9 September 2014: Air Resistance Lab 4

Objective:
1) Observe how air resistance affects terminal velocity of a falling object
2) Discover the behavior of air resistance with regards to change in mass

Materials:
1) Tape
2) Ruler
3) Coffee Filters
4) A high indoors place from which to drop the coffee filters
5) Video
6) Video analysis program such as Logger Pro

Set Up:

As you can see from this photo, we have taped the ruler as a reference point for later video analysis. We are filming far away enough to capture the whole fall of the coffee filter. We are dropping coffee filters; first 1 at a time then 2 at a time and so on until we have dropped 5 at a time. Lastly all this has happened in an area where wind cannot affect our results and also a place that is high enough for proper data collection.








Procedure:
Before we started our data collection we made some predictions about the whole experiment. First we made a free body diagram of all the forces acting on the coffee filter as it fell with air resistance.

Then we sketched a graph of what we predicted for acceleration vs time and velocity vs time:

We predicted the acceleration vs time graph would look like this because the acceleration would decrease until the object reached terminal velocity regardless of the amount of mass. We also predicted the velocity vs time graph would look like this because the coffee filter(s) would gain speed as they are falling until it reaches terminal velocity and stays constant.

Lastly in class, it was discussed that acceleration would look something like this:

Then we traveled over to a different part on campus to collect our data.
We first dropped one coffee filter, then 2 at a time, then 3 at a time, then 4 at a time, and lastly 5 at a time. We then analyzed our data on Logger Pro and created a position vs time graph and took a linear fit and recorded the slope of the linear fit of this graph.

Position vs time graph of 1 coffee filter 

We looked at the slope of the the position vs time graph because the slope of this graph represents the velocity. More importantly the slope of this graph represents the terminal velocity of the coffee filter.

Here are the graphs of the other trials:

2 coffee filters

3 coffee filters

4 coffee filters

5 coffee filters

Then we applied the knowledge that the Force of air resistance=k(terminal velocity)^n
We then calculated the forces and created a graph of Force of air resistance vs terminal velocity. We used the terminal velocity gathered from the slopes of the graphs of position vs time for each trial. The resultant graph looked like this:

To this graph we added a trend line. As mentioned before Force of air resistance=k(terminal velocity)^n. With this graph we were able to discover our "k" and "n" which were modeled by the graphs "A" and "B" respectively. 

So our k= 12.22 + 1.190

and our n = 1.60 + 0.1358

Lastly we tested the accuracy of our results by numerically solving for terminal velocity using excel. Here is a picture of how we set it up. As you can see, we used 1/30 of a second increments.

Then we created a position vs time graph with our excel data:

We then compared this graph to the one produced by our video and Logger Pro

Conclusions:

There was a big discrepancy between the excel graph and our graph created by our data. There could be many sources of error. Firstly, the background was white as were the coffee filters so when analyzing the video it was hard to identify the coffee filters. I believe our model data created in excel is much more accurate than our experimental data because of our inexperience in gathering data using our videos.