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Department
Accounting
Course
ACTG 1P91
Professor
Daniel Glenday
Semester
Fall

Description
Title: Using graphical extrapolation, Vernier Motion detectors and Labquests to determine the magnitude of the acceleration due to gravity. Purpose: The purpose of this lab is to determine, through graphical extrapolation, the value for the acceleration of gravity. Materials: Quantity Item Quantity Item Quantity Item 1 Plywood piece 1 Cart 1 Vernier Labquest 5 Textbooks 1 measuring Tape 1 Motion Detector Procedure: Place a single book under one end of a 1–3 m long board or track so that it forms a small angle with the horizontal. Adjust the points of contact of the two ends of the incline, so that the distance x in Figure 1 is between 1 and 3 m. 2. Place the Motion Detector at the top of an incline. Place it so the cart will never be closer than 0.15 m. 3. If your Motion Detector has a switch, set it to Normal. Connect the Motion Detector to DIG 1 port of LabQuest and choose New from the File menu. If you have an older sensor that does not auto-ID, manually set up the sensor. 4. Hold the cart on the incline about 0.5 m from the Motion Detector. 5. Start data collection; release the cart after the Motion Detector starts to click. Get your hand out of the Motion Detector path quickly. 6. Examine the graph of velocity vs. time. 7. You may have to adjust the position and aim of the Motion Detector several times before you get a useful run. Adjust and repeat the process until you get a good run showing approximately constant slope on the velocity vs .time graph during the rolling of the cart. To collect more data, start data collection when you are prepared to release the cart. Repeat Steps 5 and 6 until you get a useful run. 8. Fit a straight line to a portion of your data. First you must indicate which portion of the graph is to be used. a. Tap and drag your stylus across all data points in the linear region of the graph. b. Choose Curve Fit ► Velocity from the Analyze menu. c. Select Linear as the Fit Equation. d. Record the slope of the fitted line (the acceleration) in the data table. Select OK. 9. Measure the length of the incline, x, which is the distance between the two contact points of the ramp. See Figure 1. Record the length in your data table. 10. Measure the height, h, the height of the book(s). These last two measurements will be used to determine the angle of the incline. Record the height in your data table. 11. Raise the incline by placing another book under the end. 12. Repeat Steps 4–10 for the new incline. 13. Repeat Steps 4–11 for 3, 4, and 5 books. Data: Graph 1 Average Speed versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.036m 0.25 0.2 0.15 0.1 Speed (m/s) 0 0 0.5 1 1.5 2 -0.05 Time (s) Graph 2 Average speed versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.079m 0.7 0.6 0.5 0.4 0.3 Speed (m/s) 0.1 0 -0.1 0 0.5 1 1.5 2 Time (s) Graph 3 Average Speed versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.101m 0.9 0.8 0.7 0.6 0.5 0.4 0.3 S0.2d (m/s) 0.1 0 0 0.5 1 1.5 2 -0.1 Time (s) Graph 4 Average Velocity versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.146m 2 1.5 1 0.5 0 Speed 0m/s) 0.5 1 1.5 2 -0.5 -1 -1.5 Time (s) Graph 5 Average Velocity versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.184m 5 4 3 2 1 0 -1 0 0.5 1 1.5 2 Speed (m/s) -3 -4 -5 -6 Time (s) Sample Calculations Average Velocity of a cart travelling down a 0.726m ramp with a height of 0.036m Determining the sine of the angle created by the slope of the ramp and the height of the book Table 1: Raw data used to determine the sine of the angle Number of Books Height of the Length of the Sine Θ books (m) incline (m) 1 0.036 0.726 0.0496 2 0.079 0.726 0.109 3 0.101 0.726 0.139 4 0.146 0.726 0.201 5 0.184 0.726 0.253 All Labquest data (raw data collected) would also be placed here Data Analysis: Graph 6 Average Speedtime for a cart rolling down an incline made with a 0.726 m board with a height of 0.036m 0.25 y = 0.1032x + 0.0088 0.2 0.15 Speed (m/s) 0.05 0 0 0.5 1 1.5 2 Time (s) Graph 7 Average speed versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.079m 0.7 y = 0.5079x - 0.0249 0.6 0.5 0.4 0.3 Speed (m/s) 0.2 0.1 0 0 0.5 1 1.5 Time (s) Graph 8 Average Speed versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.101m 0.9 0.8 0.7 y = 1.1443x - 0.1516 0.6 0.5 0.4 Speed (m/s) 0.2 0.1 0 0 0.5 1 Time (s) Graph 9 Average Velocity versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.146m 1.2 1 y = 1.3074x + 0.0082 0.8 0.6 S0.4d (m/s) 0.2 0 0 0.5 1 Time (s) Graph 10 Average Velocity versus time for a cart rolling down an incline made with a 0.726 m board with a height of 0.18
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