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PHYS-1500 PHYSICAL MODELING FALL 2006 8/29/2006, Class 1: Free Fall NAME: ______ SOLUTIONS ______________________ Open the Excel file "freefall.xls". The file contains data that were exported from the video. In column B, the time has been shifted so that t = 0 at the instant the weight is dropped. This was done by entering the formula =A6-$A$6 in cell B6, and then copying it to the cells below it. Do the same for the values of y. That is shift the y coordinate system so that y = 0 at the point where the weight is released. Do this by entering =D6-$D$6 in cell E6, and copying it to the cells below it. Now, calculate vy as a function of t. Use the formula, vy = y/t to calculate the average vertical component of velocity over short time intervals. This can be done by entering the following formula in cell F6: =(E7-E6)/(B7-B6). Then, use the "Fill Down" command found under the "Edit" menu at the top of the screen to copy the command to cells F7 through F22. Next, calculate ay as a function of t. Use the formula, ay = v/t to calculate the average vertical component of velocity over short time intervals. This can be done by entering the following formula in cell G6: =(F7-F6)/(B7-B6). Then, use the "Fill Down" command found under the "Edit" menu at the top of the screen to copy the command to cells G7 through G22. 1. Use Excel to make graphs of y vs. t and vy vs. t. Sketch the graphs, and be sure to indicate which one is y and which is vy. 0 -0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.3 0.4 0.5 -2 v (m/s) y(m) -0.6 -0.8 -1 -3 -4 -1.2 -1.4 -1.6 0.1 -1 -0.4 y = -4.9952x 2 + 0.025x - 0.003 -5 y = -9.9285x - 0.1635 -6 -1.8 t(s) t (s) 0.6 2. Find the slope of the graph of vy vs. t. What is the value of the slope? What is the significance of the slope of the graph of vy vs. t? slope = ___9.93 m/s²______ The slope is shown on the graph. The slope is the object’s acceleration. units 3. Find the average value of the acceleration that you calculated. aav = _____9.34 m/s²____ units 4. Finally, enter a “model” formula for the position of the weight as a function of time in column H. Plot both the measured values of y and the values calculated from the model on the same graph to show that they agree. The formula used is y = – ½(9.8 m/s²)t² 0 -0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 -0.4 y (m) -0.6 -0.8 data model -1 -1.2 -1.4 -1.6 -1.8 t (s)