We gathered a video of freely-falling objects, two pieces of paper with the same dimensions. One of them was crumpled. My goal is to track the distance traversed by the object from its original height as time increases. I then compared this with what should be expected theoretically. Above is the first frame of the video we gathered.
Since it is hard to segment the paper from the hand, and since in the last frames of the video, the crumpled paper had already reached the floor, I only used frames 3 to 12. For each frame, I got two portions and binarized them to track the falling papers. I then got the centroid for each portion. From the original height located in frame 1, and the y-components of the centroids, I obtained the position versus time graph for the two objects. I compared them by the theoretical values d = gt^2 where d stands for distance, g for the acceleration due to gravity and t is time. The white markings in the frames served as scale and their real world interval was 10 cm. In pixels, the interval was 33 pixels.
The final distance for the uncrumpled paper is 0.23 m, for the crumpled paper 0.60 m, and for the theoretical distance 0.78 m. We expect the final distance for the uncrumpled paper to be less than that for the crumpled paper because of drag force. The discrepancy between the measured distances versus time for the crumpled paper and the theoretical must be due to a little drag force on the crumpled paper. But at least they are of the same order of magnitude.
SELF--GRADE: 9/10
Thank you to Lei, Aiyin, Beth, Rica for the video and sliced frames.
