Problem Solving Tips

One of the benefits of taking a physics course is learning a type of analytical thinking sometimes called problem solving.  We are talking about solving physics problems of course, not personal or social problems, but learning to think analytically can be useful in many other endeavors.

In this course you will need to solve lots of homework problems and a fair number of exam problems.  Each problem will be different, so the exact steps will differ from case to case.  Nonetheless, there are some basic techniques that will usually be helpful.
 

Step 1

Identify the important features of the physical situation in the problem, and then simplify - or idealize - the situation to isolate the important features and ignore the unimportant ones.  (A common example of this in a mechanics problem is treating an object as a particle.  This reduces the object to a point - with mass.)
 

Step 2

Draw a figure (a simple sketch) of the physical situation, showing all the distances, angles, forces, and other relevant quantities.  This is because it usually helps to visualize the problem.  If you have been given numerical values for any of these quantities, next choose a symbol to represent them, since manipulation of equations that may be needed later should be done with symbols rather than numbers. (Numbers should only be inserted at the end, when the final answer is being evaluated.)
 

Step 3

Identify the quantity (or quantities) of interest.  These are the things you are trying to solve for.  Assign them symbols as well.  Indicate them in the figure if possible.
 

Step 4

Think about the physics of the problem.  This may be the hardest part for some students, but it is also the most important.  This is where the problem is actually solved, by identifying the key idea - the physics principle that determines the answer.  In some mechanics problems, it may be Newton's Second Law (F=ma), or perhaps the principle of energy conservation or momentum conservation.  Whatever it is in a particular problem, this is where your understanding of physics is being tested.  Simply plugging symbols into randomly selected equations is not going to help.   If you are stumped at this point, you need to reread the relevant textbook chapter(s) or to review your lecture notes.  (It is important that you try to figure things out for yourself, but if you are still stumped after making a genuine effort, you need to get help.)  It is essential to understand the physics principle that governs the physical system in the problem.
 

Step 5

Once you have determined which physics principle to apply, you will have an equation (or equations) to work with, since physics principles are almost always formulated as equations (in general form).   Specialize the general equation(s) to your problem by inserting the symbols you are using in the appropriate places, and then solve for the quantity of interest.
 

Step 6

After you have solved the equations, you are not done yet.  You should test your answer to verify that it makes sense.  Specifically, it is usually a good idea to:
i)  Check the dimensions.  If your answer is an expression that contains multiple quantities, you should perform dimensional analysis to verify that the dimensions of your answer are what they should be.

ii) Graph the solution.  If your answer gives a physical quantitity (such as speed, acceleration, frequency, etc.) as a function of other quantities (such as the mass of the object, its initial speed or position, etc.), make a graph that shows the relationship between these quantities.  Then ask, does this make sense?  To answer the question, you must again appeal to your understanding of the underlying physics principle.
 

Step 7

Finally, if you need a numerical answer, now is the time to plug in the numbers and evaluate the answer.  Of course you should do this carefully, and it is often a good idea to make a ballpark estimate before resorting to your calculator.  In any case, this step - while important for getting the right answer - is just arithmetic.
 
If you look back over these steps, you will see that it is mainly Steps 1, 4, and 6 that involve physics.   Recognizing which physical quantities are important, understanding the physics principles to apply, and figuring out if your result makes sense, these steps depend upon learning some physics.  The others are more routine and depend more on mathematical skill.  To be sure, some students may stumble because they lack necessary math skills.   Before you take this course, you need basic skills in algebra, trigonometry, and elementary calculus.

The textbook, Essential University Physics by Wolfson, recommends the "IDEA strategy" for problem solving.  The seven steps discussed above do not go by a clever acronym, but it is possible to map the seven steps onto the four words represented by IDEA:

 We distinguish solving the problem (step 5) from numerical evaluation (step 7), and suggest "testing" your answer (step 6) before numerical evaluation (step 7), since having the value of the numerical answer is usually not key to figuring out if you solved the problem correctly.  As noted above, numerical evaluation is just arithmetic; you should do it carefully, and maybe check it twice, but plugging the numbers into your equations too early will only make it harder to see how different quantities are related to each other.  That is why plugging in the numbers is our last step.