Acceleration of Gravity

Intro: The purpose of this lab was to introduce the process of data collection through computer software in order to calculate the acceleration of gravity with a falling ball. The ball's motion was plotted on a position (x) vs time (t) graph as well as a velocity (v) vs time graph with the help of a motion detector. Both graphs were analyzed to find the acceleration of the ball.

Materials: Windows based computer, Lab Pro interface, Logger Pro software, motion detector, rubber ball, wire basket

Procedure: We set up everything as directed in the lab handout. The motion detector was connected to the lab pro which was connected to the computer. We opened up the graphlab application as instructed and were ready to begin our trial runs. Due to the limited amount of time, the number of successful trials had to be cut down from 5 trials to 3 trials. A successful trial consisted of plotting a near parabolic shape curve on the graph.

Results:

I decided to pick our first trial run to show on my lab report because it was the one closest to the acceleration of gravity with a .91% error.

This is the velocity v time graph of our best trial run. The derivative of the position graph is shown by the dotted line that runs through the slope. The line crosses the x-axis at the instant where the ball reaches it maximum height and that's due to the fact that the ball's velocity at that point in time is 0. The velocity is positive for the period of time where the ball was reaching the maximum height and it is negative after it has reached maximum height.

Q&A: 
Why should it be a parabola?
-It should be parabola because of the way the ball was thrown. The ball was first thrown up and then gravity pulled it down. That means that the ball started at a certain height, reached a maximum height, and then ended going down. That kind motion should create a parabolic path.

Why does the curve have a negative slope?
-Because the motion detector recognizes the pull of gravity as the negative direction.

What does the slope of this graph represent?
-The slope represents the ball's velocity at certain positions. For example, the ball's velocity is 0 once it reaches it's maximum height.


Conclusions: My lab partners and I were able to hit 3 trial runs that formed a curve with a parabolic shape. However, two of the trials that were run had a pretty high percentage errors despite the fact that they resembled a parabola. I believe this was due to the way we set up our materials. There was times where the motion detector wasn't properly positioned and times where our ball tosses were not very gentle. Perhaps with if we would have stopped to reorganize everything we wouldn't have gotten such percentage errors. Our first successful trial was the one with the smallest percentage error and it was done when everything was in order.