The 11 Steps of Numerical Problem Solving for Physics

In this post you will learn the 11 steps of numerical problem solving for physics. These steps are flexible and could also be used to solve problems in many other disciplines such as chemistry and engineering. At first glance some physics problems look overwhelming, especially when written as lengthy word problems. But if you do follow these 11 steps the physics problem becomes more clear and the answer more easy to attain. Let’s jump right in to these steps below.

Step 1: Read and reread the question

It is paramount to read the problem and begin to visualize the scenario. Get an idea of what the problem wants you to solve, then go back and read it through thoroughly again, word for word, don’t skip through the sentences as you may miss crucial information. Note the given information in your notebook, for use in step 3, and remember that sometimes too much information is given and not all the values are needed.

Step 2: Draw a diagram

With your understanding of the question, begin to draw a diagram that best describes the scenario. Be sure to label the diagram with directional coordinates, and vectors, if necessary. Don’t spend too much time drawing this diagram as you’re not in art class here, but do draw the diagram large enough with clean lines so that the when the important information is added the diagram remains legible.

Step 3: Indicate the known quantities

Review the given information, the information you noted in Step 1, and place these known quantities on your diagram. Write the variable, the value, and its units. Be sure to include subscripts on the variables, when needed, to indicate initial and final values etc.

Step 4: Determine the unknown variable(s)

The word problem usually asks you to solve for an unknown value in the last sentence. Ensure that you have understood what is to be solved, what the variable is, and what units are to be given in the answer. Now, go back to your diagram and include this unknown so that you may clearly visualize the scenario. When I include the unknown in a diagram it would look something like this, if we were solving for final velocity (vf), vf = ? m/s.

Step 5: Select the appropriate formula(s)

If you have followed the previous steps you should now have a thorough understanding of the given information in the problem and, most importantly, what the problem is asking you to calculate. Armed with this knowledge, flip through your text book or formula cheat sheet looking for an equation that suits your needs. In the case, where we have one unknown value to solve for, look for an equation that includes your unknown value and the values given in the word problem. Be sure there is only one unknown value in the formula you select. In the case that there are two unknowns in the formula you must then find another equation that is independent of the first and that includes one of the unknown values (you may remember the saying “two equations with two unknowns”. Write the formula down on your notebook, just below the diagram, for reference.

Step 6: Solve the formula(s) algebraically

Sometimes the formulas are not setup the way you like. For example, the unknown value my not be isolated to one side of the equation (ideally the left side) and is instead mixed up with the other variables represented in the given information. If this is the case, it is imperative that you solve the formula algebraically to begin with. Fight the urge to just start plugging known values into this formula, it’s hard at first, but after some practice you will reap the benefits of solving the algebra initially, that is with no addition of numerical values. This post will not go into the art of manipulating formulas algebraically as that is a whole topic of its own. What you want here is to have your unknown value isolated all by itself on the left hand side (LHS) of the equation with all the known variables on the right hand side (RHS). After solving the algebra to suit your unknown, put a rectangular box around your formula, this indicates to you and to the marker that this is the equation you are using for your calculation.

Step 7: Convert units for known quantities

Again, before jumping in and entering your known values into the equation, be sure that you are using units that jive. For example, if you have units of feet, ft, and meters, m, you will have to choose one unit type to use and stick with it. Even pay attention to centimeters, cm, and meters, m, as they also don’t jive. The best way to decide which unit type to choose is to look at the units of the unknown value, that is, what units does the practice problem ask you to provide? These unit conversions can be done before plugging your values into the formula, or if you’ve had practice doing this, you may perform the unit conversions within the formula itself.

Step 8: Plug known values into solved formula and track units

You’ve got your known values, your diagram, you know what your unknown variable is, you’ve selected a formula to use, and you’ve converted your units successfully. Guess what? You’ve already got 60% of your question correct. Now comes the fun stuff, entering your variables into your formula. This part always puts a smile on my face. And no matter what anyone tells you, be sure to include units when plugging your values into your solved formula. Why do you ask? This is a way to double check that your algebraic manipulation was correct, it isn’t a fool proof method, but if your units don’t match then your algebra is probably wrong. You can achieve this by cancelling out your units in an appropriate manner and then checking which units are left over. For example, if you’ve got meters per second, m/s, left over after cancelling units, and your unknown variable is velocity, then you’re probably on the right track. If something doesn’t look right here go back up through the previous steps and try to catch your mistake, it is commonly in the algebra or the unit conversions.

Step 9: Calculate your unknown value

Pull out that trusty calculator and plug away. Enter the values and be sure to use brackets on your calculator to force operations in the correct manner. Take your answer and write it down with the correct amount of significant digits as required by the question, and remember to include its variable and its units. Put a rectangular box around this answer and be proud. Wow, we did it. Look at that, you’ve successfully solved for the unknown variable. Now, does it make sense?

Step 10: Does the answer make sense?

Think about the problem, and think about the answer. Does it make sense? If it seems way off maybe something went wrong with unit conversions or decimal places, review your preceding steps and look for anything that stands out. It’s always good to take a minute to double check your initial work, and remember to reread the problem at this point as well. If you follow these steps you will do well in your physics class.

Step 11: Double check answer with iEquals Formula Solvers

As an additional step, for homework problems and assignments, you may use iEquals Formula Solvers for iOS to quickly double check your solution. Just choose the formula you selected in Step 6 and enter your unknown values and their accompanying units. Now simply tap iEquals and it will display the same answer you calculated in Step 9. This is also a good way to see which of you in your study group has the correct answer, no more debating, just pull out the app and enter your values. Once you’ve decided who has done the problem correctly you may all move forward and figure out how it was done. Be confident that you can move on to subsequent questions after double checking your homework with iEquals.

Thanks for taking the time to review this post. Feel free to leave questions or comments below. Happy solving!

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