12-Mar-2015: Modeling the fall of an object with air resistance

Part 1: Determining the relationship between air resistance force and speed

Air resistance is based on an object's speed, shape and the material it is moving through (type of air).

In this lab we used a simple model to calculate air resistance. We dropped objects from a high enough distance until they reached terminal velocity, where air resistance equalled the speed.

Terminal Velocity 

When acceleration is zero

Using the Design Technology building's indoor balcony, we were able to drop coffee filters from the balcony and use Capture Video to record 1, 2, 3, 4, and 5 coffee filters falling from the balcony.

One Coffee Filter

Five Coffee Filters

As one can see the increased coffee filters are heavier and have an increased terminal velocity. (Not all of the videos made it through email besides these two.)

Part 2: Modeling the fall of an object including air resistance

Using the Capture Video we pin pointed the position of the filter after every frame of the video giving us nice position versus time graphs. We took the slope of each of these graphs when the graph straightened out into a linear graph. The slope was therefore the terminal velocity of each trial. (The data of each graph in the email would not open on my computer.)

We then created a graph with F of resistance versus the terminal velocities found above.

This is the data of force of air resistance and terminal velocity. The F was found using mg, the mass of the filters times gravity. 

mass of coffee filter

(This is where the data for F vs. v would be but my partner is not sending it to me.)

Then we graphed this data to create a curved graph. The graph then had a certain power to it, which we can found using a power fit. The n is shown in the picture below. 

(This is where a graph pic would be but my partner is not responding.)

The equation of the force of resistance is now assumed to have a power and look like this:

F resistance = kv^n (The k term takes into account the shape and area of the shape.)

The model equation may not have "spit out" values close to the terminal values found without experimental data, but this is because our data varied and may have had some human error in taking the position versus time. In the end though, the correlation between velocity and air resistance became clear to how much they are dependent upon each other. The simple model showed us that the air particles that are in the way get accelerated from rest to speed so that the force on the air particles is really the mass of the air in the way. If the weight is added it seems as if the particles will retaliate with equal force, but some particle get out of the way as well creating more varied experimental data.