The Three-Step Approach to Problem Solving
The systems we will look at in this chapter won’t test
your knowledge of obscure formulas so much as your problem-solving
abilities. The actual physics at work on these systems is generally
quite simple—it rarely extends beyond Newton’s three laws and a
basic understanding of work and energy—but you’ll need to apply
this simple physics in imaginative ways.
There are three general steps you can take when approaching
any problem in mechanics. Often the problems are simple enough that
these steps are unnecessary. However, with the special problems
we will tackle in this chapter, following these steps carefully
may save you many times over on SAT II Physics. The three steps
Ask yourself how the system will move: Before
you start writing down equations and looking at answer choices,
you should develop an intuitive sense of what you’re looking at.
In what direction will the objects in the system move? Will they
move at all? Once you know what you’re dealing with, you’ll have
an easier time figuring out how to approach the problem.
a coordinate system: Most systems will only move in one dimension: up
and down, left and right, or on an angle in the case of inclined
planes. Choose a coordinate system where one direction is negative,
the other direction is positive, and, if necessary, choose an origin
point that you label 0. Remember: no coordinate system
is right or wrong in itself, some are just more convenient than
others. The important thing is to be strictly consistent once you’ve
chosen a coordinate system, and to be mindful of those subtle but
crucial minus signs!
free-body diagrams: Most students find mechanics easier than electromagnetism
for the simple reason that mechanics problems are easy to visualize.
Free-body diagrams allow you to make the most of this advantage. Make
sure you’ve accounted for all the forces acting on all the bodies
in the system. Make ample use of Newton’s Third Law, and remember
that for systems at rest or at a constant velocity, the net force
acting on every body in the system must be zero.
Students too often think that physics problem solving
is just a matter of plugging the right numbers into the right equations.
The truth is, physics problem solving is more a matter of determining
what those right numbers and right equations are. These three steps
should help you do just that. Let’s look at some mechanical systems.