September 10 2014 - Modeling the fall of an object falling with air resistance

Purpose: Determine the relationship between air resistance force and speed with air resistance by modeling the fall of coffee filters from a balcony.

The picture shows a 2 m ruler to set the height/distance for our experiment; and a coffee filter, which will be our object thrown from the balcony.

First, we are going to record our experiments dropping 1,2,3,4,5 coffee filters from a balcony in order to get our data with LoggerPro. As we drop the coffee filters, we are going to have the 2m ruler on the top of the balcony to set our parameters of the distance which we are from the ground. With the data collected, we will determine the final velocity of the object by using LoggerPro to set a graph of position vs. time. With the final velocity, of each experiment, we are going to create a graph of speed vs. Force of each coffee filter to determine k and n from the equation F=kv^n. by finding those values, we should be able to determine the relationship of air resistance with speed.

 This picture shows the videos of our experiments on the left, and on the right is possible to see a graph of position and time, the slope determined the velocity of the object falling. We did this 5 times, each one representing the quantity of coffee filters that were dropped.

 This picture shows the Speed vs. Force graph of all five experiments. As shown, the experiment using 3 coffee filters was off the expectations when compared to the other 4 experiments.

In order for us to have a more reasonable value of k and n, we didn't include the experiment using 3 coffee filters in our final graph of Speed vs. Force as seen in the picture above.

 To make sure that our result of final velocity was accurate, we did the solution numerically by using the values of k and n obtained in the graphs above. The results were accurate, meaning that our calculations were good.

This picture shows the calculation of the force in each of the five experiments that we did.


Summary: To start our lab, we practiced dropping the coffee filters in class, just to get an idea of how LoggerPro works. After that, we went to the Design Technology building and from its balcony, we did the execution of our lab by dropping 1,2,3,4,5 coffee filters and recording with the computer. After recorded, we used LoggerPro to plot a graph of distance vs. time for us to find the final velocity of each experiment with the coffee filters, and we did calculations to find the force of air resistance in each of coffee filters. We used the equation F=kv^n as standard, and after making a graph with speed vs. force, we were able to find values for k and n. With that equation, we found the relationship between air resistance force and speed. To make sure that our results were accurate, we found a solution numerically, which was close enough to our solutions analytically, showing that our calculations were accurate.