The added mass of a spherical projectile

• Published in: American journal of physics Vol. 79; no. 12; pp. 1202 - 1210
• Main Authors: Pantaleone, J., Messer, J.
• Format: Journal Article
• Language: English
• Published: Woodbury American Association of Physics Teachers 01-12-2011; American Institute of Physics
• Subjects: Inertia; Physics; Science activities; Science education; Velocity
• ISSN: 0002-9505; 1943-2909
• DOI: 10.1119/1.3644334

When a ball moves through the air, the air exerts a force on the ball. For a sphere moving at constant velocity with respect to the air, this force is called the drag force and it has been well measured. If the sphere moves with a nonconstant velocity there are additional forces. These “unsteady” forces depend on the sphere’s acceleration and, in principle, also on higher derivatives of the motion. The force equal to a constant times the acceleration is called the “added mass” because it increases the effective inertia of the sphere moving through the fluid. We measure the unsteady forces on a sphere by observing the one- and two-dimensional projectile motion of light spheres around the highest point. The one-dimensional motion is well described by just the usual buoyant force and the added mass as calculated in the ideal fluid model. This measurement is an excellent experiment for introductory physics students. For spheres in two-dimensional projectile motion the downward vertical acceleration at the highest point increases with the horizontal velocity. This effect can be described by an additional force proportional to the speed times the acceleration.