Drag Force on a Coffee Filter

Introduction:

When Objects move through fluid (such as air), a drag force is exerted on the object in the direction opposing motion. It is not a constant force, as it varies with velocity. The effect and dependence of velocity on the drag force will be investigated, and the formula that we are to verify is as follows:
                                                                       F_D=k*absval(V)ⁿ 

Purpose:

The purpose of the Drag Force on a Coffee Filter lab was to learn about the relationship between drag forces and the velocity of a falling object. We were to verify that the drag force is proportional the speed of an object given by the formula:

 F_D=k*absval(V)ⁿ  

where we were to determine n's value. The accepted value of n will be 2.

Setup:

Tools used in this lab included the Logger Pro software, lab pro, motion detector, nine coffee filters, and a meter stick.

Motion Detector

The setup for this lab was relatively simple, after connecting the motion detector, turning on the computer and opening the logger pro software, the motion detector was placed on the ground facing upwards.



In this lab we were given a packet of 9 coffee filters, and it was crucial that the shape of the filters remain constant. Since the drag force depends on the formula D = (1/4)*A*v², where A = cross sectional area of the object, if the shape of our coffee changes (eg. folding), the amount of drag force being applied to our filters will become smaller. Thus, it is important that we keep our coffee filters flat.

Procedure:

The packet of 9 coffee filters had to be held at a minimum of 1.5 meters above the motion detector before it was dropped. After performing 5 trial runs for the 9 coffee filter packets, we removed one and did 5 more trial runs. this was repeated until we got down to one filter.

What should the position vs. time graph look like? It will be a quick drop in position until the terminal velocity is reached, which is when the graph becomes linear.

Fig 1

Pictured in fig 1 is the position vs. time graph of trial 4 with the linear fit of the 8 coffee filters reaching terminal velocity.

What does the slope of our line represent? It should represent the velocity that the object is traveling at once it reaches terminal velocity.











After the information for each trial run was collected,  the average speeds from each trial were taken to be the independent variable, and the number of coffee filters was taken to be our independent variable. Copying our data into the graphical analysis software, the graph pictured in fig 2 was obtained with its numeric values to the left. Once the power law fit was applied to our data plots, we obtained our experimental value for n in our equation from the beginning of the lab.

F_D=k*absval(V)ⁿ 

The equation with the fitted values was:

F_D=2.14*x^1.95 ,

Data: 

The data that was collected from each of the trial runs was put into the data table in fig 2, along with the average velocities of the 9 different coffee filter amounts.

Conclusion:

In this lab, the effect of drag forces against the velocity of our falling coffee filters was able to be determined. The more massive the object, the greater the velocity and drag force the object experiences. The errors that may have thrown off measurements in the lab include:
       1) Possible slight folding of coffee filters after release.

       2) The filters may have experienced trajectories that were not exactly perpendicular to the ground

In order to determine the amount of experimental error in this lab, the value for n that we measured was compared to the accepted value of n=2 from the drag force equation to determine the percent difference.

(100*(2-1.95))/(2)

=2.5% difference