The Physics of Weight Loss

Today I want to talk about weight loss. Or getting into shape. Or both. This is something I’ve been thinking about lately, and while I’m sure probably everyone reading this has had to lose a few pounds at one point or another. Everyone knows the deal: To get in shape you need to watch what you eat, hit the gym, take up running/jogging/biking, so on and so forth.

Time to hit the gym

But why? Why does any of this stuff work? Everyone knows that running can help you lose a few pounds, but most people don’t actually know why, or more importantly where that weight goes. So it’s time for me to do what I do best: overanalyze things with physics.


We often use these two terms interchangeably, but in fact they are completely different—albeit related—things. Your weight is essentially your mass—how much stuff you’re carrying around with you. It’s how hard you’re pulled toward the center of the earth. Every single part of you—fat, muscles, bones, skin, organs, everything—contributes to your weight.

Your shape, on the other hand, is really about how that weight is arranged. In American culture, you’re generally considered to be in shape if you have low amounts of body fat and at least some muscle. Obviously that’s a broad generalization but we have to define our terms somehow.

When talking about either recreational fitness or overall health and wellbeing, your shape is far more important than your weight. Especially since muscle weighs more than fat. It’s not your weight that reduces your lung capacity or puts you at a higher risk of stroke and heart attack, but the amount and distribution of fat in your body. This is why the Body Mass Index (BMI) which compares only your weight to your height, is worse than useless as a measure of health. Just going by their BMIs, most professional football players would be considered obese.

Just look at this fat slob

But there’s another reason for distinguishing between weight and shape, and that’s because the two of them change somewhat independently of each other. Anyone who’s ever started lifting weights to get into shape knows this. As you replace the fat with muscle your shape will improve while your weight increases. And people who starve themselves will see their weight fall while their shape deteriorate as their bodies pack on stores of fat. There is somewhat of a correlation between the two, but what exactly that is differs from person to person depending on body type and genetics.


Physically speaking, losing weight is incredibly easy. One of the most fundamental rules of our universe is the conservation of mass. That is, mass can neither be spontaneously created nor can it spontaneously disappear. And since weight depends on mass, this gives us an equation for the change in a person’s weight:

The amount by which your weight will change over any given time is exactly the difference between how much weight you added to your body (by eating) and how much weight you removed from your body (through various excretions). Notice that this depends only on the amount of food you eat, not the quality of it. In terms of your weight, a pound of celery is just as bad as a pound of birthday cake. Also notice that this does not depend on how much or how little you exercise.  It’s simply the difference between what’s going into your body and what’s coming out.


This is where it gets complicated, and I’ll admit I’m by no means an expert in biochemistry. But I’m not too sure how many people would be interested in those details anyway so I’ll just summarize. Where your weight is all about the mass in your body, your shape is all about energy.

All of our energy comes from what we eat. It’s stored in the chemical bonds of food and we measure it in calories. In our stomachs we use acid to dissolve the food, storing that energy in glucose molecules. That glucose is then either used for energy immediately or stored in the body as glycogen in fat deposits. As our bodies consume energy throughout the day we dip into these fat reserves, so the key to staying shape, or at least the key to not gaining any fat, is to use more energy than you consume.

What makes this difficult is that it’s very hard to measure exactly how much energy your body is using. We are literally using energy all of the time, even when we’re sleeping. It takes energy just to be alive. We’re constantly spending energy to heat ourselves up, and an incredible twenty percent of all of the energy we use throughout the day goes to powering just our brains. We call the amount of energy it takes to sustain your resting body your Resting Metabolic Rate (RMR, although when I learned it we called it the Basal Metabolic Rate), or more commonly known as your metabolism. Since muscle tissue requires more energy to sustain than fat, the more muscles you have the higher your RMR will be. Any extra energy your body uses due to exercise adds to this metabolic rate to determine your body’s total energy output. If you’re consuming less energy than you’re using, your body will naturally take the difference from its stores of fat, leading to you being in better shape.


I’m sure you’ve heard before that you weigh less in the morning than you do at night, and it’s true. It’s not just because of all the food you ate during the day, either. So a big question is: where does that weight go? It’s tempting to say that it’s due to the energy our bodies use while we sleep, as mentioned earlier, but that’s not right. We’re not stars, so we can’t convert mass into energy. Honestly, I think the real answer is even stranger than that.

We breathe all that extra mass away. That might sound ridiculous, but think about it. When we breathe, we inhale air with a density of around 1.2 grams per liter and exhale carbon dioxide which is considerably heavier with a density of 1.977 grams per liter. It’s not enough to notice a difference with a single breath, but multiplied over the course of an entire night it can add up to over a pound. And if this still seems a bit farfetched, consider that the exact opposite process—inhaling carbon dioxide and exhaling lighter oxygen—is where trees get all their mass.


According to everything I’ve said so far, it would seem that there’s no link between exercise and weight loss. But anyone who’s ever exercised knows that isn’t true. I’ve come back from 10 mile rollerblading trips a full three pounds lighter than when I left. So where is that weight going?

As you can probably guess, a significant amount of this is water weight which we lose through sweat, but not all of it can be explained this way. The process of the body using fat to power itself is called ketosis, and through a lengthy series of interactions the glycogen mentioned earlier is converted into ATP, the form of energy which can be used by our cells. The biggest byproducts of this reaction are water and carbon dioxide. So as your body undergoes ketosis, the fat cells shrink as the glycogen is removed from them and you sweat and breathe out the byproducts, causing you to both lose weight and get into better shape.


You’re probably expecting me to have some final wisdom about the best way to get into shape or lose those pesky pounds, and I really wish I did, but ultimately it boils down to knowing your body and using common sense. One of the strangest things working against us in the battle of the bulge is our sense of hunger. Don’t trust it. Studies suggest that for people in developed countries (with ready access to stocked refrigerators and grocery stores) hunger is more of a social and conditioned response than a physiological one. One thing I’ve found lately is that I was just eating way more than I needed to, even though my eating habits before hadn’t been particularly unhealthy. What I’ve come to realize is that what I considered my resting state before was actually my body’s way of saying it was full. I was essentially filling the tank every time it dropped below three-quarters, and in doing so I was keeping my body from using its stored energy. If you find yourself consistently feeling stuffed after meals that might be why. Try to really pay attention to what your stomach is telling you, and just because it’s growling doesn’t necessarily mean it’s empty.

Blue Skies Ahead

Question: Why is the sky blue?


Answer: It isn’t. Not the same way that bluebirds, sapphires, and the members of Blue Man Group are, anyway. To see why, we need to first talk about what exactly we mean when we say that something is ‘blue’ or ‘red’ or any color at all.

To talk about color, we must first talk about light. Light, at the smallest scale, is broken up into photonsindividual particles or pieces of light. Those photons each have a certain amount of energy, and a corresponding frequency, that determines their color. In physics, there are only six colors in the visible spectrum (red, orange, yellow, green, blue, and violet) with many more outside what we humans can see (radio, microwaves, infrared, ultraviolet, x-ray, and gamma). Red light has a lower frequency than yellow light which has a lower frequency than blue light.

So where do the other colors come from? If all we have are those six colors to choose from, how do we get browns and pinks and even white? What may surprise you, especially if you’re artistically inclined, is that you get brighter, lighter colors by adding multiple colors together. White light is light which contains frequencies of all the other colors at once. That is why you can see every color when in a room lit only by white light–the white light contains all the other colors. Notice how this is different than what you get if you add together different pigmentslike paints. If you add pigments together you end up with a dark, blackish color. We’ll talk about why these two are different in a second, but first we must discuss what it means for an object to “be” a certain color.

For the most part, color in the natural world is a reflective property. This is because most objects don’t emit their own light (some things, like butterfly wings, are colored by diffraction but that’s a different story entirely). They only reflect light that hits them, redirecting it into our eyes. However, most objects don’t reflect all of the light that hits them, only certain frequencies or colors.

When you look at an object and see white, it means that object is reflecting all colors of light back at you. Black objects reflect little to no light (this is why wearing a black shirt in summer makes you warm). When you see a blue object, it means only blue light is reflected off of it, with all other colors being absorbed.

When we say an object is blue, we mean that it only reflects blue light. A blue object absorbs every color except for blue. This is why mixing pigments gives you darker colors. Each pigment only reflects certain ranges of colors, and if these ranges don’t overlap, less light will be reflected, giving you a darker, gray or black color.

With all of this said, we can now return to our original question: What color is the sky? To answer this, we need to know what exactly the sky is. And for the most part, it’s air. Mostly nitrogen, about 20% oxygen, some carbon dioxide, and other trace gases. It’s the same stuff that surrounds you all the time. It’s the same air that you’re breathing right now.

So look around. What color is the air around you? What colors of light are being absorbed by the “empty” space in front of you? Unless you’re living in a heavily polluted area, the answer should be clear. Literally.

Air is transparent. And thus, so is the sky.


Revised Question: Why does the sky appear blue?

Answer: You might think that was all a little bit pedantic, but the distinction between the sky looking blue and the sky being blue is crucial to understanding why the sky looks the way it does. The sky isn’t colored by reflection the way most other objects are. It’s a different process entirely, one you may have experienced yourself without realizing.

What lights up the entire sky is the sun. And the sun, despite what you may think from looking up at it here on Earth, is white. Not yellow, not orange, but white.


Courtesy NASA

What you’ll notice in the picture above is that, when viewed from space, the light from the sun doesn’t spread nearly as much as it does here on Earth. In fact, even with the glare, you can see the total blackness of space as little as ten degrees away from the sun.

What allows the sun to color the entire sky is a process known as Rayleigh Scattering, and it’s exactly what it sounds like. If you think of light as a stream of tiny particles (or photons), then you should be able to imagine those particles colliding with things like molecules in our atmosphere. As a result of those many collisions, the light gets scattered, spreading out in all directions so that, no matter where you look, you can see it.

If you have ever played with a laser pointer you’ve experienced this before. Shine a laser pointer at a wall and all you’ll see is a red dot. You won’t be able to see the beam itself. But give the light something thick like smoke or fog or chalk dust, and the beam will scatter off of it, becoming visible to all.

So the scattering of light can explain why the sky has color, why it’s not just pitch black around the sun. But why is it blue?

I will try to stay away from doing too much math (there was enough of that in my last post), but there is an equation which governs the amount of scattering that occurs via this process:


It’s a messy formula, and if you’d like more information about what each variable represents you can check here, but the important part is the dependence on frequency. The higher frequencies of light scatter more than the lower frequencies. This is why you can see blue and violet all over the sky, but red and yellow only when you look directly toward the sun. The lower frequencies don’t scatter as much.

Only a few more questions to clear up. If higher frequencies of light scatter more, why is the sky blue instead of violet? The answer is because the sun emits more blue light than it does violet. The violet does scatter, but it is overwhelmed by all the blue light around it.

Why is the sky red during sunrise/sunset? At these times, when the sun is reaching the horizon, the blue light scatters too much, having to pass through too much of the atmosphere to reach us. Once all of the blue and purple light has been scattered away, all we’re left with are those beautiful red, orange, and golden sunsets.

Well, this was a fun one. What I like about questions like this is how trying to answer one question opens up–and then answers–many more. For example, you may have thought that it would be simple to explain why the sky is blue, but in the process of doing so we got to talk about what color is, how things get their color, and the scattering of light in a medium. These are the kinds of questions I like most, where the answer takes a winding road through different areas and disciplines. It’s because of questions like this that I started teaching. Unfortunately, given our prescriptive and standardized attitude toward education, it’s rare that kids be given the chance to really explore a topic like this in school.

That about wraps it up for this week. If you have any other questions you want answered, let me know.

Why Does Helium Make Your Voice Sound Funny?

In my class we just began learning about waves, and so today I figured I’d write about one of my favorite demonstrations. I’m sure you’ve seen this somewhere or another, whether in a classroom or at a party. Someone swallows some helium from a balloon and suddenly they sound like Alvin the Chipmunk.

Have you ever wondered why that is?

Plenty of physics teachers love this demonstration. And why not? It’s eye (or ear) catching, funny, and has a lot of powerful physics behind it. Unfortunately, it’s almost always taught incorrectly, at least from what I’ve seen. Here’s how it’s usually taught, why that’s wrong, and what’s really happening when you swallow a balloon full of helium.

[At this point I should probably include a disclaimer about doing this yourself. Swallowing helium directly from a pressurized tank should never be done by anyone under any circumstances. However, swallowing helium from a balloon is perfectly safe…provided you don’t swallow too much or too quickly. The helium displaces the air in your lungs, which means if you do this too quickly or for too long your body will asphyxiate for lack of oxygen. When this happens you will pass out, and can injure yourself by collapsing. It’s not fatal (helium is so light that it’ll all leave your lungs while you’re unconscious and you’ll be able to breathe again), but can be dangerous if you hit your head on the way down. I recommend you always have someone watching you while you try this.]


Most teachers use this demonstration to illustrate the fundamental wave equation, the formula shown below (warning: Maths ahead)


Since helium is less dense than air, the speed of the sound waves produced when you speak is higher with helium in your lungs than with air. Since speed increases, something on the other side of the equation above must also increase. Most teacher will then have their students conclude that when speed increases, frequency increases.


This is a horrible misconception to be perpetuating in a classroom. The frequency of a wave is like its fingerprint or DNA. Once a wave has been created, nothing can change that frequency. If it did, it would be an entirely different wave. And it’s not the gas in our throat and lungs that is creating the sound of our voice but our vocal chords, which function the same way regardless of what we’ve been breathing. Combining that with the logic and equation above, we see that it’s not the frequency of our voice that changes when we ingest helium but its wavelength.


In order to correctly explain this phenomenon, you need to realize two things:

  1. The human voice is composed of more than one frequency. When we speak, our vocal chords don’t just vibrate in a single mode but in several, creating harmonics of different frequencies all at once. This is why two people singing the same note sound different from one another.
  2. When people speak, our throats function in a very similar way to a pipe organ. The source of the sound is our vocal chords, which transfer their vibrations into the air in our lungs as sound. This is equivalent to the strings hidden within an organ. From there, our throat takes over, which serves the same function as the pipes in an organ: Amplification. Both the organ pipes and our throats accomplish this amplification through resonance. When a sound wave with a wavelength matching the length of the tube/throat passes by, it gets amplified.

Now we can begin to make sense of this. First, the frequencies of sound (the pitches) that we produce are exactly the same regardless of what is filling our lungs at the moment. Those frequencies depend only on how we vibrate our vocal chords. Changing the speed (and thus the wavelengths) of those waves does not change the frequency or pitch we hear.

However, it does change which frequencies get amplified via resonance in our throats (because remember that does depend on wavelength). After swallowing a less dense gas like helium, our throats selectively resonate the higher frequencies among the range that our voice always produces. Similarly, if you were to ingest a denser gas [this is far more dangerous than swallowing helium as denser gases will settle in your lungs, producing a much higher risk of suffocation], your throat would selectively resonate the lower frequencies among that range, making you sound more like Darth Vader.