More on Friction, and Terminal Velocity

Friction

It is easy to measure the coefficient of static friction between two materials: simply place one on the other, tilt the lower until the upper one starts to slide, and then
```
        mu(static)  =  tan(theta)
```
where theta is the angle required to cause motion.
When a body moves through air, water, or some other substance, there is a force of resistance which opposes the motion. For example, in air, a body experiences air resistance.
Forces of resistance often depend upon the speed v of an object through the medium:
```
         force  =  (constant) * v
    or
                                 2
         force  =  (constant) * v
```
The "constant" depends upon the cross-section area of the object, and on properties of the medium.
As an object falls through the air, it experiences a constant downward force (gravity), and a growing upward force (air resistance). If the object falls fast enough, the upward force can cancel the downward force; at that point, the object stops accelerating downward and falls at a constant terminal velocity.

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Now, faced with a differential equation, we can try to solve it analytically (pencil and paper), or numerically (with a computer). Let's try both methods.