How to Solve Physics Problems
HAve you hit the point of frustration when solving problems?
First, I want to reassure you that frustration is normal when solving problems and learning new things. It does NOT mean you are stupid. It means that your brain thought it detected a pattern or “recipe” for solving problems while you were doing the easier, introductory problems and is suddenly finding out that the recipe doesn’t work for more complicated ones; this is actually a sign that you’re about to break through to a deeper understanding! (You can skip straight to the steps if you prefer.)
Rather than trying to memorize algorithms for solving problems, which will lead you to dead ends, think of it as putting together a jigsaw puzzle. You need to find the correct pieces and then assemble them. The method below helps you do this by having you pull the information out into a list so you can easily see what you do and don’t know and can start to match it up with formulas.
Another sticking point is that you may need to combine more than one formula. How do you know when that’s the case? When you look at the formulas that contain the variable you need to find and you don’t have all of the information to plug into any of them, it’s time to pull in another formula to find the missing piece. I’ll write more on that in another post as I roll out my formula sheets that have been arranged to help with thinking through that part.
You may wonder if it’s really necessary to take the time to solve the formulas symbolically rather than plugging in numbers right away. It really is. For one thing, it’s good practice if you plan to study science at a higher level where you will need to collaborate with a team; there are no lone scientists, and it’s important that other people can follow and understand your work. In terms of more immediate payoff, when numbers have been put in straight away, it becomes much harder to locate where you went wrong if you don’t get the correct answer; solving it symbolically saves time in the long run. Many instructors will give you a higher score if they can see that you had a relatively minor error but knew what you were doing, and you don’t want to make them work too hard to figure that out. Plus, you’ll have a much easier time reviewing it before a test or as a refresher later on.
Why carry the units through your calculation? Isn’t that needless writing and effort? Actually, carrying the units through is a great double-check of your calculation. If the units come out correctly, chances are that your numbers are good, too. (If you come up with a complicated-looking mishmash of units, you may want to check my list of compound units to help simplify it to something more recognizable.)
If you’d like a free abridged one-page printable of the steps below plus a printable worksheet to help remind you of what to do, just sign up for my mailing list and you’ll get the download right away.
Step 1: List & Convert
List everything you know using the format of “variable = magnitude [units]”
ALWAYS include the variable and the units, not just the numbers.
Be sure to include all zeros, even the “hidden” ones like the zeros you know are there from wording like “comes to a stop” or “starts from rest” or acceleration when you are told that the velocity is constant.
Remember to include the variable and units of the quantity that you need to find. (You can put it equal to a question mark.)
If there are any quantities not already in S.I. units, convert them now. (Meters-Kilograms-Seconds, etc.) This will keep you from forgetting to do it and make your work on solving the actual problem less cluttered.
Break vectors into their components if you aren’t given the components.
If there are separate parts, list those separately. For example, for freefall, list the fall separately from the impact at the end of the fall. Or for projectile motion, list the horizontal (x) and vertical (y) parts separately.
Step 2: Make a Sketch
LABEL everything in your sketch.
A picture can help you sort out exactly what you need and what you know and will also help you remember in which directions each vector is acting.
Step 3: Decide on an Initial Approach to the Problem
It’s okay to make a wrong start; don’t let it discourage and stop you!
This is the step that many students find frustrating. Don’t worry if your start winds up being a dead-end – that’s normal for complicated, multi-step problems. If you try to memorize steps for solving a particular problem, you’ll soon get overwhelmed because problem-solving doesn’t work that way.
Think of it as putting together a jigsaw puzzle: you’re finding the correct pieces to fit together to create the picture at the end. Look at the equations that contain what you need to find. Do you know everything that you need for the equation? If not, is there another formula? Or do you have enough information to solve for the missing quantity/quantities?
Step 4: Do the Algebra/Trig/Calculus Symbolically
Always solve for the appropriate variable symbolically first BEFORE plugging in numbers!!!
(After writing the full formula(s) out, it’s okay to plug in any zeros before solving, but zeros are the ONLY numbers you should plug in at this stage.)
Why? Because it’s much easier to find errors in your work, not to mention to understand what you did when you look back at it later to study or consult it as a reference, if you can see the algebra unobscured with numbers.
SIDENOTE: Good math grammar means writing the isolated variable on the left.
Step 5: Calculate
Remember to Include the units with the numbers.
Check your answer for reasonableness. Does it make sense? If not, first make sure you copied the numbers down correctly and didn’t make any typos in your calculator.
Also make sure that your calculator is set correctly for degrees or radians. (I’ve had answers that were way off only to discover someone had set my calculator to radians but I assumed it was still on degrees as I had left it!)
If the numbers are fine, then head back to the symbolic section to look for errors.
Check that the units came out correctly. (If your units worked out, there’s a good chance that your numbers did as well, barring any typos inputting them into the calculator.)
And you’re done!
At least for this part of your problem. Repeat as needed for any other parts. 🙂 Remember you can get a printable of these steps and a worksheet to keep yourself organized by signing up for my e-mail list.
Image Credits: I made the header image with Crello and the image is used with permission.
