Coffee Filters

Description: Dropped coffee filters illustrate terminal velocity and the velocity dependence of the drag force.

Drop a single coffee filter and note its motion. Drop two filters, nested, and compare.

Drop the single filter from a height of 1 meter. Inquire from what height the two nested filters would need to be dropped to reach the ground at the same time as the single filter when dropped from 1 meter. It turns out that this height is very close to 1.4 meters. This suggests that the drag force in this case goes as the velocity squared.

The velocity of the filters may be measured by means of the Vernier software motion sensor and MacMotion. Plots of the position and velocity as a function of time for filters from the Physics coffee machine (9.5 inches diameter when pressed flat, mass approximately 1.6 grams) are shown below for one, two and four filters. The position plots have been offset slightly so as not to interfere.

A string was hung from the ceiling above the motion sensor to provide a guide for dropping the filters. The filters, especially the single filter, had a tendency to flutter. No great care was taken in acquiring these data.

Cautions:

Concepts demonstrated: Air resistance

Equipment: coffee filters, meter sticks;
motion sensor, computer and display unit if desired

Setup Time: Short; longer if computer is needed

Difficulty/Commitment: Straightforward

Visibility: Visible

Related demonstrations:

References: PIRA 2C30.65
DaR M-136; Ehrlich(2) 2.13 p 40;
Angell, Carl and Trond Ekern, "Measuring Friction on Falling Muffin Cups" TPT 37(3), 181-2 (March 1999)

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