Modeling the fall of an object with air resistance

Ana Leyva, Andrew Imm, Victoria
3/13/17
By doing this experiment we were trying to find a relationship between the air resistance force and speed.
With this experiment we were trying to find the terminal velocity of 1,2,3,4,and 5 coffee filters as they fall from  a second story balcony. We calculated the terminal velocity by first getting a linear fit for our 5 position vs time graph for all five coffee filters. Once we did the linear fit we got the slope for each five of those graph and got a value for our terminal velocity. Then we plotted a velocity vs Fnet graph to get the values of k and n. We did this because our formula F_resistance=kv^n lets us know that if we plot a velocity vs F_resistance graph we will get our values for k and n. We will then use these values in order to use excel and to find the terminal velocity of our coffee filters.

Linear fit for two coffee filters

We started this experiment by heading to the design and technology building and capturing on video different numbers of coffee filters falling from the balcony. From these videos we were able to get a position vs time graph for 1, 2, 3, 4, and 5 coffee filters falling. From these graph we were able to figure out the terminal velocity for the coffee filter by doing a linear fit on the end portion of our graph. Given the equation F_resistance = kv^n  we realized that if we plotted a velocity vs. Fnet graph and did a (y=ax^b) auto fit we would be able to find the values for k and n.

After this was done we used the values of k, and n to plug them into excel in order to find another way to predict the terminal velocity of our coffee filters. We set up our excel sheet by setting delta t, m, g, k, and n as set values that could later be adjusted. We then used these values to calculate t, v, F_net, a and delta v.  t was calculated by adding t_initial + delta t, v = v_initial + delta v, F_net = m*g-k*v^n, and finally delta v = a*delta t plugging all of this in correctly let us see the terminal velocity for the different number of coffee filters.

The terminal velocity that we calculated from excel and those that we got from the graph were not off by too much, which means that we have a pretty good model. They were all mostly correct to the first decimal place.