Several groups of students conducted an experiment to investigate the relationship between the terminal speed of a stack of falling paper coffee filters and the mass of each stack. Their procedure involved stacking a number of coffee filters, like the one shown in the figure above, and dropping the stack from rest. The students change the number of filters in the stack to vary the mass m while keeping the shape of the stack the same. As a stack of coffee filters falls, there is an air resistance (drag) force acting on the filters.

 

 

The students suspect that the drag force FD is proportional to the square of the terminal speed v of each stack.   where C is the drag coefficient, A is the cross-sectional area of the filter, and ρ is the density of air.   Using this relationship, derive an expression relating the stack's terminal speed vt to its mass m.     When the students graphed their data as Terminal Velocity vs Mass, they obtained the following graph in EXCEL.   Why did the group place the mass on the x-axis of this graph?

What does the exponent on EXCEL’s “trend line” tell the students about the relationship between terminal velocity and mass?

(b) Use the empty column to modify the data to create a graph of their which will be linear. Label your y-axis, scale both axes, and plot your modified data points. Construct a LINE OF BEST FIT, find and list two GRID points, and show your calculations to find the line’s slope.

(c) Based on the slope of the line, calculate the effective area of the coffee filters. You may use C = 1.12 and ρ = 1.225 kg/m3.

(d) Based on the graph in part (b), what would be the terminal velocity of a stack of coffee filters having a mass of 0.0120 kg?

(e) Based on the information from the 3rd trial [mass = 0.00296 kg and vt = 0.83 m/sec] determine how many seconds those filters needed to fall 2.60 meters.

(f) Complete the following sketches while these filters were moving at terminal velocity.