The added mass of a falling coffee filter

Abstract

Falling coffee filters are a common object of study in introductory physics laboratory classes. They are usually used to demonstrate the terminal velocity, and determine how the drag force depends on this velocity. However they can also be used to demonstrate other ways that the air affects the motion of the falling coffee filter. In particular, a qualitatively different fluid force acts during the initial acceleration from rest, and causes this acceleration to be much less than the acceleration of an object in vacuum. This fluid force, commonly known as the ‘added mass’, is easily observable with coffee filters using either a sonic motion sensor or video analysis. Here the added mass is experimentally measured for a falling coffee filter. In addition, the theoretical value for the added mass of a coffee filter moving through an ideal fluid is calculated. The two values agree relatively well. Finally, it is shown how the added mass is relevant to experiments that only measure the terminal velocity.