable values. Try deleting Run # 1 by clicking on it and pressing the delete key. Don t let too many runs accumulate. 3
3.3 Checking on DataStudio It is a good idea to see if the equipment is working as it should. For example, if I were an MD and about to declare someone brain dead, I might as well put the electrodes on my own head to be sure that the machine was OK. Here we will check up on DataStudio. Set up a stationary stable reflector about 0.6 m in front of the motion sensor. Open digits displays, for position and for the motion timer. Measure the position and the motion timer to 3 significant figures. Use the speed of sound and the motion timer to calculate the position. Compare your calculated value to the DataStudio calculated value as given in one of the digits displays. How do these values compare to what you get with a meter stick? What the motion sensor actually measures is the round trip pulse time. DataStudio then calculates the distance. Is it doing this calculation correctly? 3.4 Measuring Velocity Add Velocity to the digits display and take another run, seeing what happens as you move your notebook in various ways. What does a minus sign mean in the display? What does no sign mean? 3.5 Doing statistics on velocity Carry out an experiment to see how fast you can move your notebook toward and away from the sensor. Hint: Click the 3.14 button in the digits display and select statistics. Now click the and select Maximum. The digits display will now show the maximum velocity achieved. Repeat for minimum, Mean, and Standard Deviation. Between you and your partner, whose pulse is steadier? Hold the notebook at 1.0 meters from the motion sensor and record the average and standard deviation of the position. Now, have your partner do the same. The standard deviation will indicate to you whose hand shakes the most. Do you think the default sample rate of 20 Hz is OK for this experiment? You can change it if you want. To do so, delete all data and double click on the motion sensor icon in the right experiment set up window. Remember that if you increase the sample rate the maximum distance that the motion sensor will detect is reduced. 4
4 Part 2 4.1 The Library Experiments DataStudio has a library of experiments. Two of these are included in this lab. These experiments are mot1.ds and mot2.ds. 4.2 Library Experiment P01 To open the document titled mot1.ds, click on File, select open activity and look in My Documents. When you click on open activity a window will pop up asking Should DataStudio save this activity? ALLWAYS CLICK NO! After, click on mot1 and press open. Activate the graph entitled Position vs Time-Match Graph by double clicking Position vs Time-Match Graph in the Displays window. Determine the slope of the graph line and its uncertainty as follows: In the toolbar select Fit and then Linear Fit (Be sure to have the desired run highlighed before clicking Fit), and then click and drag to create a box around the part of the run essential to the slope of the graph. Click the smart cursor button in the toolbar in order to see the exact coordinates of a point. Move the smart cursor by clicking in the middle of the box and dragging it to the desired location. The smart cursor will automatically lock onto points in your run. 5
Examine the graph before you take data and predict what your motion should be. Create a similar graph to P01 by moving a notebook with your arms rather than using your whole body. Keep in mind that you will be moving backward, so be certain that the area behind you is free of obstacles. Watch the plot of your motion on the Graph, and try to move so that the plot of your motion matches the Position vs Time plot. Try several runs to obtain the best match. Press start to begin the recording of the data. Answer the following questions. How close should you be to the motion sensor at the beginning? How far should you move? How long should your motion last? Was your prediction a good one? In the graph, what is the slope of the best fit line for the middle section of your plot? What is the description of your motion? (Example:Constant speed for 2 seconds followed by no motion for 3 seconds, etc.). With respect to the motion of the notebook, does it matter how far you are from the motion sensor when you take the data, assuming that you are always within the operating range of the sensor? To print out a copy of the graph for your report, put your bench number on the title bar. Double click on the box in the graph that states Data. A graph settings window pops up and you can rename your graph in the Legend Title next check show legend title and click OK. After click File, and then Print. 4.3 Library Experiment P02 Open experiment mot2.ps in the same way that you opened mot1.ps. Again, click NO when asked Should DataStudio save this activity? DataStudio will not allow you to recreate the data set seen in PO2 similar to your experiment in PO1. Instead, print out the PO2 graph,cross out the label Position on the vertical axis(y-axis) and replace with Velocity.Analyze the graph and explain what is happening with regards to position, velocity and acceleration. Use the graph to answer the following questions: Which direction (positive or negative) would you go at the beginning? What is the maximum speed (positive or negative) you should achieve? How long would your motion last? Do not calculate any slopes of the given graph. Note your position vs. time graph as you match the given velocity vs. time graph. Make a very rough sketch of your position vs. time. The derivative of your position vs. time curve should roughly produce the given velocity vs. time graph. (Assume the corners of the velocity vs. time curve are rounded. Your position vs. time curve is the integral of the velocity vs. time curve.) 6
5 Finishing Up Please leave your lab bench as you found it. Thank you. 7