13-Mar-2017: Modeling the fall of an object falling with air resistance

Every day, most of the people need to drive to school, work, or some other places. When we drive on the freeway, and we need to accelerate, then we will step deeper on the gas pedal. However, even though we did not slide out the gas pedal, the car will not keep accelerating forever. The main reason for that is there is a friction force increase while the car accelerated. The following lab is designed to figure out what relationship is between velocity and friction force.

Purpose:

Determining the relationship between air resistance force and speed.

Set up:

By the handout from http://spiff.rit.edu/classes/phys311/workshops/w6b/drag_expt.html, we know that the relationship between air resistance and velocity is

(The k term takes into account the shape and area of the object)

To collect the data of speed and air resistance, Professor Wolf brought us to building 13, where has a large interior space. Then, professor threw 7 times coffee filters with 6 different numbers from the top. After we collect by video, we took them back to the lab to detect the data.

Analyze:

From the data we collected, we can found the there is a relationship between velocity and mass (which can convert into force).

Then, we plugged them into the Logger Pro and modeled them by mg = kv^n.
We got k = 0.004877, n = 2.245. (from Logger Pro)
(Sadly, I forgot to take a screen shot for that, so the following is done on Excel, which is slightly different)
Through the fuctions

We know it can convert into a y = kx + b function. Then, graph by Excel, we got

Next, we put the data we collected to model the first experience.

The data came out that they are matched in the end, which means this model succeeded to model the situation of coffee filters.

Similarly, we got some close answers when we plugged into other experiences.

Conclusion:

From the lab, we could know that the relationship of coffee filters between velocity and friction force is

However, in our daily life, because the different shape and size, the coefficient k would change. But in this method, we have a new way to roughly detect the relationship between friction force and velocity.