Terminal Velocity - Stacked Coffee Filters

Purpose

To illustrate terminal velocity quantitatively.

Equipment

Coffee filters, meter stick.

Suggestions

Practice.

Images

Description

Stacks of different numbers of coffee filters are dropped from various heights. The viscous force is proportional to the square of the velocity, so the terminal velocity is proportional to the square root of the number of filters in the stack. A stack of four filters will have a terminal velocity twice that of a single filter; the stack of four will therefore take the same time to fall two meters that a single filter takes to fall one meter. A stack of two filters will fall 1.4 meters in the time a single filter falls one meter, as is being demonstrated by the gentleman in the photograph.

References

Byron L. Coulter and Carl G. Adler, Can a body pass a body falling through the air?, AJP 47, 841-846 (1979). Neil M. Shea, Terminal Speed and Atmospheric Density, TPT 31, 176 (1993).