9/9/2014 Modeling the fall of an object falling with air resistance

Purpose and attempt of our lab:

The purpose of our lab today was to determine the relationship between air resistance force and speed. Will attempt to find the relationship by gathering data of a falling coffee filters and graph this data to find a power fit for the air resistance formula F-resistance - kv^n. After graphing our data and finding the value for k and n we will use Excel to  compare our experiment graphs to our modeled graphs.


Collecting the data:

To collect our data we used a camera to film falling coffee filters. We first dropped one filer then two continuing until to our last drop of five coffee filters. The purpose of the camera is to have a known distance which we used a meter stick as a reference point in the video to calculate the number of pixels in the known distance. With this we can track the falling coffee filter on Logger Pro to find a terminal velocity (where the graph was linear) to get data of time and distance the object has fallen which in return calculates velocity. Unfortunately in the hype of experiment I forgot to take pictures of the falling objects in the room, yet here is a still from the video capture.

Here is the picture of the camera and laptop we used to capture the five falling objects.

Here is a picture of are table of data which did not all fit in the picture:

With Logger Pro we graphed all the falls time vs distance as shown below.

After that we used our data to calculate our power fit graph to find k and n. This shows a value for k as 0.008542 and a value for n as 1.794.

Modeling the data:

So with are experimental data now collected we used the values of k and n to make a model of a falling object including air resistance. We did this by using Excel  and using a time interval of 1/30 of a second. 

Here is a picture of a portion of our Excel data:

With this Excel model we find have a table of data we used to graph time vs distance for one coffee filter and five coffee filters.

One coffee filter:

Two coffee filters:

Now that we have a graph the data from our model and our experiment we combined both graphs to compare our experimental data and our model data.

Conclusion of data:

With any experiment in physics are data is only as good as our equipment and using cheap cameras to get our data is not a reliable source. The first set of data is much better then our second even though both graphs are very similar when comparing the slope. Overall I think our model data is much better then our experimental table because of the our inexperience using the camera to collect data and the amount of work needed to get reliable data from a camera.