How To Solve A Physics Problem
~Max Mroszczak
O’ young physicists and students of today. I hear your struggles and cries every day in physics class. You squeak the butt end of your pencil across the problem set and place your palm aggressively on the side of your head, subconsciously saying to yourself “Hey dumb idiot, this problem shouldn’t take so long! What gives?” But do not fret, I am here. Your saving grace. Your knight in shining armor. The second coming of Sir Issac Newton! Your days of battling against gravity and frictional forces are over, for I have come with the most astute of observations and realizations of your problems and worries.
So without further ado! First, stop. Breathe. Look into my eyes. Scratch that. Look at the words I have typed on your screen. Now look at your problem. Now look back at your screen. Now look back at your problem. See, you just looked back at your problem, meaning it’s in the past, so don’t worry about it anymore! There you go! Now you know how to solve just about any physics problem. All you have to do is put it in the past and pretend it’s no longer there! Bottle it deep deep down and into a pit of despair where it will forever accelerate downwards in freefall (9.8m/s2). Congratulations. You’ve solved your first ever physics problem. Stuff it far down at the bottom of your bag, folded up in a folder you never use and stick it in the middle of the graded social studies summer work you were passed back at the start of the year all so no one will ever see it again.
What? That doesn't help? You've done that before? Mr. Physics just came back to bite you in the tuchus?
Now your bag is full of physics and your gradebook is full of zeroes? Is that why sometimes I catch you turning in homework with dry tear drops all over it? Because of that bottled up physics? Is that why you finally came to ask for my help in the first place? You’ve hid enough physics questions in the dark? You’re not laughing after all that either? Fine, I’ll actually try to help you out. I've gone through this stuff before.
Let me tell you something before we start. And this is actually important. It’s going to be okay. You’ll get through this. We all will. You’ll finish your work on time. Tomorrow, you will wake up, eat breakfast, watch some FloatHeadPhysics videos on youtube, and when you’re all finished, you’ll take a second to breathe, say a few prayers, find your physics textbook, and start working on the problem that was giving you so much trouble the day before. You’ll take a seat and try to figure it all out. And with sheer will and determination, you won't rise out of that chair until you do. You’ll get the chance to calculate the derivative of position with respect to time (dxdt ) or find the horizontal range at which a projectile was launched at an angle.
And you will do so with failures. You will use your eraser and by the time you solve your problem you’ll end up with shavings. But you will also end up with a passing grade. And if not, hey, that's just how it goes for the life of a physics student. Failures and successes. Confusions and understandings. It’s all there. For everyone. You’re not alone in that. Never think you are, because when you take a minute to turn around during your next test, I guarantee you, you’ll find at least one other person with their hand holding up their head and that same look of “Hey dumb idiot, this problem shouldn’t take so long! What gives?”
So, let me walk you through a problem. Let me show you what to do. Consider this. A man pushes a 300 kilogram safe across a horizontal floor with a constant horizontal force of 720 newtons. The coefficient of kinetic friction between the safe and the floor is 0.22. I need to know what on God’s great earth the acceleration of the safe is in this problem. Now, what do you do? How do you start? Will you bottle this physics up too? Stuff it deep deep down again? That’s your call. But I say instead, you put it all out there. That's right. Make it obvious to yourself and to the world what you are doing and what you are trying to solve. Physics won't resolve itself. It’s up to you to take it by the velocity and pull it in a positive direction. So again, make everything known. Put it all out there. You can’t solve a thing when you let all those variables and numbers scatter around in your head and on the paper. You can’t let those units bottle up. Start with the mass. On the side of your paper, write down “m = 300kg” Then do the same with “F = 720N” Under that write “Uk = 0.22” That’s everything you know and everything you are sure of right in front of you. It’s not lost or unfiltered or hidden in the problem. Everything you know is now in a place where you can read and picture it. A perfect starting point. A cure to the chaos. You have taken the first step of pulling the problem out from under your books and notes and now you have it in front of you, unsolved, but ready to be. That took courage. That took will. That took strength. But you still have a ways to go. Don’t lose hope yet. The answer is somewhere in front of you. And those three knowns will get you there.
I now want you to find your forces. Find out what's pushing and what's pulling. What's causing all this chaos in the first place? What is actually happening in this problem? Write this out too. Draw a picture. Make a box and draw exactly what the problem discussed. You need to visualize what is truly going on around you. If you can’t figure out what the true situation is, you’re going to be lost for the rest of the problem set. You know there is always a force of gravity, correct? Yes? Then draw an arrow going downwards from the box. Label this “mg” as you know mass times the acceleration due to gravity gives you the force of gravity. You remember Newton's third law; that for every action there is an equal and opposite reaction. Meaning the ground is also pushing up onto the box with the same force. Label an arrow going up from the box as “Fn” or “the normal force” Lastly, draw an arrow to represent the 720 N force of the man pushing towards the right side of the box and a “frictional force” arrow towards the left side of the box working against the man. You now can picture the situation. You understand the multitude of processes involved in this problem. You can blame your problem on these causes, on these forces. You can blame everything on what’s around the box. So many things working together to cause a change. But these forces - the man, friction, gravity, the ground - they are the key to solving your problem. Identify the causes, cause that’s where your focus should be directed. Follow what these forces are doing. The box didn’t start moving on its own. This problem is merely a reaction of something else. Remember, that is where your problem really lies. You will work from here to solve.
You don’t have a lot to go off of, but your variables are listed out, you know your forces, and now you just have to work with what you got. Recall Newton's second law, 𝛴F = ma. This equation is the best place to start. You want to solve for acceleration, a, but clearly you are missing the knowledge you need. Mass is given, but not your net force. Focus here. Don’t worry about acceleration, you’ll get to that. Sometimes you have to solve a subproblem in order to solve your main problem. Forces intertwine, and you can’t change that. Work your way backwards one variable at a time. One baby step after another. You probably won’t be able to fix everything in one shot. So take multiple. You know that 𝛴F is merely the net force. Look back at your picture. The force of the man is being fought by friction. These are your opposing forces. Logically, what follows is that the force of the man minus the force of friction will give you the net force. You’re getting closer, but what is the force of friction? You were given another equation on your notes sheet, “frictional force” = Uk Fn. You know Uk, but Fn is still alien to you. Look back at your forces one last time. The force of gravity, mg, is equal and opposite to Fn. This means by calculating mass gravity, Fn will be known. Find your calculator and plug in 300kg 9.8m/s2 (This is earth's gravitational acceleration constant, g, and is always known).
Sweet, Fn is 2940 N. Climb back up the totem pole of reasoning that you just laid out, because soon everything will start falling into place and not into the dark depths of your back pack. You have just taken your first step. You put two and two together and out of nowhere you have found another missing variable. Another clue and piece to the puzzle. Use this progress. The more tools you fix, the more tools you will be able to use to fix things. Everything will build off of everything else. So, when you are moving blindly down a path, not knowing where it leads, relax. Progress is still progress, no matter how small. So keep moving.
With Fn you can now calculate “frictional force”. As stated above, Uk Fn = “frictional force”. This becomes 0.22 2940 N = “frictional force” which becomes 646.8 N = “frictional force”. Yikes! That is one ugly number. I really hate when that happens. Don’t you just wish with all your heart that you could get rid of that decimal place? Maybe make the number a nice multiple of five? Yeah me too. That would be perfect. Wait a minute. What’s stopping us! We are free and at liberty to do just that. You have that ability and no one will stop you. Such an insignificant fraction should not be the component which ruins your entire process. You should never ignore your problems, but tiny things like that should be of no concern. This very principle leads me to my next point. Don’t sweat the small stuff. You will have insignificant barricades and obstacles throughout your path on uncovering your answer. However, a missing 1.8 N will never stop you from getting there. Ultimately, to prevent confusion and inaccuracy and simple error, the “frictional force” will henceforth be 645 N. You’ll thank me later.
Okay, let’s get back on track. Keep working backwards. You already thought this through. You have already tread this path. “Force of the man” - “frictional force” = 𝛴F becomes 720 N - 645 N = 𝛴F which becomes 75 N = 𝛴F. Woohoo! See? Wasn’t that easy? Oh come on! Why are you shaking your head? All that was just multiplication and subtraction! Nothing more! Fine, maybe it wasn’t easy. Maybe it was boring and tedious and a thousand-million steps. Maybe you did just read through that like a chipmunk trying to read though a car repair manual. I got something to tell ya’ though. It wouldn't be a problem unless it was hard to solve. The point was this. With practically three pieces of provided information, with simply three clues of the situation, you were able to discover so much more. You took each unsolved mystery at a time. One problem leads you to another, leads you to another, leads you to another. And that’s probably where you got lost. That’s probably why the issue at hand seems impossible to solve. Because you had to dive into places you never even thought of to find what you needed to find. The answer exists, but the path to get there is always what’s tricky to find. And yet, you found it.
Be proud of yourself and pat yourself on the back; you are almost there. Now, put all your pieces together. What you now have is this: 𝛴F = 75 N, m = 300kg and a = ?. You draw Newton's second law, 𝛴F = ma. It’s up to you to solve for a. I’m not gonna do that part for you. It should be easy. Pencil in hand and calculator in the other, find acceleration. You can do it.
You’ve been beat down and crushed and hit by question after question. Problem after problem. You have suffered greatly. I can tell. I know how that feels. You never searched for help until this moment. Day after day, week after week, you hid away what you thought would never be fixed. It ate you up inside, knowing that a dilemma so large was weighing you down and that you could do nothing about it. That was until you took a breath, composed yourself, searched again. That was until you pulled it up and faced it once more, organizing the known, finding the unknown, facing each unknown separately. That was until you took a force and found something new. Until you took what was new and progressed. Until you simplified and calculated. Until you rationalized and boxed in your answer. Until you solved for acceleration.