The purpose of this lab is to determine the relationship between speed and the force of air resistance. This is going to be done by dropping coffee filters from a balcony and recording it with a camera which is then analyzed later in logger pro.
Experiment
For this we went to the Design Technology building and dropped coffee filters repeatedly from one by itself then two stacked together all the way until 4 are stacked together. While the filters are being dropped we recorded them with the laptop and analysed the data as when we got back to class. The video was analysed by first making a scale so that the point we are plotting has a vale, we then plot points at each moment as the filter fell.
After plotting the points we are given a graph of y-position vs time in which if we take the linear fit of it, we get an equation of the line whose slope represents the velocity of the filter as it fell. The process of the video analysis and graphs was then repeated for the rest of the trials as well.
The velocity from each trial is then taken and then graphed against the down ward force of the filter as it fell, which was calculated by multiplying the mass of the filter(s) with gravity. We then saw that the the graph was a power relationship of x = A y^B, which is similar to our equation for drag force F = k y^n
Since we know the drag force we can take that information and find out how long it would take the filters in each trial to reach terminal acceleration with excel. In excel the time increments in the time column is increased at increments of .01 second. The acceleration column is calculated by taking the power function in force vs velocity graph with the y being the speed of the object which is the previous column, then divided by the mass of filter(s) and then it is all subtracted by gravity. How we came up with solving for acceleration this way was by taking the sum of the total force and rearrange the equation to solve for acceleration. The change in velocity column is calculated by taking the the acceleration and multiplying it with the difference between the previous and current time, as for the current speed it is calculated by taking the previous speed and adding the change in speed. The change in distance is calculated by taking the average of the previous and current speed then multiplying it with the change in time. The last column the actual distance is calculated by taking the initial distance and subtract it from the the change in distance. We also set some variable on the side so it would be easier as we did the other trials, where we would only have to change those variable values rather than starting over.
Once we have all equations for each column typed out we then drag them all down all the way until the acceleration reaches zero. We go until the acceleration is zero because that is when the filter hits terminal velocity meaning the velocity no longer changes. From there we can see how fast the filter(s) terminal velocity it, how long it took the filter(s) to reach it, and how far the filter(s) fell before it reached terminal acceleration.
It can be seen that the velocity and acceleration does change slightly but it is so small that is it negligible, but the distance will still change however because the filter(s) is still falling nonetheless. There were error in this experiments however in that the filter did not always fall down in a straight line, which was caused by drafts either from air vents or people entering/leaving the building. Another possible error is that through repeated trials the filter may not have been able to retain it's same shape perfectly each time as it fell.
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