09-Mar-2015 Lab 4: Modeling the fall of an object falling with Air Resistance

Purpose:  To determine the relationship between air resistance force and speed of an object, first by graphing data and fitting it to a power equation model, and then using that model to verify our experimental results.

Materials:  5 coffee filters, meter stick

Procedure:

Part 1:

• We first took videos of coffee filters falling from a height of around 2 stories, in the balcony of the Design Technology Building.  In the first trial we dropped one coffee filter, in the next we added one filter to the top and dropped the two together, and did this until we dropped 5 together.

Dropped from second story, filmed from staircase.

• Together the class measure the white portion of the balcony in order to scale the proper height to the video.  Back in the classroom, we used LoggerPro to plot positions of the coffee filters to corresponding times on each video, and got 5 different position vs. time graphs.

Postion vs. Time graph for third trial using 3 coffee filters

• By taking the linear fit to the end positions of the coffee filters, we were able to find the terminal velocities for each trial.  
• We also found the mass of 50 coffee filters (46.2 g), and dividing by 50, which gave us a mass of 0.924 g per single coffee filter.  We multiplied the masses during each trial by 9.8 m/s^2 to find the downward force of each coffee filter.
• We plotted this data of terminal velocity vs. Force into LoggerPro, and used the power fit of Fresistance = kvⁿ 

Graph of velocity vs. force, with a power fit of C=Ax^B, where C=Fresistance, A=k, x=velocity, & B=n

• Our graph shows the following:
• k = 0.01243
• n = 1.819
• The value of k takes into account shape and area
• The value of n changes as a fractional power of velocity.  If an object is moving twice as fast as another object, it collides with twice as many particles.  In this case, the particles are colliding at a speed with respect to the various velocities of the coffee filters.

Part 2:

• We then used the values of k and n we derived from Part 1 to determine the final velocities of each trial using excel and comparing them to the experimental data.

Equation for acceleration

• Δv = aavg*Δt
• v = v+Δv
• Δx = vavg*Δt
• x = x+Δx
• Plugging all this in and setting time = 0.002 seconds, we were able to fill the data down to find terminal velocity (where velocity changed very little), and then compared these results to the results from our experiment.  The following excel graph is from our 5th trial (using 5 coffee filters):

• At around t = 0.53 seconds, the coffee filters began to reach terminal velocity.  Our chart shows a terminal velocity of around 2.00-2.01 m/s, and from our graph of position vs. time we found the terminal velocity to be 2.019 for the same trial.
• The remaining models were not as close in velocities, but were somewhat similar.

• The results may not have matched as well as we had hoped due to a number of factors: the coffee filters somewhat fluttered, or fell in a back and forth pattern, there could have been error in the precise placement of position of coffee filters in the video, or we didn't find the best fit line for the position vs. time graphs for each trial.