Buoyancy, Gravity, and Drag on a Sphere Immersed in a Liquid

This Demonstration shows the velocity and position as functions of time for two spheres immersed in a liquid, rising under the influence of the forces of buoyancy, gravity, and drag. You can vary the base mass and radius of the blue sphere, and also the red sphere's mass and radius relative to the blue sphere. The spheres start out at the bottom, defined as 0 meters on the scale, and travel upward to a height of 100 meters, where they will have achieved terminal velocity.

The forces are due to gravity, buoyancy, and drag, which appear in that order in the above differential equation. The Demonstration restricts the controls to make certain that the spheres are buoyant. The buoyant force acts upward, while gravity acts downward, as does the drag, which acts as a retarding force proportional to the square of the velocity. When the upward and downward forces reach equilibrium, a terminal velocity is attained.