Hints on Solving Physics Problems
Here are a few hints on a "scientific" approach to problem
solving.

Start early: Start working on a problem set when you receive it,
not the night before it is due.

Read the question carefully: Make sure that you understand both
the information given and the information requested.

Stop and Think: While this may seem obvious, many students rush
into a problem without carefully thinking about it. It is often possible
to make an "order of magnitude" estimate of the solution of a problem.
It may also be possible to solve a simpler problem which will help to verify
your solution to the full problem.

Draw a picture: If appropriate for the problem, drawing a picture
will often help you to visualize the problem better. Even if a picture
is included as part of the description of the problem, a drawing from a
different perspective or angle may help you.

Write down all given information: Include the units for all the
quantities. For unknown quantities, write them as a ? with the appropriate
units. For example, if you are to solve for an unknown velocity, write
it as v = ? m/s.

Write expressions relating the quantities: Use variables such as
x,v,m to represent some of the given quantities such as position,
velocity and mass. Frequently, unit analysis will help with this step.

Simplify expressions using algebra: Before plugging numbers into
the equations, algebraically solve the problem. It is much easier to manipulate
a symbol such as t than it is to be moving around a number such
as 2.20×10^{6 }sec. Another reason for algebraically solving
the problem is that sometimes intermediate calculations will cancel out.
Also, if a general expression is derived it may be possible to use the
same expression for related problems.

Plug in the numbers: When the appropriate equations have been derived,
put in the numbers and perform the necessary calculations. Make sure
that you carry units along each step of the calculation.

Are the units correct? If the units of the answer do not match with
the units which you desired for the answer, you have probably made a mistake
along the way. For example, if the problem calls for a velocity (units
of m/s) and at the end of the calculation the units are m^{2}/s,
you should double check both your algebra and the numerical calculations.

Does the answer make sense? As the final step of any problem you
should ask yourself if the solution is logical. For example, if typical
speeds are on the order of 1 m/s and typical distances for a problem are
on the order of 1 m, typical times will often be of the order of 1 s; if
the answer for this problem is a time on the order of 10^{6 }s
or 10^{6 }s, one should question the result.

Check the answer: Only at this point should you check the answer
at the back of the book. It is important that you gain confidence in your
own problem solving skills. If your answer differs, double check your problem.
There is always the possibility that the answer in the back of the book
is wrong.

Recopy your solution: For a complicated problem, it is important
to rewrite the answer leaving out any incorrect steps taken along the way.
Explain how you went from one step to the next. With a carefully worked
out solution, you will be able to understand the solution a few weeks later
when reviewing for a test. Another person (e.g. the grader) should be able
to follow your method from start to finish without becoming confused.
Some Common Mistakes
Below are a list of some common mistakes (although no means inclusive) made
by students in introductory physics courses.

Adding or subtracting numbers with different units: We all know
that the sum 1 meter + 1 inch is not equal to either 2 meters or 2 inches.
When numbers are added, the units must agree. Similarly, one must keep
track of the powers of ten implicit in a number: for example 1 m + 1 cm
is not
2 m.

Writing a number with the wrong power of ten: As before, an answer
such as 10 cm + 20 cm is not 30 m.

Writing an answer without units: You will not get full credit (on
either homework or a test) for 10 cm + 20 cm = 30, because the number "30"
has no units. If you get in the habit of carrying units along each step
of a calculation, many of these common mistakes can be avoided.

Typing powers of 10 incorrectly on a calculator. A number 1×10^{6}
is sometimes written without the mantissa (the 1 in this case) as just
10^{6}. On a calculator where the EXP key is used to enter
exponents, some people will mistakenly enter 10 EXP 6 to type in
the number 10^{6}, when the correct method is to enter
1 EXP 6. This will introduce a factor of 10 error in the calculation.
Electronic Copy: http://physics.gac.edu/~huber/classes/ph16/solving.html
Revised: 2SEP1998 by Tom
Huber, Physics Department, Gustavus
Adolphus College