We’ve pointed out our old and reliable force tables before – classics of the undergraduate physics experience – which arrived here in several installments. Previously, 1957. This young’un only appeared in April of 1964, intended for the Physics 107-8 lab. Not listed in any recent course catalog, we’re uncertain of exactly what that was.
We could probably go pester some librarians, because surely there’s a record, but those folks are awfully busy on more important matters. Leave the idle wondering to the fellows here in the basement.
At any rate, they paid a healthy sum of $96.75 for this precision-machined beast. In today’s dollars: $985.65.
You can’t tell from the photo, but the tone is lovely.
Both Physics and Astronomy courses do a lot of work with waves, and while light is one of the most important types for study, sound is exceptionally handy for demonstrations. There’s an immediacy, a feel, that can make sonic demos feel more intuitive.
We have a few of these about, metal bars with supports at the nodes of a standing wave, seated over a wooden box. The string goes where the bar doesn’t vibrate, and hence doesn’t dampen the sound, while the box helps it resonate louder. Ka-bong! They’re quite fun.
Quality!
And, yes, Carl J. Ulrich of Minneapolis, Minnesota did some fine work here.
Sometimes you just have to love the directness of the manufacturers of scientific apparatus and equipment. “Sensitive Research Instrument Corporation” is not, by any standards, snappy. But it is clear about their product line.
An accuracy guarantee of 0.25%, standardized by Louis Miller on 10/29/62. Charmingly hand-written on this label affixed inside the case. (Sadly, no one marked this one with the price.)
Behold: a box which counts! That’s it, for the most part. It counts pulses of positive voltage. Very quickly, and you can set some thresholds to tell it to count certain values but not others.
It also gates over an interval you set, so you can tell how many pulses it receives over, say, one second. It counts, displays the total, then counts again. Displays the new number.
We use these for our wave/particle duality lab experiment, which relies on counting individual photons. Yes, those. The teeny, massless quantum packets of energy, the messenger particles of electromagnetism. Light. It acts in non-intuitive ways, and the students who think “that’s amazing and I want more!” sometimes become Physics majors.
Part of using this box – just one aspect – is helping convince those students that only one photon at a time can be reaching the photomultiplier tube sensor. At the speed they move, a mind-boggling number of photons can zip through that meter-long box without bunching up. c in air isn’t all that far from c in a vacuum, so if your one-second counts aren’t remotely near 299,792,458 (adjusted for PMT sensitivity and other losses), you know some of those photons are pretty lonesome. Sometimes you need a little math to make sense of things you can’t directly sense.
Crickets.
One other fun aspect is a little switch hidden on the back: cricket. It’s the volume switch, letting the box emit a little beep for every pulse it counts.
If you’re counting pulses from a radioactive source, which arrive randomly, it can be informative to hear these irregular signals, gated and grouped into numbers which show a decaying curve.
If you’re counting 100,000 photons every second, in a room of other lab benches also counting thousands of photons? Less informative, more irritating.
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.
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.
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.
Most impressive is that the yellow paint has lasted this long.
It seems the university has drifted away from this, but if you look around at old equipment, a great deal of it is marked with the date it was acquired and – if it’s old enough – the cost. They’re fascinating glimpses into the past.
Here, an optics bench made by the Central Scientific Co. of Chicago, Illinois. Or, as they’d prefer, Cenco of Chicago, U.S.A. This particular 132cm chunk of cast iron and steel joined the department in late September of 1943, for the low, low price of $40. According to the U.S. Bureau of Labor Statistics’ CPI Inflation Calculator, that’s an excessively specific $681.17 in today’s dollars. (Significant digits!)
Surely there’s a reason for the cities listed in that order.
Up until now, it’s been in more or less continuous lab use, only recently replaced by brand-new extruded aluminum optics benches. Almost 80 years, and they’re not entirely kaput just yet.
After all, if an apparatus continues to be useful, we’ll keep it around. This one is getting repurposed for future labs, so we’ll see how many more decades it has in it…
