Physics Activity: Air friction and terminal velocity

Link to air friction lab activity.
This lesson satisfies Part 1, Topic 7f of the Physics syllabus used in Sierra Leone.

If dealing with Newton's laws of motion and everyday forces, having some understanding of air friction, or drag, can help students understand several aspects of this force. The first is that air friction's strength depends on how fast an object is moving. Note that this is true for fluids in general (gases and liquids); students trying to walk through water in a lake or pool say it is much more difficult to try and run through the water. We assume and use the equation
                                                      f_air = -kv
where k is a constant and v is how fast an object is moving through air. The minus sign, -, just means that the friction force is always opposite the motion of the object. Keep in mind this is a very simplified, approximate math model for air friction. In reality, many other factors would affect the strength of air friction, such as material and shape of the object; the cross sectional area as it moves through the air; and the air temperature, density and pressure.

There are two main types of problems we typically can do with students. The first is thinking of an object moving horizontally through the air, and air friction is the only horizontal force. The second is thinking about an object moving through air while also having a second, constant force acting on the object. The links here show how to do the math involved with air friction, which involves some calculus for more advanced students. This could be a skydiver or anything that is falling through air - gravity, which we assume is a constant force, mg, pulls down while air friction is directed upward. Or this could be something being pulled sideways by a constant tension force with air friction being opposite the motion. If you have access to the Internet, there is a good computer simulation showing the effects of air friction on an object thrown through the air (projectile motion).

This experiment involves dropping a coffee filter, or other piece of paper that is shaped more like a cup, that simply is dropped and falls gently through the air. Because it is so light weight, the paper almost immediately falls at a nice, constant drift speed called the terminal velocity. One can also drop a small object into a pool or tall graduated cylinder of water, and it will also drift down at a constant speed. Terminal velocity is the result of a constant force and air friction being opposed in direction, where the object moves so fast that the air friction force balances the constant force. The acceleration of the object would be zero when the forces balance each other:
                                           F = ma = mg - kv
                                           If mg = kv, then the acceleration a = 0, and v_t = mg/k.

Students can measure the terminal speeds in this lab activity, and get a feel for how air friction behaves.