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Discussion And Results |
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After we obtained a photo with three rubber bands and two images of a BB before and after each using our eight flashes, we were ready to analyze. We printed out a copy of the picture and did the measuring and analyzing by hand. The very first step would be to create a scale factor of the distance between each BB on the picture itself, and how far the actual distance was. In our photos we placed a meter stick, and used this to find our scale factor. We used a simple ratio to convert the measured distances on paper to actual distances, which looked something like this: Scale factor = Actual distance / distance measured photo. This allowed us to convert distances we measured with the meter stick into actual distances in the photo. A table was then made in our lab notebooks to keep the data in an organized manner which included the image number of BB, measure distance between BB on paper, converted real-life distance using ratio, and the time interval at which the BB was taken. Now that we had all the information needed, we were ready to find the velocity of the BB before and after each rubber band, and find the change in velocity from the beginning to the end. We used the equation V=chgDistance/chgTime to calculate the velocities. We did this analysis twice for 2 different images, although the other image was a bad analysis photo, we had to use it, and the estimates from that image were close to the one we did below.
Velocity analysis: bandd1102e2 Scale Factor= Actual distance/ measured distance = 140mm/120mm D1 measured = 40.1mm x/40.1mm*140mm/120mm D1 actual = 46.8mm D2 measured = 36.9mm x/36.9mm*140mm/120mm D2 actual= 43.1mm D3 measured = 30.5mm x/30.5mm*140mm/120mm D3 actual = 35.6mm D4 measured = 28.9mm x/28.9mm*140mm/120mm D4 actual = 33.7mm Velocity = change in distance / change in time VD1 = 46.8mm/.244ms = 192 m/s VD2 = 43.1mm/.244ms = 177m/s VD3 = 35.6mm/.244ms = 146m/s VD4 = 33.7mm/.244ms = 138m/s Change in velocity of above photo = -54 m/s Change in velocity of the other photo we analyzed = -64 m/s This small difference in the speed could be result of the inconsistencies in the pellet gun, the elasticity of the rubber band, or slight measurement errors in the photograph. We noticed on all of the three-rubber band cases that we investigated, none of the third rubber bands in the sequences were punctured. All absorbed the impact of the BB and then either stretched until the attached ends of the rubber band snapped or stopped the BB. This gave us a rough estimate at what speed was needed to break through the bands, and anything under this speed wouldn't puncture . There was also a noticeable difference in the shape of the bands as the BB's velocity decreased. Like the first couple of bands in the above picture, the shape resembles more of a rectangular shape because the leading edge of the band has nothing to shift it forward because the BB is passed through it. But, as the BB takes longer to pass through the band you get more of a pointed triangular shape, until eventually it doesn't break through the band at all, causing a triangle to form.
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