Why is that in order to keep a boat moving in water, you must continue to row? Why do feathers float to the ground much slower than a book? The answer to these questions is resistance or drag. Drag is a force that resists motion. It is caused by shear stresses between the fluid and the body. For most cases we look at high Reynolds number **glossary term** flow where the viscous forces due to the shear stresses are held entirely within a small space called the boundary layer. Since drag is a resistive force, we must counter ballance it to maintain a constant speed. This is why it is necesarry to row a boat continuously. Some objects like the feather have large drag coefficients, while others like airfoils have relatively low drag coefficients. This is why a feather fall much slower than a book.
This is a free body diagram of a pendulum in a fluid. We can see all the major forces acting on the pendulum. The first force is the tension force which restrains the pendulum form moving in the radial direction. The next force is buoyancy force. This force is caused by a pressure difference over the entire body. It works out that this force is equal to the weigth of the fluid that the object displaces. We have already discused the basics of drag, and know that it is always opposite of the velocity vector. It is also perpendicular to the tension force. The primary force that makes all pendulums work is the weight of the pendulum. In our pendulum we neglect the effects of the rod and focus only on the sphere. By solving Newton's equations of motion, we find that the pendulum is governed by the following equation:
To make sure we have the right equation we plug in zero for the density of the fluid, and get the ideal pendulum equation:
Below is an applet that calculates the forces acting on a pendulum. The red lines show where an ideal pendulum, or a pendulum in a vacuum, would reach its maximum distance from its center point. You may choose any of the fluids or even vacuum conditions from the menu. The applet runs for about a minute before having to be restarted. If the pendulum stops all you have to do is select another fluid or reselect the one you already have selected.