Thursday, September 22, 2016

Ask a Physicist: Conservation of Mass Violation...In a Bowl of Couscous?

Cal, from Italy, wants to know:

"When I add hot water to couscous in a bowl, and then zero out the scale it sits on…
…it magically starts increasing in weight over time as it absorbs the hot water!
I can understand it increasing in volume, but not in weight. How does this happen?"

I love questions like this! It's like a puzzle, where sometimes there's an opportunity to use physics and logic to peer into the inner workings of things and figure out a solution from thousands of miles away. It's a magical, second-sight kind of feeling.

I'll be honest, my first reaction to your question was disbelief. “Oh, there’s probably lag time on his scale’s display and it’s just registering the last of the water he added.” After all, conservation of mass is a pretty fundamental tenet of physics—we’ve never seen it violated in a lab before, so the odds that such a thing should be observed for the first time in a bowl of couscous struck me as pretty slim.

For our readers unacquainted with North African cuisine, couscous is a grainy, starchy dish
which is made from wheat and apparently exempt from the normal laws of spacetime.
Think of a cross between quinoa and oatmeal.
Image Credit: Khonsali, via Wikipedia (CC BY-SA 3.0)
But as soon as I decided to give you the benefit of the doubt, trusting that your observation was something that needed to be explained rather than rationalized away, I understood instantly what was happening!

When you put something on a kitchen scale, its mass applies a force to the weighing plate. This force is given by the simple formula:

...where m is the object’s mass and g is the free-fall acceleration of an object near Earth’s surface, 9.81 m/s2.

This force on the weighing plate is counteracted by a spring inside the scale. Now, there are different kinds of springs—in some, the coils are naturally all scrunched up, like a slinky, and it takes force to pull them apart. In others, like a bedspring or a shock absorber, the coils are naturally far apart, and it takes force to push them together. The one inside the scale is the bedspring kind of spring.

When you place an object on the weighing plate and the force of gravity pulls it down, it compresses the spring by a certain amount, determined with a formula called Hooke’s Law. How much the spring is compressed depends on the magnitude of the force, but also on something called the spring constant, so the formula looks like this:

...where x is how far the spring gets compressed, and k is the spring constant. The spring constant depends on the material that the spring is made of, how thick it is, and a number of other factors—this number is usually determined experimentally, by applying a known amount of force to the spring and seeing how much it compresses, then using that data to solve for k.

So placing an object on the scale creates a balance of forces, between gravity pulling it down and the spring pushing it back up. Since the object is at equilibrium (not accelerating), we know that the forces pulling it down and the forces pushing it up must be equal to each other. We can express this equivalence mathematically, using the two formulas above:

And this is how the scale determines an object’s weight. It measures how far the spring has been pushed down, does some quick math using the spring constant and the force of gravity (both of which are programmed in by the manufacturer) and then solves this equation for the only unknown variable, m, which it spits out to you on its display!
So how does this translate to magic couscous? Well, I mentioned earlier that the spring constant depends on a number of different things—one of them is temperature! When metal heats up, it becomes easier to bend and deform; this is why blacksmiths have to get a hunk of metal glowing-hot before they can shape it.

When you add your boiling water to a bowl of couscous on the scale, the bowl heats up, and transfers some of this heat to the weighing plate of the scale. If the scale’s weighing plate isn’t properly insulated from the rest of it, this heat can transfer to the spring, and when the metal gets hot, its spring constant drops! Slowly, as the spring’s k value changes, the same amount of force creates greater compression in the spring. The scale isn’t equipped to handle this—it assumes the spring constant is…well…constant. (A reasonable assumption given the name, wouldn’t you think?) The scale sees the spring compressing more and more, and concludes that the weight on it is increasing, leading to the appearance of magic, mass-increasing couscous!

Not to get preachy, but if there’s a lesson to be learned here, it’s this: It’s important to understand how your instruments work, so you can be sure you’re actually measuring what you think you’re measuring. About five years ago (almost to the day, actually) OPERA announced that they had detected neutrinos moving faster than the speed of light, when in reality a cloudy fiber-optic cable had been messing with their signal.

Stephen Skolnick

P.S. After further correspondence with the asker, in the interest of proper science, we have determined that the effect arises with or without couscous, but does not occur when room-temperature or cold water is used, confirming the source of the effect.
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Wednesday, September 21, 2016

When the Brain Bulges: The “Stressful” Impact of Removing Part of the Skull

Physics is usually associated with frying the brain rather than saving it. Unfortunately, students often leave introductory physics classes wondering more about the relevance of physics than the world of possibilities it opens. Whatever you wonder about, one thing is clear. The part of you that does the wondering is fundamental to who you are.

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Tuesday, September 20, 2016

How Pollutants Navigate Manhattan Streets

Imagine that a highly-toxic pollutant is released in the middle of Manhattan on a windy day. What is the appropriate response? Evacuate one square block? Ten square blocks? The whole city? How much time do patients at a hospital five blocks north and 20 blocks east have to get out before the concentration is dangerously high?

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Monday, September 19, 2016

Spider Silk Lets Scientists See Like Never Before

Scientists who use conventional light microscopes—like the one you probably peered through in high school science class—face a limit on the size of objects they can view. Basic properties of light prevent them from focusing on anything smaller than the tiniest known bacteria.

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Friday, September 16, 2016

Ask a Physicist: How Much Energy is in Me?

"Game Maker" wants to know:

I'm designing a fire-wielding superhero who uses his own body as fuel for his powers. How much heat energy would be created if a person were to burn off 50-100 lbs of fat in the span of 5 minutes? (Assuming he has the requisite "secondary superpowers" to avoid dying in the process).

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Wednesday, September 14, 2016

How Quantum Mechanics Can Help Protect Your Secrets

Most of us aren’t very comfortable thinking about randomness. People like five-year plans and the comfort of “everything happens for a reason.” Even the messy among us claim there’s order in their chaos. Despite this, many processes that are fundamental to our way of life rely on random numbers.
Random numbers are key to stock market predictions, the security behind online shopping, and the integrity of clinical research trials. Last week in The Optical Society’s journal Optica, a team of scientists introduced a new device for generating random numbers that is based on the quantum mechanical properties of light. It is a record-breaking combination of security, size, and speed.

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Tuesday, September 13, 2016

Why Modern Football Will Never Be Safe

Preseason is over and, if last night's game is any indication, we're in for another season of epic passes and bone-crunching takedowns. More and more, however, there's been talk of the most serious problem in modern American pro football. It lurks at the backs of our minds during the game, brought to the forefront whenever we wince sympathetically at a hard tackle—you can practically hear the players' brains rattling around in their skulls. Concussions can be devastating to a person's quality of life no matter what their profession, but almost no other job involves taking hits the way football does—as evidenced by the memory, mood, and mental health disorders that beset NFL retirees at an extraordinary rate.

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Monday, September 12, 2016

Stronger and Lighter Than Frosted Glass, Translucent Wood Reflects the Future of Construction

This is not frosted glass. It’s translucent wood.

Translucent wood from the lab of Dr. Liangbing Hu.
Image Credit: Eran Moore Rea, American Physical Society

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Friday, September 09, 2016

Moving to the Music

Composers usually arrange musical notes to express emotion. To set a mood. To get people dancing. To give life to inspiration. To sell records. A team of scientists at Aalto University in Finland is arranging notes for a totally different purpose—to move objects. Their work isn’t likely to top the charts, but it could bring us closer to game-changing medical technologies like lab-on-a-chip devices and new drug delivery systems. It could also be a means for sorting objects and characterizing materials.

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Thursday, September 08, 2016

"Growing" a Solution to a Complex Biological Problem

Like a complex highway system, a network of vessels carries blood from the heart to all corners of your body and back again. This “distribution network” is not only complicated, it is also huge and astoundingly efficient. Even when one part of the body is injured, flow to and from the rest of the body is rarely interrupted.

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