How to do Air Friction on a Sky Diver

Here is a case where air friction acts on a falling object, such as a sky diver. This is one of the trickier math problems we will do in physics, as it involves calculus (anything with air friction will, since it is a non-constant force: f = -kv). We specifically want to solve for the velocity as a function of time for the sky diver. Check this out to get a feel for how Newton's 2nd law sets up the equation, and then we do almost all algebra with a step of calculus to solve for velocity. Note that terminal velocity is the speed you reach when air friction matches the strength of gravity, and the person falls with a constant speed at that point. Also note that we do a very simplified model of air friction. Other factors we do not worry about here include the shape of the object, air density that varies with altitude, wind, air temperature that varies, the material of the object, the gaseous composition, and so on (for us, all this information is contained in the constant, k).

How to Interpret Potential Wells

We have looked at potential wells, which are just graphs of potential energy as a function of position. The classic way of thinking about this is to imagine one object fixed at the origin, and have a second object moving along the x-axis. The graph tells us the potential energy between the two as you move that second object. We look at the potential energy gradient in order to determine the force function, F = -dU/dr, or in other words the force graph is found by plotting the negative slope of the potential energy graph. I outline this by using the 'Nike' problem from an old AP exam. Check it out!