Tag Archives: physics

Preparing to Take Physics: 3. What are significant figures and why are they significant?

When I first learned about significant figures, back in high school, they seemed totally arbitrary and annoying to me. Now, though, I know they’re incredibly important. The rules seem silly at first, but actually they make sense. So, if they seem dumb, please, please stay with me.

Ok, here we go. Let’s say I give you a ruler that only has inches marked on it. (So, none of the little tick marks in between, just 1 inch, 2 inches, etc.) Now, I ask you to measure the height of a cup I have. What answer might you give?

4 inches?

4.5 inches?

4.56712 inches?

Really, you can only say for sure that it’s close to 4 than it is to 5 or 3. You might be able to guess that it’s halfway between 4 and 5, so you could say 4.5 pretty reasonably, but you definitely couldn’t say 4.56712. Because how would you know that?

In science, we’re measuring stuff all the time, and not only do we need to know what we’ve measured, but we also need to know how precisely we’ve measured it. Like, is the acceleration due to gravity really 9.8, or were we only able to measure it to one decimal place? (Actually, it’s different in different places, and even points in slightly different directions if you’re near a big mountain or a pile of gold.)

For example, I was out in the woods one day as a search and rescue volunteer, looking for crime scene evidence, and I was pacing out distances. If you’ve never paced out a distance, when most people take two steps they go a pretty constant distance, maybe 4 feet, so you can use pacing to measure how far you’ve gone. Well, I was out in the woods with the other members ESAR, and we were pacing along looking for evidence, and I found a piece of trash. I reported it to my teach lead and he asked me how far I was from the place we started. I have a 4.5 ft pace, and had gone 5 and a half paces, so I did the math in my head and then, without thinking, said something like 24.75 ft. The team lead was laughed and was like “oh yeah? wow.” Because, here I am being incredibly imprecise, wading through bushes, and I’m telling him that the piece of trash I’ve found is exactly 24 ft and 9 inches away. But, that’s what my math told me.

So, the problem is, when we do math with imprecise numbers, we sometimes get things that look more precise than they are.

Like, if I take 1 and divide it by 3. I get 0.333333333333333333333333333333333333333…

The first two numbers (1 and 3) are integers, I have no idea if they’re 1.4, 1.6, 3.1, or what, but when I divide them, I get something that looks like I’ve measured it out to the infinite decimal place. Silly.

So, we have to watch out for situations where math spits out numbers that don’t mean anything. 

After that first 3, the other 3’s don’t mean anything at all. 1 divided by 3 might be 0.32 or 0.34447. Because, I don’t know whether the 1 was really a 1 or whether it was actually 1.1 but I didn’t have good enough tools to measure that carefully.

Does this make sense?  The key here is that 4 is different from 4.000000000 because if I just say 4, then that might actually be 4.1 or 3.9 or 4.12321111.

Because really, in the real world we don’t often have things that are precise, we only have measurements (unless I say something like “I have 2 dogs.” That’s probably exact. But, I’m 5′ 4″ tall, but I have no idea how many nanometers that is.

I hope that wasn’t boring. I realized partway through that maybe no one cares about sig figs, except that you’re made to calculate them. If you just wanted to learn how to calculate them, you can look through this short powerpoint I made that summarizes all the rules and shows some examples. Feel free to steal it and use it however you like (I mean, within reason):

Significant Figures

What to do to prepare for taking physics: 2. Making sure your math skills are solid

In physics, math suddenly becomes something useful. It’s now a tool that will tell you how quickly something gets somewhere, or how high it will go if you shoot it out of a cannon. This is awesome, but it can also be hard, because if your math isn’t solid then when you’re in the middle of a tough physics problem you might get distracted as you try to figure out how to solve for the root of a quadratic. By the time you figure it out you’ve forgotten why you were solving for it. (Also, this happens to everyone, so it’s not bad, we just want to minimize it as much as possible.) Hopefully, the math has been practiced enough that it’s somewhat second nature, so you can focus on the reasoning behind the math you’re doing.

Luckily, there isn’t too much math you need to know, it’s not too fancy. Here’s a quick quiz you can take to see if you’re ready:

 Math for Physics Diagnostic Quiz

Work through the problems, and if there are some you can’t get that’s no problem, it just means there is some stuff you might want to review before you start your class. Here is the answer key so you can check your answers:

Answer Key

Next, for each question you missed, here’s a homework assignment for you:

1 or 2.  First, watch this video. Then, do this worksheet. Check your answers as you go.

3. First, watch this video. Then, do this worksheet. Check your answers as you go.

4 or 5. First, watch this video on quadratic equations, then watch this video on solving for their roots. Then, do this worksheet. Check your answers as you go.

6. First, if you’re new to vectors, watch this introduction and this overview. Then, watch this video on finding the components of a vector. Work through this worksheet.

7 or 8. Start by reviewing trig ratios with this video. Then, watch this video about how to use them. Then, do this worksheet.

What to do to prepare for taking physics: 1. Introduction

Over the next week I’ll be writing some posts about good things to practice and know before you start taking a physics class. This includes making sure your math is solid, and getting a head start on the basics before school starts. Each day I’ll post a short practice assignment. You can post answers here in the comments, or email them to me with questions.

Here’s what I’ll be covering:

1. Introduction (ie. this post 🙂 )

2. Are your math skills ready for physics?

3. What are significant digits and why are they significant?

4. Why does everybody think physics is hard? (An introduction to problem solving.)

5. SI Units and the Metric System

6. When should you start studying for the AP test, and what can you do at the beginning of the year to make that easier?

7. A head start on 1-dimensional kinematics (usually the first thing you learn).

In each of these, I’ll be giving links to resources (using them will be part of the homework) so that when school starts you’ll already have a ton of places to go to get extra information (plus you can always ask me questions here or on my facebook page.)

The Photoelectric Effect is like Red Rover (except I like it a lot better)

The photoelectric effect is the basis for solar panels. It’s really famous because it’s also some of the first evidence we had that light was a particle (this of course became extremely confusing when the double slit experiment gave us evidence that light was a wave, but that’s for another time.)

First, remember that materials are made of atoms, which are made of protons and neutrons and orbited by electrons:

1

Different materials hold their electrons more or less tightly. Metals happen to hold their electrons pretty loosely, like kids in a neighborhood where all the kids just run around wherever they want:

2

These kids wander around wherever they feel like it, but they generally stay inside the metal (in this case copper). However, they can get knocked out of the metal by light (photons).

This is kind of like a game of red rover (I hated this game so much when I was a kid.) Let’s imagine that the kids line up at the edge of their town, and they play red rover with the neighboring kids, who just happen to be photons (light). The kids are there just hanging out in the metal, and the photon comes and tries to knock them out.

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If the photon is weak enough, nothing happens.

4

In fact, if the photons are too weak, it doesn’t matter how many of them hit the metal, no electrons are knocked off.

5

In photon-terms, a weak photon is one without a lot of energy. The energy of a photon is its frequency, which is also its color. For example, red is a lower frequency than blue. And, infra-red is lower frequency than red. Ultra-violet is higher frequency that violet. Radio waves are lower frequency than infra-red, and x-rays are higher frequency than ultra-violet. (All of these are just frequencies of light that we can’t see.)

So, if the light hitting the electrons gets more energy, let’s say its violet now (like violent!)

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Now, the more photons that hit the metal, the more electrons will be kicked off.

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Different metals hold their electrons more or less tightly, so different metals require different energies of photons before electrons will get kicked off. This is called the “work function” of the metal, and it’s often denoted with the Greek letter phi:

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Sometimes the incoming photon has more energy than it needs to kick off an electron. If that’s the case, then the leftover energy becomes kinetic energy of the electron. (i.e. the stronger the kid from the neighboring town is, the faster you’ll be going when he tosses you out of the line of electrons.) Here’s the fancy equation for that, if you’re interested:

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But, we said earlier that the energy of a photon depends on its frequency. It turns out we can calculate the energy of the photon by taking its frequency (in Hertz) and multiplying it by planck’s constant (6.6 x 10-34). This gives us the energy in Joules. So, another way to write the above equation is this:

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For example, the work function of copper is 4.7 electron volts, which is 7.53e-19 Joules. This works out to a frequency of 1.14e15 Hz, which is a wavelength of 260 nanometers of light. This is higher than the visible spectrum, it’s just into the ultraviolet range, so you need ultraviolet light to knock electrons off of copper (or gamma rays 🙂

The really cool thing is that this is evidence that light is a particle. Because, if you hook up some wires to the piece of copper, and you hook those wires up to a detector that makes a sound every time there’s some current (ie. every time an electron gets kicked off- current is just moving electrons) it would make a sound like rain on a tin roof.

Thoughts? Questions? Comments? Concerns?

What to do if you’re taking calculus-based physics next year and you haven’t taken calculus yet

Every year I have a couple of students who are taking calculus-based physics at the same time as calculus. Traditionally, you take calculus first, and then  you take physics with calculus. The calculus used in these introductory physics classes is usually simple enough that it’s not impossible to take them both at the same time, but it’s definitely a challenge. I wouldn’t recommend it if you can avoid it, but if you can’t there are some things you can do over the summer that will make next year go much more smoothly:

  • Recognize that you’re at a disadvantage. The worst thing possible outcome is that you end up thinking you’re bad a physics. Even if there isn’t much calculus in the course, a lot of the ideas in physics are covered in calculus. There is a lot of conceptual overlap. So, just keep in mind that everyone else who took calc last year has had a whole year to get comfortable with these ideas and to practice them. Also, you’re having to learn two challenging things at once. Not only that, but you’re having to put them together. It’s as if you just learned how to juggle and you also just learned how to ride a bike, but you’re forced to practice them both at the same time.
  • Get a head start on calc. I recommend Calculus Made Easy, which is actually the book I used to help me learn calc when I was in high school. Start at the beginning and work up through chapter 8. Take your time. Focus more on the ideas than on the math.
  • Work through my book Rates of Change. I feel like recommending this to you is a bit of a conflict of interest on my part, and I agonized over whether to include it in this post, but I really do think it helps make the fundamental ideas much clearer.

Lastly, once school starts, don’t hesitate to ask for help, either from your teacher, a tutor, or me.

What I wish someone had told me when I was just starting out as a physics major

(And a girl. Not that I was starting out as a girl. I had been a girl my whole life, but I was just starting out being a girl physics major.)

It’s not supposed to be easy

I had this idea that if you were smart things were easy. You either knew something or you didn’t. You either got it or you didn’t. My first few physics classes reinforced this. I had already taken high school physics, so the intro classes weren’t so bad. Then I got to my first real physics class, Mathematical Physics, taught by an old Russian professor. I assumed it would be easy. Then the first midterm came. Three problems. I had no idea what to do for any of them. I had no idea how they even related to anything we’d done in the class so far.

Suddenly I felt like I was out of my depth. I went to go talk to the professor. I had skipped class a couple of times and I think he knew that because he wasn’t that keen on helping me. What he said was “Maybe you’re just not going to get it.” After that I panicked. I felt deep down that I just wasn’t smart enough to study physics, even though it was something I had loved since I was a kid. I thought maybe I had just hit the limit of my natural intelligence.

I hadn’t. I had simply hit the limit of the place where I had learned things before. In my experience, 90% of the things that look like talent are actually practice. When you see someone with a perfect golf swing or a genius math brain, you’re only seeing the result, you’re not seeing the great coach they had, the hours they spent practicing, or all the times when they were a little girl sitting in the passenger seat of their dad’s truck talking about the differences between even and odd numbers.

I didn’t know this. I thought I had just hit the ceiling of what I was capable of. I wish I could go back and tell myself that there is no ceiling. There is no capable, not capable, or highly capable.

I work with a lot of students, and I can see some of them falling into this trap. They encounter a difficult problem and they start thinking they’re dumb. They’re wrong.

It’s hard because it is made of ambiguous problems. A lot like life. You learn some tools, some equations, some concepts, and then they set you loose on problems. At first, you will have no idea what to do. This is not bad. This is a feature of real problems. (See my post on problem solving for ways of tackling these things.)

In order to be successful in physics, you have to make the mind shift from “I’m not smart enough” to “this is hard.”

It’s okay. It’s okay if it’s hard. It’s okay if you look at a problem and have no idea what to do. It’s not supposed to be easy.

Unlike in most of your previous schooling, you’re not just learning one thing at a time and being asked to do something repetitively. You’re being asked to do something crazy hard, which is, stumble around until the pieces fit together. Or maybe they won’t, and you’ll ask for help. But not from someone who will tell you that maybe you won’t ever understand. Because if you keep trying you will.

Some people pretend they know more than they do

Another thing that left me feeling stupid was how much my classmates seemed to know. For some reason, the reputation that physics has for being difficult brings out some pretty intense egos. Be careful not to assume, just because someone is talking about something fancy-sounding that you’ve never heard of, that they know more than you do.

In this same first physics class, I met several people. We studied together. They talked a lot about things in ways that made me feel like they knew what they were talking about. Again, I felt like an idiot who didn’t belong.

Then we got our grades back. I did the worst I had ever done in a class, but it was still a 3.1. Those same people who I thought knew everything got 2.5’s or worse.

Never think someone knows more than you do just because they’re speaking authoritatively. They might just be covering insecurity with arrogance.

Ask for help

The next quarter I started my next physics class. I was completely panicking. Sure I would fail. Sure I wasn’t good enough. I had to take mathematical physics II.

Then, randomly, I did the best two things I’ve ever done for myself in the context of my physics degree.

1. I introduced myself to some other girls in that class.

2. I went to the professor after class, told him I was worried I was unprepared and that I wouldn’t do well.

The first thing immediately diminished my anxiety. Suddenly, I had people to commiserate with, to study with, to hang out with and laugh with. It was amazing and great and so much fun and the opposite of isolating. They told me later that they were so glad I had introduced myself, because they were feeling terrible and scared, too. It’s hard to do that, because sometimes other people look arrogant when they’re scared. Or they look closed and unfriendly when they’re scared. But, if you just introduce yourself it can be amazing. Having allies is probably the most important thing when you’re trying to do something hard.

The second thing was really good for my grade. Luckily, this professor was an extremely, extremely, nice guy. He laughed a little when he heard what my previous grade was. He told me it would be ok. He gave me a book. This book was basically a more detailed version of the textbook we’d used the previous quarter. It was waaaay better. (Incidentally, I do not recommend you use any textbook by Mary Boas. She leaves out waaay too many steps when she solves math equations.)

In that class I got a 3.9, and I made some awesome friends.

At some point in your life you will (hopefully) reach a place that will feel like the limit of your ability. It is not. It is the end of the mapped territory. It is the end of the things you already know how to do. It is a place where you will need to make a large step up in order to continue. Maybe physics will be this for you, maybe it won’t. Maybe it will be easy for you. If so, that’s great, but I hope you eventually find yourself in that place where you think you might just not be good enough.