TABLE OF CONTENTS It seems at first sight odd to have chosen the subject of forces, and their effect, as a unifying theme for an entire chapter on modeling. A superficial argument can be made that a single example, or perhaps two or three examples, would suffice to demonstrate the use of Newton's law. That law is commonly, and somewhat, restrictively stated as Force = Mass Acceleration. This ignores two important facets of this relation. The first is the variety of forces or changes in velocity that can arise under different physical circumstances. Among forces, those due to gravitation, electrical fields, or magnetic fields immediately spring to mind. Pressure and stress, which are defined as force per unit area, are additional sources of expressions involving force. So is work, which involves the application of a force over a given distance. Changes in velocity, which is a vector, can come about as a result of a change in its magnitude (speed) or because of a change in direction. The second facet is that Newton's law also applies to static or stationary systems, in which case one uses the special form: Sum of Forces = 0. The Examples and Practice Problems we present in this chapter reflect this variety of situations.
Gravitational forces in dynamic systems are at the core of Examples 4.5 (Path of a Projectile) and 4.6 (The Law of Universal Gravitation). In its static form, gravity is used to calculate the lift capacity of a hot air balloon...
