Procedure: This lab was broken into 2 parts. The first part was to log into the graphical analysis program and modify a graph that was already saved. Our group changed f(x) to [sin(x2)]/(x2). The result of this is shown below:
Part 2 required that we log into another program that we are to be familiar with. The name of this program is Logger Pro. For this portion of the lab we also needed addition equipment. A motion detector was used to track the trajectory of a falling ball. With the Logger Pro application, we were able to graph the data that was tracked by the motion detector and put that into a graph. An image of this graph is shown below:
3:
Dimensional Analysis: time = sqrt(d/g)
Unit Analysis: d = gt^2
| time | position | velocity | accel | dimen | unit | |
| 0 | 1.531 | -0.105 | -4.139 | 0.395051 | 0 | |
| 0.05 | 1.528 | -0.323 | -5.887 | 0.394664 | 0.0245 | |
| 0.1 | 1.507 | -0.691 | -7.667 | 0.391942 | 0.098 | |
| 0.15 | 1.46 | -1.129 | -8.797 | 0.385782 | 0.2205 | |
| 0.2 | 1.395 | -1.591 | -9.375 | 0.377097 | 0.392 | |
| 0.25 | 1.303 | -2.086 | -9.071 | 0.36445 | 0.6125 | |
| 0.3 | 1.184 | -2.553 | -6.729 | 0.347409 | 0.882 | |
| 0.35 | 1.046 | -2.998 | 2.663 | 0.326536 | 1.2005 | |
| 0.4 | 0.885 | -2.753 | 18.693 | 0.300357 | 1.568 | |
| 0.45 | 0.701 | -1.549 | 37.643 | 0.267316 | 1.9845 | |
| 0.5 | 0.496 | 3.388 | 17.789 | 0.224857 | 2.45 |
The relationship of Dimensional analysis and Unit analysis can be show with basic algebra. t = sqrt(d / g) raise both sides by the power of 2 and you get t^2 = d / g. Then multiply both sides by g and you end up with d = g * t^2, which is the formula for the unit analysis.
Conclusion: I feel comfortable using the 2 programs and the motion detectors that will be needed for the labs that will be required to complete this class. Overall, I felt that the instructions were slightly vague, but that may be by design to challenge the class to think for themselves. If that is the case, it was not apparent.
