Question

1) Read Lab 2 manual. Study the Analysis section to make sure you have a firm grasp of what is required for this lab. A student wants to figure out how far a ball fall, y, based on g 9.81 and the time that it is in the air. The student drops a ball 10 times and measures the time it takes to fall. The average of those times, as well as the uncertainty is shown below. average (S 0.75142 average (s) 0.0056 2) Using the data above find ymin and ymax as described in the lab manual 3) Calculate yaverage in two different ways: a. First, as the average of ymin and ymax b. Second, just using the formula yaverage average) There should be a difference between your answer to 3a and 3b above. Is this difference important? Use the idea of 4) Sy to justify your answer

Answer 1

g = 9.81 mL s^2 t^bar_average = 0.75142 sec: 8 t^bar_average = 6.0056 sec we know, for a freely falling body from rest, y = 1/2 gt^2 = > y_max = 1/2 g t^2_max t_max = t^bar_avg + 8 t^bar_avg = 0.75142 + 0.0056 = 0.75702 sec = > y_max = 1/2 times 9.81 times (0.75702)^2 y_max = 2.811 m y_min = 1/2 g t^2_min t_min = t^bar_avg - 8 t^bar_avg = 0.75142 - 0.0056 = 0.74582 sec = > y_min = 1/2 times 9.81 times (0.74582)^2 y_min = 2.728 m \r\n y_max = y_min + y_max/2 = 1/2 g t^2_min + 1/2 g t^2_max/2 = 1/4 g [t^2_min + t^2_max] = 1/4 times 9.8 times [(0.74582)^2 + (0.75702)^2] = 2.766850 m The values of (3a) and (3b) are different 3a) y_max = 2.766850 m 3b) y_max = 2.769520 m y_avg = 9/4 [t^2_min + t^2_max] y_avg = 9/4 [(t_avg - 8t)^2 + (t_avg + 8t)^2] y_avg = 9/4 [2 t^2_avg + 28 t^2 - 28 t