Tag: science

Beats

Posted on by Brian Garthwaite
wobblewobblewobble

In acoustics, there’s a phenomenon known as beats, which is when two similar tones generate an interference pattern that sounds like a pulsing beat. It happens with waves of all kinds, waves being moving energy and all that, but sometimes it’s easier to really get the sensation when you hear it. Graphing out the sinusoids and showing the constructive and destructive interference helps explain it. Hearing that wubwubwubwubwub cements it.

We have what looks, at first glance, like a glockenspiel, with its metal bars all in a row. Tap one with the mallet, and it sounds almost the same as the one next to it. Almost. Tap two at once, and you get the beats.

At one end, it’s 440 Hz. Then 439, 438, 437, 436, and 435 Hz. Not only can you hear the beats, but you can very clearly hear the change in beat frequency as you combine tones in different combinations. It’s very cool.

Also quite unnerving after a while. woobwoobwoobwoobwoob

Pendulum bobs

Posted on by Brian Garthwaite
Aluminum and brass pendulum bobs.
Shiny!

Does the mass of a simple pendulum affect its period of oscillation? The small-angle formula doesn’t include mass, just the length from the pivot to the center of mass and g, the gravitational constant. It’s an approximation that’s pretty good for angles up to 15-20°, and after that it’s into introductory differential equations. Which still don’t use the mass, as it cancels out when applying Newtonian mechanics.

That, however, is for an ideal pendulum, with a massless string and point mass bob in a system without friction and other losses. We’re all out of massless string at the moment, and those point masses are proving elusive. And as neat as it might be to swing a pendulum in a vacuum, the setup sounds like a real challenge.

On top of that, it’s an interesting question that’s really addressing a student’s understanding of measurement and uncertainty. Equations and models illustrate principles, and sometimes do an excellent job of making sense of the world. It’s just that the real world is messier, and wading into that mess – even a little bit – can be enlightening.

Two new pendulum masses, machined to the same dimensions, or close enough that you won’t notice without accurate calipers. Threaded to screw on and off. Aluminum (2.7 g/cm³), checking in slightly under 50 grams each. Brass (8.7 g/cm³), a little over three times the mass, a shade above 150 grams apiece. If we can work with the material, we could make more from anything available.

Lightweight plastics, like Delrin acetal (1.4 g/cm³)? Sure. Denser stuff, like lead (11.3 g/cm³)? Not impossible, but okay, well, no. Even denser? Tungsten, gold, and depleted uranium are all in the 19 g/cm³ range. McMaster-Carr has a range of tungsten alloy rods in stock! (For a small fortune.)

For now, though, it’s two masses, a string, and a stopwatch. Real physics in action.

Inverted balloons

Posted on by Brian Garthwaite
Balloon on flask.
It’s like a hat.

What can you do with a large Erlenmeyer flask, a kettle of boiling water, and a bag of balloons? Science, of course!

Get the flask hot with a pour of boiling water first, then pour out. Add a small amount of boiling water – as hot as can be – and quickly seal with a balloon. We’re looking for steam, and lots of it.

Then wait and see what happens!

Balloon in flask.
Cool!

Spectrometer

Posted on by Brian Garthwaite
Spectrometer and sodium lamp.
Rainbows!

Astronomy is roughly 98% figuring out how to look at stuff better than our eyes can do it.

Gathering more light with large-aperture lenses and reflectors. Gathering more light with long camera exposures. Using detectors for light outside the visible spectrum, from radio waves to gamma rays. Launching telescopes a million miles into space to get away from our pesky atmosphere. Splitting the broadly blended colors we perceive into their component wavelengths.

That last one’s the easiest to accomplish in a student lab setting, and it’s a broadly useful scientific tool across many disciplines. Turns out that certain particular constraints caused by quantum physics make all sorts of other observations possible. Who knew?

Pictured above is a low-pressure sodium lamp, just like the ones that once illuminated nighttime streets around the world with their flattening orange glow. Looks orange to our eyes, but it’s primarily a mix of red, orange, and yellow wavelengths. If you measure those carefully enough, you can discern a certain “fingerprint” on a spectrum of light that would tell you if sodium is or isn’t present in what you’re observing.

Same applies to hydrogen and helium. Nitrogen and oxygen. Argon and neon. Carbon dioxide. Water. Every atom and molecule – including different ionized states, which is a particularly useful bit of information for astronomers – has its own unique spectrum of light it emits. You just need to look at it in the right way.

Even if it’s millions of light-years distant.

Fan carts

Posted on by Brian Garthwaite
Fan cart on track.
An object at rest.

Newton proposed three laws of motion, and it’s the second one that makes for the most interesting labs. Maybe there’s some way to make inertia both fun and educational, but let’s leave the first law for lecture. Equal and opposite reactions are pretty great, but that’s ideal for big demos. Read: rocket launches.

Force, though. Force lets students do stuff and observe what happens. Doing stuff and getting results is how you make physics more interesting.

One tool in our Newton’s-second-law arsenal is the fan cart. An assemblage of a cart with low-friction wheels and a simple DC motor holding a plastic fan. The fan mount pivots, providing variable direction of force. Runs on AA batteries, and is held together mostly with hot glue.

Two very good reasons for the hot glue: 1) When one of these invariably plummets to the floor, the less-than-rigid connections absorb a good deal of the impact when it all falls apart. Usually it falls into pieces, but nothing’s really broken. 2) After one has taken a tumble, it’s mere minutes to get it re-glued and running once more.

The reason for the fan is that it provides a close approximation of constant force, F. If F is constant, and mass (m) is constant, then by F = ma, acceleration (a) is constant, too. Give a running cart a little backwards push – an additional force – and study how its position and velocity change over time. Simple? Sure, and that’s helpful when tying together various concepts.

Relationships between force, mass, and acceleration according to Newton’s second law. Two-dimensional vectors come into play when rotating the fan. Our motion detectors read position, so it’s an illustration of integrals and derivatives underpinning the acceleration, velocity, and position of a moving cart.

The importance of catching a speeding object before it bangs into the end of the track and crashes to the floor.

Rockets

Posted on by Brian Garthwaite
Estes rocket.
Assembled. May or may not be recovered post-launch.

It’s nearly rocket day! Okay, well, it’s nearly time for a physics lecture on momentum conservation – good ol’ Newtonian mechanics – and nothing livens up a discussion of theory and mathematical modeling like making stuff shoot up into the sky. Or, quite possibly, fail to shoot up into the sky, but we’ve been running some advance tests and prepping backup plans because we really, really want things to go zoom.

Zoom, not boom. It’s much more of a hissing zzziiippp than anything else.

The demonstration usually shows three different rockets in succession, each more impressive than the last. The first one, a soda-bottle water rocket, actually illustrates the principle best. Pressurized water shoots out and down, so the rocket moves up. Mass, velocity, terrible aerodynamics. Occasional light spray, so keep your distance.

Then it’s off to model rocket land, with high-velocity solid fuel instead of water. Less mass but at a much, much higher velocity, and in no time that B-size engine has launched the little cardboard-and-plastic rocket high enough to be a speck that’s hard to discern. As long as the weather isn’t terrible, though, a standard B launch is not only recoverable, but entirely possible to catch before it reaches the ground, drifting lazily beneath its parachute.

Scaling on up to a C-size engine, we’ll have our final launch. Bigger engine, more momentum, and even the slightest breeze ensures it’ll drift far beyond our sight and ability to track. Anyone so lucky as to find the rocket afterward can keep it.

If it’s you, maybe stop on by and let us know?

Vectors

Posted on by Brian Garthwaite
Force table apparatus.
Three-way tug of war.

The humble force table. A flat surface, graduated with single-degree marks. Three pulleys which may be clamped at any position. Loops of string connected to a central ring surrounding a post, each of which is pulled by a mass hanger of 50 grams.

Move those pulleys about, slip on some extra masses, and try to keep the central ring from touching the post!

If you’re going by gut intuition (and not just doing the silly trivial 120° spacing with equal masses), be prepared to make mistakes and incremental adjustments. There’s no way you’re nailing this on the first attempt. Slowly making corrections, adding and removing masses, trying to get that central ring to hover just right, it’s fun. Yes, folks, vectors and statics can be genuinely enjoyable.

The students get to explore that, of course, but it’s also an opportunity to learn a bit of Excel. Build your spreadsheet properly, and you can predict the precise angles and masses needed for equilibrium. Set it up and, presto, it works!

As a test, they run it in the opposite direction, too. Set some angles, add some masses, get it to balance. Type those numbers into the spreadsheet, and… it’s not quite right. The math says it’s off, but the ring says it’s fine. Weird! It’s a handy introduction to measurement uncertainty, a tactile illustration of a critical concept.

It’s very cool.

Circuit Boards

Posted on by Brian Garthwaite
Broken circuit board.
Guts.

Ah, the printed circuit board. Svelte. Densely packed with teeny marvels of modern electronics. Those parts big enough to be labeled usually require magnification to read the text. The really little ones? It’s not really possible to replace those anyway, so just trust that they’re working as intended.

Until the whole gizmo isn’t working as intended, of course.

When that happens, it’s time to make an assessment of what can be fixed. Sometimes it’s a loose wire. Sometimes it’s a frayed cord, or a bad switch that’s not part of the circuit board itself. Not that these are likely, but it’s best to be thorough.

Assuming you can get the housing open to inspect it. These suckers aren’t built with repairs in mind, given that purchasing a whole new item is less expensive than the cost of labor plus the replacement value of what’s 98% of the whole item. So many tiny screws. So many snap-fit plastic parts. At some point you realize how much thought and effort went into designing this object for quick assembly, and how little went into ease of disassembly.

Pictured above, a faulty motion sensor, has no obvious loose connections or broken parts. It simply fails to collect consistent data, with erratic drop-outs punctuating the signal. Oh, well. Maybe it’s good for parts?