Kinematics using LabPro
1. How To Use the LoggerPro Interface
Open LoggerPro from the docking bar menu. Choose the sensor. Position measurements are initiated with the Start button.
The initial plot which appears on the screen is position vs time. The axes can be changed (e.g. from position to velocity or acceleration) by clicking on the labels. More graphs can be viewed simultaneously by selecting from the menu INSERT then GRAPH. Select from the menu PAGE, then AUTO ARRANGE to move the graphs into positions so they do not overlap each other. A change of the scale of the axes can be effected by moving the cursor onto the numerals located at the ends of the scales. As a box appears encompassing that number, click the mouse and the number will be selected. Type the desired scale end point value. The view of a particular area of the graph can be expanded by holding the command key down and using the mouse to draw a box around the area. The x and y coordinates of a graph can be read directly on the screen by choosing ANALYZE, then EXAMINE. Other choices of the ANALYZE menu allow you to obtain the slope at a point, the area under the curve, and a functional fit to the curve.
In the menu, select EXPERIMENT, then DATA COLLECTION in order to specify a sampling rate. Select an appropriate Data Rate and Collection Time. This selection window can also be obtain be selecting the icon that looks like an alarm clock.
You can also select from the main menu FILE, then SETTINGS FOR UNTITLED (The word "UNTITLED" will be replaced by the name of the file that you have saved it under if you have already saved your work.) You can now choose the number of points that LoggerPro uses in the calculation of velocity and acceleration from the position and time data. Choose a reasonable value for the determination of velocity and acceleration. Note that the choice of these parameters may vary from one week to the next depending on the experiment. Note that you may need to change these parameters during a single lab. Check that the detector is calibrated by measuring the distance the sensor is from an object and collecting some data to see if these values correspond.
The Motion Detector operates on the same "echo" principle by which bats are able to "see", by sending ultrasonic pulses and measuring the round trip time interval it takes for the sound to travel from the detector to the object of interest and then to return to the detector.
To convert time measurements into distance measurements it needs to know the speed of sound in air (343 m/s at 20 C, dependent on air temperature).
Note that the Motion Detector (or "Distance Probe") has a limited range of distances in which it works OK. Try to determine what is the useful range.
2. Walk This Way!
Several detailed descriptions of movements are listed on a card. Move relative to the motion detector in order to produce each of the given movements. You might find useful to carry a flat surface (like a book) facing the motion detector. Experiment with it !!!. In each case plot x, v and a as a function of t. Interpret and discuss your results. For example, if you were given a velocity-time curve to produce, are the corresponding position-time and acceleration-time curves consistent with your result?
Please print the graphs of x vs. t, , v vs. t and a vs. t for each of the three tasks. Identify clearly the card assignments on each graph.
3. The Way the Ball Bounces
Note: You might want to take a look at Conceptual Example 2.11 ("Follow the Bouncing Ball") in Serway's textbook.
Measure the position of a golf ball as it falls and bounces in a glass tube. Be sure to Save your results.
You may use Copy/Paste to transfer the Data Table to an Excel file for later analysis (only data values are copied this way). But the recommended procedure is to use FILE -> EXPORT AS, then choose TEXT in Logger Pro to save the data as a text file ("filename.txt"), and then FILE/OPEN it in Excel as text (tab delimited); this way the file info and column headings appear on top of the data values in the Excel spreadsheet..
Repeat this procedure until you are able to record at least five "good" bounces in which the ball does not hit the side of the tube or show an unusual discontinuity in motion
4) Data Analysis
You should complete the following analysis for the set of bounces.
Determine the velocity of the ball immediately before (Vb) and immediately after (Va) each bounce. Do this in four different ways:
1) Vb is the final downward V before the bounce, and Va is the first upward V after the bounce;
2) Vb is the greatest V before the bounce and Va is the greatest V after the bounce. (1) and (2) use V values obtained from LoggerPro's calculated velocities.
3) Vb is Dx/Dt just before the bounce and Va is Dx/Dt just after the bounce (x-t values are obtained from position data).
4) Vb is calculated using the starting height hb before each bounce; Va is calculated using the final height ha reached after each bounce (h values are obtained from position data). Use v = sqrt(2gh).
The coefficient of restitution is defined as e = |Va/Vb|, and is a measure of the momentum retained by the ball following its collision with the floor. e2 is a measure of the energy retained by the ball.
Are the heights (h) to which the ball rises after each collision consistent with the preceding Va values?
Compare the results for e and e2 obtained by each of the methods (which one is more reliable?).
Compare the x vs t, v vs t and a vs t graphs. Are they consistent?
Does e vary with successive bounces?