Drag Force on a Coffee Filter

Drag Force

 

Equipment: computer with logger Pro software, lab pro, motion detector, nine coffee filters and a meter stick.

 

Drag force opposes a objects motion as it moves through a fluid such as air.  This force increases with the velocity of the object.  In this lab we are investigating the velocity dependence of the drag force. We will assume the drag force Fd has a simple power law dependece on the speed given by

 

             Fd= k /v/ ^n

 

Set up:

     In our computer we started the Logger Pro software, opened the Mechanics folder and graphlab file.  We labeled our axes and set the data collection rate to 30 Hz.  We placed the motion detector on the floor facing upwasrd and held the packet of nine filters 1.5m directly above the motion detector.  When we release our filter and start collecting our data we are expecting to see a positon vs time graph that looks like the following   

                                                      

a straight line ar the time the data collector starts runing.  Then a line with negative slope that        represents the object falling followed by another straight line at zero taht represents teh object       when it hits                                                            thefloor.                                  Experiment:   we relased the filters      and our data collector revealed a graph like the one we were expecting.  After a few trials we were able to verify that our data was consistant.  At this point we toke one of our graphs and selected a small range of data (in uniform motion) where our packets had moved with constant speed.  We then used a curve fit option to fit a linear curve of the form ( y = mx + b ) to the selected range of data.  Our curve fit gave us values for   our variables but the one we                               were interested   in  was the slope (m) of the curve.  The reason for this is that the slope of the position vs time curve should represent the value of the terminal velocity.  Since we are looking at a curve fit selected range of data in uniform motion, which means that we have no acceletation the particle should continue falling at this speed untill it hits the   ground.  If we have no acceletation then Drag force is = to Gravitational force, this is known as terminal velocity.

We repeated this measurement five times and calculated our average velocity. Then we recorded all data in an excel data table.  After our first trial had been completed

we carefully removed one filter form the packet and began the same testing for eight filtes and keeped removing filters one by one untill we were left with a single coffee filter.  The best x vs t graph showing motion and the linear curve fit was printed.  A two column data table with packet wight and average terminal speed was created.  On the y-axis  we assigned packet weight and to the x-axis terminal speed.  We then performed a power law fit of the data & recorded the n power given by the computer.    

 

                                                                                  Error:    our graph gave us a N power of 2.289 +/- 0.1124.  If we subtract the 0.1124 from 2.289 we get 2.177.  Not bad when compared to the theoretical value of 2. 

Conclusion:
It turns out that the Df = Weight = to the # of filters.  We can now say we have found the dependence of drag force on speed.
So if  

   The power law dependence                                                Drag force
              equation                                           &                          equation
                            FD = k /v/ ^2.1               FD = (1/4 AV^2) 
Then the value of n that we found is the same as the value of n given in the text. From this observation we can conclude that the size of the drag is proportional to the square of the objects speed.