9- Sept. - 2014 Air Resistance Lab

Air Resistance Lab

Objective:

 1) Determine the relationship between an object's terminal velocity to its mass.

 2) Model a falling object with air resistance.

Set- up:

 To set up for this experiment we needed a computer with logger pro, a video recording via smartphone or FireWire, an area with very little draft or wind (room seen in fig. 1a), a stack of coffee filters (fig 2.), and a scale reference (meter stick). We are to record the coffee filters falling with each trial having a slight more mass than the previous trial up to 5 trails (5 filters stacked).

Figure 1a. The area in  which we drop our coffee filters as well as
the frame of perspective we were advised to film our trials.

Data Collection (Part I):
 Before starting this experiment, we first , predicted what our relationship between force of air resistance Fres.  to be related to a mass's terminal velocity vter. by a power rule:

Fres. = k*vterm. ^n

Where n and k are constants.

Using the set up we have, we attempted to fulfill our experiment, but our last trial with 5 filters was lost      

and so our Data will only have 4 trials listed hence forth. Now since the room    

Figure 2. Coffee filters of different colors

to make them easier to chart movement with

 a white background.  

is indoors with limited draft can be assumed negligible. We filmed our four trials and charted its movements. If you notice, that graph was linear fitted at the most linear interval where it can be determined as the terminal velocity in the trial as seen in (fig 5). The reason being, just like in the initial prediction, we were trying to find the terminal velocity by finding the slope of the mass's position graph when the slope is linear representing m= vterm for that particular mass.

After graphing each trial and finding their terminal velocities, we used the total mass of each trial to graph a Fair vs. vter graph because at the terminal velocity the force of air resistance is equal to the mass's weight w. Our ordered pairs of this new graph are shown in (fig 3a.) numbered by the trial they represent. Lastly, we were told to create a power fit for this new scatter
plot to find our n and k values for our initial formula:

Fair.= k*(vter.)^n

Figure 3a. Found vter. for each trial and
F is the total mass of the filter stacks
respective to trial number.

So after we created our power fit for our 4 points (trials), we looked for which points fit closest to our power fit is on trial number 4 seemed to fit the graph very well seen in (fig 3b) which is helpful in choosing our best reference interval for part 2. 

Figure 3b. The resulting scatterplot of the previous figure of force vs. calculated terminal velocity. There is also a power fit where the value of y is Fres , A is the value of k, and B is the value of n.

With this we have also identified our n and k constants:

n= 2.162 ±  0.1645 

k= 0.0109 ± 0.0007 

This are our experimental values for our values in this power law we made for air resistance.

Data Collection (part 2):
 We then tested our accuracy of our results by finding terminal velocity numerically for one of our trial in which we previously mentioned to be trial 4 seen in (fig 4). We graphed both results in increments of (1/30th) of a second. With our current values for n and k, the two graphs are very similar so there wasn't a reason to alter them.

Figure 4. The movie capture graph from our 4th trial (4 filters)
with a linear fit of v is approximately 1.942 m/s while the model
with a close fit has a slope of 1.8836 m/s or 1.884 m/s.

Figure 5. The lay out for the numerical calculation on excel for trial 4. Velocity seemed
 to approach 1.8836 m/s and can be determined as the terminal velocity for this trial.

Figure 6. The work on deriving different sections of the excel lay out. There is also the
propagated uncertainty of the force of air resistance due to the uncertainty for n and k as well as the error between theoretical and experimental values of terminal velocity.

Conclusion:

We have concluded that the amount of uncertainty (shown in fig 6. above) for the force of air resistance due to the uncertainty which are:

dk= .0007

dn= .1.645

We have propagated an uncertainty for our Force of air resistance for trial 4 as:

Fair. theoretical= .0429 ± .008 N

or  ± 18.6% uncertainty
Fair experimental = .04586 N
+6% more than theoretical

Seeing that the level of uncertainty is poor, our model would not be very useful in calculating the force of air resistance. It may be due to the difficulty of tracking the filter's movements with a similar color background making the filters hard to track. The inaccuracies in the tracking may have caused this large amount of         uncertainty.