Good Wednesday evening, friends Worldwide from Dr. TJ Gunn in Houston!
This semester I started tutoring in the physics and math study center. I am the only “pure” physics tutor – the rest of the tutors are mathematicians or engineers who feel very comfortable with mathematics (justly so, they’re all quite awesome). Most of them shy away from physics problems, though, letting me – and a handful of other tutors – deal with the dreaded subject.
In general, physics seems to have this aura to it that scares people before they even start solving a problem. This begins with very basic physics, but continues with higher level material. The difference seems to be that only those who like physics – and find a good way of dealing with it – stick around to deal with the higher level stuff.
Physics? Oh Noes!
Physics – and most science subjects – can be very complicated. Describing our world is not always intuitive, and sometimes requires a mathematical and conceptual understanding that is very advanced. That much can explain why not everyone goes for a physics career. That and, well, the salary.
In basic physics – material covered in high school and low level university courses – the methodology is straightforward. There’s no need to panic. Quite often, it’s the panic itself that prevents students from dealing with the subject carefully and getting the most out of those courses.
What’s the Strategy?
In my experience tutoring for (and taking) low level physics classes, I have worked out a few ground rules that can help you conquer problems. These will help whether the problem is in a homework assignment or on an exam. We will go over them now.
1. Don’t Panic.
Sounds obvious, right? And yet, it’s harder than it sounds. You look at the question and the sentences loom at you menacingly, confusing you to no end. You have no idea where to start, even if you recognize the basic concepts. Whose cars go in which direction? What type of wave travels on the string? Help me, you think in terror. Help me…!
This is your time to take a deep breath, close your eyes, and count to five.
In lower level physics, most questions can be solved by simple formulas. As long as you remember these formulas, you are most of the way to an answer. From now on, the only thing that you need to concentrate on is converting the horrible, confusing chunk of text into readable bits that fit into your formulas. You can do that.
2. Try to Understand the Situation
What is going on in this problem? Is this a ball free-falling from some height? Is it Superman’s velocity as he flies to save Lois Lane a certain distance away? Or perhaps it’s a question about magnetism? Electricity?
Figure out the context first. You don’t have to understand all the small details, but once you know what you’re dealing with in general, you will know how to formulate your answer and which equations to use.
3. Read the Question Carefully
So you understand the physical situation now, and you know what subject this question deals with (or multiple subjects). Now, read the question again, and make sure you are clear on what it actually requires you to find. The same type of problem – say, bouncing ball – can ask you to find initial velocity, maximum height or angle of launch. Each of these will require a slightly different strategy. Make sure you know what you need to do.
Another good tip to remember at this point, too, is that many physics problems have very crucial information in the wording. A car starting from rest, for instance, means your initial velocity is zero. Two objects falling from a window might behave differently if they are both attached to one another.
Read the question carefully – this isn’t the time to skim. Make sure you don’t miss crucial information.
4. Organize the Information
Word problems are confusing only because they hide the actual variables inside them. Sometimes, you will be given extra information that you won’t really need. Other times, there will be variables whose purpose is revealed in a later part of the question.
For example, if the question has a car that starts to move from rest and takes 5 minutes to reach a speed of 20 km/h, you should write down the basic variables like so:
- v(initial) = 0 km/h
- t(final) = 5 minutes
- v(final) = 20 km/h
- a = ?
Do this with all the information you get out of the question. This will help you see the variables in front of you clearly, find the proper equation to use, and see what you’re missing. It will also make the original, confusing text unneeded. If you organize your information, your brain will be free to deal with actual physics instead of reading comprehension.
5. Sketch the Scene
In physics, drawing a picture can really make things easier. For example, getting a visual idea of your frame of reference, or of the difference between up (positive) and down (negative), can mean the difference between a right answer and a wrong one.
You don’t have to be good at drawing. Draw a rough schematic according to the situation. Arrows are your friends in physics questions – they show you which direction an object is moving or what the possible sum of forces applied to it are. They organize the information for you. Use them.
Some questions already come with a drawing – use it! Questions about forces, for example, are best solved by schematic, and you can miss some crucial information that you don’t immediately see if you don’t sketch it.
Go on, Picasso, give it your best shot, and move on to the next step.
6. Verify Units
Sometimes your professor will test your unit conversion skills. That isn’t without a purpose – in physics (and science in general), units are crucial. You have to make sure your units are the same throughout the exercise, otherwise formulas will not work. If you multiply velocity by time, you will get the distance (assuming constant acceleration), but if the car moved at 10 km per hour for 5 minutes, multiplying 10 by 5 will not give you the right answer. Rather, you will need to either convert the kilometers per hour to kilometers per minute, or (and probably easier) convert 5 minutes to units of hours.
The best way to do this is by fractions, but there are enough unit conversion guides out there that explain this concept. Remember not to panic, do it carefully and you will get your correct values.
If we continue our example from the last part, we should convert the t(final) from minutes to hours. This isn’t too hard to do:5 minutes∗1 hour60 minutes=112 hour
(See how the ‘minutes’ units are canceled with the ‘minutes’ units in the denominator, leaving the ‘hour’ units with the final answer? that’s a great way to check that your conversion is right)
Now that all your variables are in the correct units, you can continue solving the question.
7. Consider Your Formulas
This is true for most of physics questions, and absolutely true in the lower level physics. As a student of basic physics, you are not expected to reinvent the wheel – or even understand how the wheel was invented in the first place. What you are expected to do is to understand the concepts and use the tools available to you.
The most important of those tools are the formulas.
Some professors will require that you memorize relevant formulas, while others will give you a “cheat sheet.” Either way, you have what you need. Memorization might sound horrible, but most physics subjects don’t have that many equations to memorize. I remember taking an advanced electromagnetism course where I had to memorize about 20 different formulas. At first it seemed terrible, and I kept remembering them wrong. However, the more you use the formulas, and the more you understand what they mean and – if you care enough to check – where they came from, the easier it gets to remember them.
Organize your formulas in front of you. If you have a cheat sheet, align it next to your variables. What formula can you fill up, leaving the least amount of missing variables? Which formula can help you solve the question?
See it? Use it.
But Wait, Which Formula Do I Use?!
You look at your formula sheet and you have three different ones that are marked under the problem’s subject. How do you know which one to use?? Naturally, you begin panicking again.
Physical equations didn’t just land on scientists from the sky, all wrapped up nicely in mathematical formulation. They are derived from physical properties, and they are all interconnected. In most physics problems, there is more than one way to reach a solution, often meaning that more than one equation can work. In fact, in the vast majority of questions, no matter what equation you use – assuming that it is relevant to the subject matter, and that you insert the proper variables – you will reach a solution.
The way to know which equation to use depends on two main issues: the variables given to you in the equation and your experience. The more problems you solve, the more you will become familiar with strategies for picking the right formula. Until that happens, though, look for the formula that has the variable you already know (from your list of variables) and connects those to the one variable you are missing. If you have two missing variables, you will likely need two equations.
Slow down, look at your variable list, and find the right ones. It’s like a puzzle, and the more you do it, the better you get at it.
You have your variables, you have your sketch, you know what’s going on – plug in, solve and get your answer.
Just remember: you might end up with a relatively lengthy equation to solve, or sometimes two (or more). Don’t forget your goal. Keep glancing over at your list of variables. See that little variable marked with a question-mark, noting the one you’re missing? That’s the one you need to solve for. Focus. Keep the goal in mind. Solve the equations.
9. Verify Your Results
This is a step many students skip, and then pay for. I paid for it dearly in my high school final physics exam, in fact, and I will never do it again. Verifying results can be as easy as skimming through your equations and taking 15 seconds to think about the answer you got.
That can make the difference between 100% and 70%, and sometimes worse.
What do I mean by verifying the result? Well, if the answer you got for the velocity of your car is more than the speed of light, you’re likely wrong. If the units of acceleration come out to be anything but the proper distance/time^2 units, you made a mistake. If your question asks for minutes and your answer is in seconds, you missed a step.
Read the instructions carefully and verify your method. It really is important.
10. Practice. Practice. Practice.
Yeah, yeah, yeah, you think to yourself right now, I bet. Everyone says it. Practice makes perfect. Practice to become better. How.. obvious.
But it doesn’t seem to be properly obvious to many students.
I sometimes get amazed looks from the students I tutor when I come up with the perfect way to solve a question they just spent half an hour trying to solve. “I would have never thought of it!” they exclaim, in awe of my genius. Well, as much as my ego would love to accept this compliment, I am no genius. The reason I see the solution quickly is usually because I have experience – I did so many of these questions that I already anticipate which method would likely work best.
Am I right all the time? Of course not. Sometimes I start with one method and find it was the wrong way. But those “errors” only serve to teach you how to approach different sets of questions. The more you do them, the less time it takes you to recognize the actual effective way to solve them.
It’s all about experience. Don’t panic and don’t give up. Physics is less hard than you think (most of the time).
Example Problem and Solution
So we’ve tried to construct a method of attacking general physics problems. Let’s see how this works in practice by choosing a sample question I picked up from this online document.
A man drags a box across the floor with a force of 40N at an angle. The mass of the box is 10kg. If the acceleration of the box is 3.5 m/s^2 (and friction can be neglected) at what angle to the horizontal does the man pull?
- Don’t Panic.
- Try to Understand The Situation
In this case it’s fairly straightforward. A man is pulling a box on the floor, only he’s pulling it at an angle. The box is accelerated forward.Since we’re only told about the forward acceleration, we will need to consider the horizontal forces (or the horizontal projection) – the vertical projection doesn’t seem to be relevant to this problem for now.
- Read the Question Carefully
In this case, the question is short, and it’s hard to miss data. Still, we recognize that we have some force on the box, and that we are expected to find the angle of that force. Now we know what we need to do, and we can move on to the next step.
- Organize The Information
Here’s a list of our variables:
- Force(man) = 40N
- m(box) = 10 kg
- a(box) = 3.5 m/s^2
- Sketch the Scene
In this case, there already is a drawing in the original document, but I left it out on purpose. Try to sketch it on your own. We have a box, a force pulling it at an angle. Like this:
Now we can see what we are expected to find, and what we already have.
- Verify Units
All of our units fit in this case. No need for conversions.
- Consider Your Formulas
Well, these are the main formulas that deal with basic forces:
- Fy=Fsin(θ)Formulas #2 and #3 are the deconstruction of the force vector (if you don’t know what that means, you should go over the material) – these are the formulas that link the force (which we know) to the angle (which we want to find out)
Remember our “Understand the Problem” part? We said there that since the acceleration is on the horizontal, we will need to consider the horizontal force or projection of that force. And we know that F=ma, which means that the acceleration is a direct result of the force. What is the force on the box, then?
Fbox=mboxabox=10 kg∗3.5m/s2=35N This is the force responsible for the acceleration – and since the only force at play is that done by the pulling man, this has to be the horizontal projection of that man’s force.Remember our trigonometric formula for the projection? Let’s take the horizontal component, and plug in what we have:
- θ=28.96 Which is our answer.
- Verify Your Results
Well, let’s think about this for a moment. The man pulls the rope with an angle. But the projection (35N) is not too far off of the actual force he uses (40N) – it’s quite logical, then, that the angle will be relatively small – even smaller than 45 degrees.
Psst… You’ve done it!
Don’t let the subject bog you down before you even tackle it. Physics sounds horribly complicated, but most of its basic level questions are similar – once you get the concept, you get the solution.
So, to summarize:
- Don’t Panic.
- Try to Understand the Situation.
- Read the Question Carefully.
- Organize the Information.
- Sketch the Scene.
- Verify Units.
- Consider your Formulas.
- Verify Your Results.
- Practice. Practice. Practice.
There. That wasn’t so bad, was it?
It’s about experience, confidence and organization. Study the material well so you understand the concepts (even if you hate the math) and understand the equations you need to use. Tackle the problems patiently and with organization, and you will see how you suddenly become good in physics. Maybe even very good. Heck, maybe you’ll make it your university major!