Physics 271: Advanced Honors Physics I

Recitations: Problem-Solving Toolbox

Fall 2017

**Solving differential equations I:** Check to see if it is
separable (for a review of separable diff equations, see the Week 1
resources on the main page). Once you separate it, see if you can do
the indefinite integrals. Then, choose the constants so that the
function satisfies the initial conditions (or other given
information)

**Solving systems of simultaneous linear equations:** Systems of
two linear equations in two unknowns come up frequently and
occasionally we have to solve systems of three equations in three
unknowns (usually the latter are special cases that allow simpler
solution by hand than the general case). You should be able to do
these quickly and accurately by hand. One tip is to rewrite and
organize the equations neatly together to get the solution started.
Another tip, to reduce work, is to look at the problem to see what
quantity or quantities are asked for, and solve by eliminating the
quantity or quantities not asked for.

**Solving min-max problems:** If you need to find the maximum or
minimum value attained by a certain quantity, and there is no
obvious shortcut, you should use the procedure you learned in
calculus class. First, write the quantity to be maximized as a
function of the quantity that you can vary. Then compute the first
derivative and set it to zero to find the extrema. Evaluate at the
extrema and also at the endpoints of the domain, and choose the max
(or min) value.

**Check the units:** After doing the algebra to express the
quantity (or quantities) desired in terms of the given quantities,
check that your answer has the right units. This is necessary but
not sufficient for a right answer, but it's quick and can help you
pick up some mistakes.

**A rule to decide which direction to draw the friction force when
making force diagrams:** First solve the related problem in
which the coefficients of friction are all zero. Then look at the
relative motion you find for the surfaces with friction: the
direction of the friction force will act to oppose the relative
motion. This works both for static friction forces and kinetic
friction forces in all the problems we have considered so far, so it
is looking good as a general rule -- if you find an exception, let
me know!

This page is maintained by Karin
Rabe.