Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

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.

Viewgraphs

Viewgraph 1

Viewgraph 2

Viewgraph 3

Viewgraph 4

Viewgraph 5

Viewgraph 6

Viewgraph 7

Viewgraph 8

Viewgraph 9

Viewgraph 10

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.

Analytical solutions

Viewgraph 10a

Viewgraph 10b

Viewgraph 10c

Viewgraph 10d

Viewgraph 10e

Viewgraph 10f

Viewgraph 10g

Viewgraph 11

Viewgraph 12

Viewgraph 13

Terminal Velocity

Viewgraph 14

Viewgraph 15

Viewgraph 16

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.