D, e, f

INDING GRAPHICAL ANALYSIS EXERCISES Suppose that you've elevated the end of the air track from which you released the glider whose motion was the subject of the Check Your Understanding exercise in Graphing Experimental Data. You release the glider and measure its position as a function of time and obtain the following set of data. X t (s) 0.00 0.30 0.60 0.90 1.20 1.50 1.80 2.10 2.40 x (m) 0.00 0.02 0.09 0.20 0.36 0.56 0.81 1.10 1.44 t, (s') 0.00 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 a. Use a sheet of graph paper (at the end of this manual) to plot a graph of the position of the glider (x) on the track of the inclined plane as a function of the time it has been moving (t). Recalling that the scale you choose for the x-axis does not have to be the same as the scale you choose for the t-axis (Why should it? You are, after all, plotting different physical quantities on the horizontal and vertical axes.), choose scales that will result in your graph filling most of your sheet of graph paper. Compare your graph with the graph shown in Figure 9 (page 33). b. If this graph is non-linear (i.e., not a straight line), linearize your data and use a second sheet of graph paper to plot the graph that results from this linearization. Hint: Include a t row in your table. Compare your graph with the graph shown in Figure 10 (page 33). Use the eye-ball criterion to fit a straight line to the graph of your linearized data. d. Use the rise-over-run definition of the slope to determine the slope of the straight line that you think best represents your linearized data and use this value to obtain a value for the acceleration of the glider. Show your work. 1. 10 - 0.2 0.75 0. 9 4 X 1. 2 Hope 2. 10 - 0.9 e. Determine the vertical-axis intercept (aka y-intercept) of your graph. f. Write an equation that expresses how the position of the glider (x) depends on the time it has been in motion (t)