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Physics:Dont Panic! 10 Steps to Solving (Most) Physics Problems

Created on 06 October 2010 Moriel Schottlender 23 Comments

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, theyre all quite awesome). Most of them shy away from physics problems, though,

letting meand 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 physicsand find a good way of dealing with it stick around

to deal with the higher level stuff.

Physics? Oh Noes!

Physicsand most science subjectscan 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 physicsmaterial covered in high school and low level university coursesthe methodology is straightforward. Theres no need to panic.

Quite often, its the panic itself that prevents students from dealing with the subject carefully and getting the most out ofthose courses.

Whatsthe 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. Dont Panic.

Sounds obvious, right? And yet, its 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.


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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 Supermans velocity as he flies to save Lois Lane a certain distance

away? Or perhaps its a question about magnetism? Electricity?

Figure out the context first. You dont have to understand all the small details, but once you know what youre 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 problemsay, bouncing ballcan 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 carefullythis isnt the time to skim. Make sure you dont 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 wont

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 youre 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


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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 dont have to be good at drawing. Draw a rough schematic according to the situation. Arrows are your friends in physics questionsthey show

you which direction an object is moving or what the possible sum of forces applied to it are. They organize the informat ion for you. Use them.

Some questions already come with a drawinguse it! Questions about forces, for example, are best solved by schematic, and you can miss some

crucial information that you dont immediately see if you dont 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 isnt 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 isnt too hard to do:

(See how the minutes units are canceled with the minutes units in the denominator, leaving the hour units with the final answer? thats 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 wheelor 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, youhave what you need.

Memorization might sound horrible, but most physics subjects dont have that many equations to memorize. I remember taking an advanced


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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 andif you care enough to checkwhere 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 problems subject. How do you know which one to use??

Naturally, you begin panicking again.

Dont panic.

Physical equations didnt 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 useassuming that it is relevant to the subject matter,

and that you insert the proper variablesyou 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. Its like a puzzle, and the more you do it, the better you ge t at it.

8. Solve

You have your variables, you have your sketch, you know whats 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). Dont forget your goal. Keep glancing over at

your list of variables. See that little variable marked with a question-mark, noting the one youre missing? Thats the one you need to solve for. Focus.

Keep the goal in mind. Solve the equations.

Now breathe.

9. Verify Your Results


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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, youre 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 doesnt 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 t rying 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 th is compliment, I am no

genius. The reason I see the solution quickly is usually because I have experienceI 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.

Its all about experience. Dont panic and dont give up. Phys ics is less hard than you think (most of the time).

Example Problem and Solution

So weve tried to construct a method of attacking general physics problems. Lets see how this works in practice by choosing a sample question I

picked up fromthis online document.

The Problem

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?

Strategy

1. Dont Panic.
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2. Try to Understand The SituationIn this case its fairly straightforward. A man is pulling a box on the floor, only hes pulling it at an angle. The box is accelerated

forward.Since were only told about the forward acceleration, we will need to consider the horizontal forces (or the horizontal projection)

the vertical projection doesnt seem to be relevant to this problem for now.

3. Read the Question CarefullyIn this case, the question is short, and its 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.

4. Organize The InformationHeres a list of our variables:

1. Force(man) = 40N2. m(box) = 10 kg3. a(box) = 3.5 m/s^2

5. Sketch the SceneIn 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.

6. Verify UnitsAll of our units fit in this case. No need for conversions.

7. Consider Your FormulasWell, these are the main formulas that deal with basic forces:

1. F=ma2.3.
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Formulas #2 and #3 are the deconstruction of the force vector (if you dont 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)

8. SolveRemember 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?

This is the force responsible for the accelerationand

since the only force at play is that done by the pulling man, this has to be the horizontal projection of that mans force.Remember our

trigonometric formula for the projection? Lets take the horizontal component, and plug in what we have:

1.2.3.4.5. Which is our answer.

9. Verify Your ResultsWell, lets 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)its quite logical, then, that the angle will be relatively small even smaller than 45 degrees.

Psst Youve done it!

Summary

Dont 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:

1. Dont Panic.2. Try to Understand the Situation.3. Read the Question Carefully.4. Organize the Information.5. Sketch the Scene.6. Verify Units.


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7. Consider your Formulas.8. Solve.9. Verify Your Results.

10.Practice. Practice. Practice.

There. That wasnt so bad, was it?

Its 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 youll make it your university major!

Do you have any more advice on how to approach physics questions? Do you run into problem regularly with certain types of problems? Add your

input in the comments!

Credits

UnintentonalChaos, for incredibly awesome editing help. Daniel Grrrrrrrrrrrrrrrrrrreenberg, for his (as usual) keen eyes and good advice. For Toby, for pointing out the final corrections even though she doesnt quite like physics (no ones perfect). Picture credit:RLHydefromFl ickr .

two large, juicy steaks
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