Sunday, November 6, 2011
Week 7
Last week, I see the data that we collected to calculate the height of the peak of the potato's launch. My calculations can be found in my previous post. Also that week, Audie and I attained all the materials for the wind tunnel and began working on the project. We will continue the wind tunnel next week.
Tuesday, November 1, 2011
Accelor the Potato Accelerator
Audie, Brandon, Dustin, and I launched a potato with the potato accelerator and recorded the data from the launch, which is as follows:
Total distance: 535'
Total time: 7.13s
Angle of elevation: 40 degrees
Observed height: 5'6"
We used two different methods to calculate the approximate height of the potato at its peak, then compared the two to determine whether the theoretical equation 1/2gt^2 (one half times the acceleration due to gravity times the time from peak to impact squared) was accurate.
Using the equation, we plugged in the acceleration due to gravity (9.81 m/s^2) and the time from peak to impact (3.565s), which was found by dividing the total time by two. Our equation then looked like this: 1/2(9.81)(3.565^2). After solving the equation, we found the height to be approximately 62.339m or 204.524'.
Our second method was to use trigonometry to find the approximate height. For this method, we had to find the distance from launching point to peak, and the angle of elevation from the observer's eye level to the peak point. We took the total distance and divided by two to get the distance from launch to peak (267.5'), and measured the angle of elevation to be 40 degrees. We then determined that, since the height, x, was the opposite side of an imaginary triangle from the angle of elevation and the distance from launch to peak was the adjacent side, we should use the trig function tangent (opposite/adjacent). Our equation now looked like this: tan(40)=x/267.5. Using algebra, I rearranged the equation to read: x=267.5tan(40). However, in order to account for the lost height due to the observer's eye level's distance from ground level, we had to modify the equation again to read: x=267.5tan(40) + 5.5. After some calculation, I found the approximate height to be 229.959'.
Based on these two calculations (204.524' compared to 229.959'), we determined that the theoretical equation was indeed reliable.
Total distance: 535'
Total time: 7.13s
Angle of elevation: 40 degrees
Observed height: 5'6"
We used two different methods to calculate the approximate height of the potato at its peak, then compared the two to determine whether the theoretical equation 1/2gt^2 (one half times the acceleration due to gravity times the time from peak to impact squared) was accurate.
Using the equation, we plugged in the acceleration due to gravity (9.81 m/s^2) and the time from peak to impact (3.565s), which was found by dividing the total time by two. Our equation then looked like this: 1/2(9.81)(3.565^2). After solving the equation, we found the height to be approximately 62.339m or 204.524'.
Our second method was to use trigonometry to find the approximate height. For this method, we had to find the distance from launching point to peak, and the angle of elevation from the observer's eye level to the peak point. We took the total distance and divided by two to get the distance from launch to peak (267.5'), and measured the angle of elevation to be 40 degrees. We then determined that, since the height, x, was the opposite side of an imaginary triangle from the angle of elevation and the distance from launch to peak was the adjacent side, we should use the trig function tangent (opposite/adjacent). Our equation now looked like this: tan(40)=x/267.5. Using algebra, I rearranged the equation to read: x=267.5tan(40). However, in order to account for the lost height due to the observer's eye level's distance from ground level, we had to modify the equation again to read: x=267.5tan(40) + 5.5. After some calculation, I found the approximate height to be 229.959'.
Based on these two calculations (204.524' compared to 229.959'), we determined that the theoretical equation was indeed reliable.
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