Drag, viscous forces and terminal velocity

Last time

Before we start: last time, in Newton's laws and force as rate of change of momentum, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

A skydiver stops speeding up

A skydiver leaves the plane and speeds up rapidly. After about ten seconds she is falling at a steady speed of fifty metres per second, even though gravity is still pulling. The fluid pushes back harder the faster she goes, until the forces balance.

Drag and viscous forces

When an object moves through a fluid, the fluid exerts a force on it that opposes its motion. This is called drag, or a viscous force. The drag depends on the speed. At low speeds it is about proportional to speed; at higher speeds it grows faster. It also depends on the shape of the object, and on the fluid: honey gives more drag than water. The drag is zero when the object is at rest in the fluid.

Falling with drag

At the start, the speed is zero, so there is no drag. The only force is weight, so the acceleration is g. As speed rises, drag rises. The resultant force falls, so the acceleration falls. The speed still increases. When drag equals weight, the resultant is zero. The acceleration is zero, and the speed is constant: terminal velocity. The object keeps moving. Zero acceleration does not mean zero velocity.