4-Sept-2014: Modeling the fall of an object falling with air resistance

Purpose:
The purpose of this lab is to determine the relationship between air resistance force and speed. Also, to explore the fall of an object with air resistance.

Apparatus:
Using the structure of building 13 at Mt. SAC, we were able to set-up our apparatus. The camera was set on the staircase, and the coffee filter was dropped from a bridge at the center of the building. Each drop had different amount of filter: the first drop had 1 filter, the second drop had 2 filters, the third drop had 3 filters, the fourth drop had 4 filters, and the last drop had 5 filters. Each drop was recorded with a camera and inserted into Logger Pro. Then we plotted a position vs. time graph for each, which gives us the velocity                                                             of each drop.

Explanation:
The relationship between air resistance force and speed is shown by the equation F_resistance=kvⁿ, where v represent the velocity, k represents the constant relationship, and n represent the exponential increase of the velocity. To find the value of k and n, we take velocity of data from 5 different trials and the mass of the coffee filters. The videos shown below are the ones that were captured by Logger Pro application and camera. We used the video to track the movement of the filters as they fall within a certain time period. 

Video 1: One coffee filter

Video 2: Two coffee filters

Video 3: Three coffee filters

Video 4: Four coffee filters

Video 5: Five coffee filters

Graph a velocity vs. force chart and power fit the graph and get an equation of F=kvⁿ, and the value of k and n is shown. We obtained the formula to be F=0.006207v^1.827.

After finding out the value of k and n, we used excel to model the fall of an object with air resistance. We started out with time and initial acceleration. The time interval was 1/200th of a second. With the difference in time and initial acceleration, we found change in velocity, which can give us instant velocity. to find instant acceleration, we used the drag force formula we obtained from before and subtract that from the gravity we had previously. To find change in height, we took half the sum of the velocity interval and multiply by the time interval, and with this we were able to find the distance traveled by adding the previous to the change in height.

We then filled downward till we found were acceleration was constant, which was well over three seconds and the acceleration reached -1.7x10^-13.

To get these results, we had to choose which video gave us the best results, and use that for our excel charts. We decided that trial 2, with two coffee filters, gave the best results and entered our excel values according to trial two.

Summary
Air resistance is a factor of acceleration, where the force of the resistance is the same as the force of increasing acceleration. In other words, acceleration is constant after a certain time period. We used coffee filters to measure air resistance, and modeled it with excel to see how long it takes for the force of air resistance to match the force of increasing acceleration. We found that it would take about three seconds for 2 coffee filters to reach constant acceleration.