Tag: labs

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.

Compass

Posted on by Brian Garthwaite
Magnetic compass face.
North!

We have many, many compasses scattered about the department. The vast majority come and go as part of the toy kits for PHYS 212, tiny ones useful for illustrating the effects of magnetic fields. Probably more that than for wilderness orienteering. Note: a physics toy kit, despite its educational and entertainment value, is probably insufficient on its own for wilderness survival. Check with the fine folks at Outdoor Education & Leadership for that.

One of the entertaining compass demos is to array a circle of them around an unshielded wire, and seeing the effect of turning the current on and off. Half a dozen little red arrows snapping to attention never loses its neat-o quality.

There’s also this little gem, tucked away in one of our closets. Inscribed with a nice little dedication, reading “TO BUCKNEL / A FRIEND” on the side. Which, the longer you look at it, seems a little less clear each time.

Compass inscription.
Oh. Okay?

Maybe you had to be there? Interpret it as you will.

Tempera powder

Posted on by Brian Garthwaite
Rainbow of tempera powders.
So colorful. So messy.

When astronomers study objects they can’t reach, they’re typically limited to visual clues to glean information. Sometimes that’s color variation, like when the ejecta from a crater redistribute layers of rock and soil. Laid down at different times, and made of different materials, the dark and light rings and patches can provide a great deal of insight into how and when a lunar crater formed, for example.

The moon is somewhat less vividly colored than a sink full of tempera paint powder, of course. Electroshock hues make the distinctions easier for the students. We have black, brown, and white in the mix. They work just as well, but never elicit the excited reaction of a brilliant orange or a neon-level magenta.

Intended for mixing your own paint, these are effectively the same as the bright, thick paints in nearly every kids’ art classroom you’ve ever seen. Combined with the play sand, the whole lab starts to smell a little bit like a fun day at preschool.

Bins of colorful sand.
The aftermath.

In the end, it all becomes a smeared, brownish-gray mix of sand, pigment, and the occasional lost marble or ball bearing. That and a room where every horizontal surface has a new layer of fine, fine dust…

Vernier calipers

Posted on by Brian Garthwaite
Vernier calipers with purchase date and price.
60 years of precision.

A reliable set of Vernier calipers, still working just fine. We use all manner of measuring calipers around here, with varying degrees of precision for different duties, but it’s nice to see the classics still performing well after six decades. Purchased in April of 1962, for the low, low price of $7.85.

Today’s dollars: $77.46.

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.

Colorful candy

Posted on by Brian Garthwaite
Box of bags of M&Ms.
Inside: milk chocolate, a statistics lesson, some artificial colors.

New concepts work better when there’s a hands-on element to engage students. It might be rockets, bouncy balls, lasers, or in the case of basic statistics concepts: candy. Specifically colorful candy. The physics labs have a long history of using M&Ms, though we hear that Skittles and Starbursts have their partisans, too. One bag for each student, TA, and instructor.

It’s a lot of milk chocolate.

The trick is that while each bag contains about the same number of M&Ms – there’s a statistics question all its own – they come in a range of different and unevenly distributed colors. How many blues are in your bag? Opening one won’t tell you much about how many to expect in another bag, but two might. Or thirty. Or three hundred. The more data you collect, the better you can understand the range of possible blue M&Ms and the likelihood of any particular value.

It’s very helpful in a variety of topics in physics and astronomy. It’ll show up later for those students who study radioactivity, which functions in a completely random fashion on an atom-by-atom level, not revealing its predictable patterns until you look at large populations. It’s critical for understanding uncertainty in measurements, because they’re never perfect. It’s foundational for techniques in astronomy used to separate out faint signals from distant celestial objects among the electromagnetic noise of the universe.

Plus they get to eat them when they’re done.

Blue M&M on the floor.
Included in the data set, or not?

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.

Force table

Posted on by Brian Garthwaite
Force table with acquisition info.
More yellow paint!

Some equipment just keeps on working, year after year. This force table – an apparatus used to illustrate static equilibrium and vectors in a way that’s loads more fun than Excel, but the students still have to learn Excel – was purchased in February of 1957 for the not-insignificant sum of $87.50.

Today’s dollars: $935.89.