Archive for: June 2012

Slinky physics (cont.)

In previous installments, we brought you video of the amazing levitating Slinky, and Peter Barss wondered how the Slinky had been calibrated to work exactly this way. I asked physicists to come forth, and they have—not just physicists, but an astrophysicist. (Who better to explain levitation?)

Saint Mary’s grad Jonathan Dursi, now a senior research associate with the Canadian Centre for Astrophysics, furnished this detailed by elegant explanation:

Sometimes you hear that there’s three things taught in first year Engineering (or Physics, or whatever); things fall down; F=Ma; and you can’t push on a string.* It’s exactly those three things at play here, and it’s fun to see how they play out.

“How does this happen without calibrating the force exerted by the energy stored in the “spring” of the slinky to match the force of gravity?”

This calibration is done by the slinky itself, or in fact, any spring (or string, or…)

The spring stretches to the point that the tension in the spring — the force pulling the lowest link up — is exactly equal to the force gravity exerts on it to pull the link down. If those weren’t in balance (say, gravity was pulling more), then the lower parts of the spring would stretch out, and the tension would grow, and they would balance. (Hooke’s law, that the tension in the spring is directly proportional to how far it is stretched: F = k x, larger k means harder to stretch out the spring, is often a good approximation for these sorts of problems; but those are details. As long as the tension increased in any manner as you stretched out the spring, this would play out the same way). If it was the spring force which exceeded that of gravity, the spring would pull back, tension would reduce, and again things would end up calibrated.

This is F=ma; when you’re holding the top of the slinky, the fact that the parts aren’t accelerating upwards or downwards (a=0) means that at every point in the spring, the tension pulling upwards is the same as the gravitational force pulling downwards, so that the net force is zero (F=0, so m g = k x). If you went somewhere with a different gravitational acceleration (g), or placed a weight at the end of the spring, the spring would stretch out to achieve the same balance under the new force — the final length would be different, but the balance would again be met.

That much is true of really anything – an iron rod, or a slinky. But they all behave pretty differently when you hold them and drop them. If you hold up an iron rod vertically, it is also true that the bottom of the rod is being pulled upwards by a tension inside the rod and downwards by gravity, each perfectly balanced: but when you let go of it, the bottom does *not* stay in place until the top catches up!

This is where the “you can’t push on a string” bit comes in. The iron rod has a lot of internal rigidity; just try and squish one. When the top starts falling, not being suspended from above by any tension, it can’t catch up with what’s below it; it pushes what’s below it down with it, and the whole thing falls as a single rigid body.

But back to springs — the slinky *is* carefully built to _not_ be rigid. (It has to be able to flop over itself, after all, to climb down stars, alone or in pairs, and make a slinkity sound).

So imagine a three-link slinky, each link having a very small mass, and the whole thing is held up by the top, and there’s no internal rigidity. Each link is feeling a force of gravity down (m g) and a tension from the spring above it (k x) where x is the distance between links. The spring constant of a slinky, k, is really small — you can pull a slinky apart without exerting a lot of force.

Now let go of the top link. It immediately starts accelerating downwards, under the force of gravity. (The acceleration is g = kx/m). This *doesn’t* start _pushing_ on the bottom link — there’s no way to push! — but it slowly starts reducing the upwards tension on the second link, because the distance between them is reducing.

*But*, because the spring force is so small, the distance between links is large, and we’re accelerating from a full stop, this whole process takes a while. So it slowly starts falling, and as it falls, the tension pulling the second link upwards starts lessening — but only proportional to the amount of that distance the top link has fallen so far. Let’s say it would take the top link 1 second to fall the whole distance to the second link. It will take 0.5 second for it to drop even 1/4 of that distance, lessening the upwards force on that second link by only 25%. It will take 0.7 seconds for it to drop 1/2 of that amount, lessening the upwards force by only 50%. It’s only as the top link gets quite close to the second link that the second link looses most of its upwards support, and itself begins accelerating downwards in earnest, repeating this pattern to the lower link.

So, roughly speaking, the n’th link in the chain doesn’t start moving much until the n-1’st link has caught up to it.

Now imagine a more tightly wound slinky, so that it’s significantly harder to stretch it out. That means when you hold it up, it’s much shorter (harder to stretch it) so there’s a much smaller distance between links. There’s still no internal rigidity (say), but this whole process happens much faster, because the distance between links is much faster; the bottom “levitates” still but for a much briefer period of time. Keep tightening your mental slinky, and it happens faster and faster and faster until there’s no obvious moment of levitation at all.

This is what is meant by the “bulltwaddle” about information transfer and signals. The “We’re falling now” signal is sent from one link to the next by removing the upwards tension force. That signal travels at the same speed as the wave of now-collapsed top links moving downwards.

Quite generally, a wave travels at a speed proportional to the square root of the force which generates the wave (here, the spring tension) divided by the density of the medium. This is what sets the speed of sound in water or air (the square root of pressure over density); the speed at which a guitar string vibrates when plucked (square root of string tension over string mass), ripples on a pond, etc. Here, the wave travels at a speed proportional to the square root of the tension (k x) over the density of the spring (m/x). Because the spring adjusts itself initially so that k x = m g, this means that the wave speed is proportional to g * sqrt( m / k ), and it takes a time x over velocity, or sqrt(m/k), for the signal to travel. The looser the spring (small k), the longer it takes this signal to travel downwards. In a tighter slinky (larger k) this signal speed will get faster and faster and there will be a briefer and briefer moment of “levitation.”

(I will choose to overlook those cautious quotes Dr. Dursi placed around “levitation.”)

A reader who styles himself “Krackalakin” offers both a shorter explanation…

Consider that by holding a suspended Slinky by one end, you are holding a spring in tension… The force of gravity is the tension, or what is forcing the spring to extend and is directly proportional to that of the force puling it down – gravty! So there is no collusion or “transfer of secrets” that happen.

…and a link to an MIT classroom video wherein Prof. Walter Lewin explains the underlying principle.

The spring stuff starts about 1:30 in, but if you watch the whole thing, you can imagine what it would be like to be an MIT student.

Much obliged to both readers.

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* I’ve heard this rule applied in a different context, but this is a family blog.

If you happen to be in Cape Breton… (part 783)

One of my favorite photographers, Cory Katz, a 25-year-old autodidact, has a show on at the Cape Breton Centre for Craft and Design, from now until July 16. Katz springs from that unlikely hotbed of artistic talent that is New Waterford. Yes, New Waterford.

Why the dollar zone works and the euro zone doesn’t

The Atlantic’s Derek Thompson explains it in four terse sentences:

Europe has Greece. We have Mississippi. Europe uses the term “permanent bailouts.” We call it “Medicaid.”

And he illustrates the point with a map from the Economist:

Thompson again:

[T]he poorest states like Mississippi, New Mexico, and West Virginia rely on ginormous transfers of federal taxes in the form of unemployment benefits and Medicaid. Like the United States, the euro zone is all on one currency. Unlike the United States, the euro zone collects a teensy share of total taxes at the EU level and has no legacy of permanent fiscal transfers from the richer countries, like Germany, to the poorer countries, like Greece. The result is the chaos playing over your computer screen day after day.

Here in the U.S., states like New Mexico and Alabama are always “in fiscal trouble.” But it’s not news. In the last 20 years, the seven states in orange and red in the graph have accepted federal money worth around 200% of their annual GDP. Perhaps you’ve had a bar debate about whether we should boot Mississippi from the union, but that sort of thing hasn’t made its way to Washington.

In those terms, I would put Canada halfway between the US and the euro zone: Like the US., we have a common currency and fat transfer payments; Unlike the US,  we host a raft of organizations (CD How, Fraser, AIM, and the National Post) that make a nice living bitching about it.

Calling all physicists

Yesterday, I posted a slo-mo  video of a Slinkeys, which, when dropped while their springs were completely distended, appeared to levitate momentarily, until their springs had time to re-compress, whereupon they began their expected downward trajectory. My pal Peter Barss (who is descended from a real pirate, kids) has a question “for anyone who remembers their physics better than I do.”

During most of the its fall, the bottom of the Slinky remains absolutely motionless, which, to my mind, means the gravitational force acting on the slinky pulling it down is exactly balanced by the force compressing the bottom of the slinky upwards. How does this happen without calibrating the force exerted by the energy stored in the “spring” of the slinky to match the force of gravity? It seems to me that the two forces would have to be precisely balanced for the bottom of the slinky to remain motionless while the top collapses.

I wondered the same thing. Is that precise balance an inherent quality of a Slinky—the same quality that enables it to walk down stairs? Some hints in this article at Phys.Org, a web-based science, research and technology news service, and in this paper by UBC physics prof Bill Unrah. Turns out the late, great Martin Gardner kicked off the discussion a dozen years ago. [Animated gif via KnowledgeForDummies.]

Sometimes you gotta love spam

Every once in a while, between pleas from search engine optimizers, deposed African Generals, and cut-rate Viagra pushers, spam coughs up a gem. Like the 5,711-word message I just received from Father Yahweh, yea Jehovah, Most High God, aka Linda Newkirk of Little Rock, Arkansas. It began like this:

It can now be reported that many of the wildfires in the western United States have been started by highly trained and well equipped foreign terrorists. It can also be reported that these terrorists are also responsible for the numerous explosions that occured in Michigan on the 6th and 7th of June 2012. You may not of heard of the Michigan explosions as there has been a news blackout in place.

One of the major explosions in Michigan that sent radiation monitors thousands of times higher in two different locations was the result of a tactical nuclear weapon. The underground nuclear explosion and numerous smaller explosions, that were sometimes heard in rapid succession, were aimed at setting off the New Madrid Fault! The smaller explosions were created with scaler electromagnetic technology. Both the US and the USSR are known to have developed this type of tectonic plate weaponry.

The purpose of this email is to expose those who were behind the attacks. For reports and background information on what actually took place in and around the Michigan Indiana border, visit the following sites. Link here [deleted], and additional link here [deleted].

It has now been revealed that the attacks were carried out by Russian Special Forces who were brought into the USA under the guise of joint training excercises with the US Military. There is plenty of corroborating eyewitness testimony following the prophetic warning you are about to read. There are also descriptions of the expensive motorhomes they are travelling in.

You haven’t heard of those June 6 & 7 Michigan blasts, have you? What more proof do you need? As you may have guessed, the central figure behind this dastardly conspiracy is none other than Barack Obama. Newkirk knows this because T.M., the militant Communist wife of V. M., a “level-headed Russian scientist,” told Tom Fife as much way back in 1992, when none of us had ever heard of Obama. Fife was setting up a software development joint venture in Moscow with scientist-colleagues of V.M.’s when e visited the couple’s flat one evening, and T.M. just blurted the whole thing out.

What if I told you that you will have a black president very soon and he will be a Communist? Yes, it is true. This is not some idle talk. He is already born and he is educated and being groomed to be president right now. You will be impressed to know that he has gone to the best schools of Presidents. He is what you call “Ivy League”. You don’t believe me, but he is real and I even know his name. His name is Barack. His mother is white and American and his father is black from Africa. That’s right, a chocolate baby! And he’s going to be your President.”

Doesn’t that put your worries in perspective?

The amazing levitating Slinky

All the actions is in the first 140 seconds.The remaining four minutes of explanation, involving claims of “information transfer” and “signals,” strike me as, frankly, bulltwaddle. Much more plausible is the explanation furnished by Andrew Sullivan’s Daily Dish, which in turn came from an even more thorough explanation on Rhett Allain’s blog at Wired.com.

What you’re seeing:

If a slinky is hung by one end such that its own weight extends it, and that slinky is then released, the lower end of the slinky will not fall or rise, but will remain briefly suspended in air as though levitating.

Explained:

[T]he best thing is to think of the slinky as a system. When it is let [go], the center of mass certainly accelerates downward (like any falling object). However, at the same time, the slinky (spring) is compressing to its relaxed length. This means that top and bottom are accelerating towards the center of mass of the slinky at the same time the center of mass is accelerating downward.

H/T: JHE

Quick, let’s get asbestos removal started before school ends for the summer – updated

H/T: YNW

[Update] Our friend the cranky physicist comments:

A true contrarian would look at the actual risks of the asbestos and it’s removal as well as the cost to taxpayers from how we overreact.

That was also my first reaction, because I get that not all asbestos is dangerous in all circumstances. But, hey, school ended today. Couldn’t they have waited a week?

You gotta like a president who shoots a marshmallow gun

A marshmallow cannon, actually, and he shot it inside the White House.

Contrarian may be the only blogger you read who actually owns a marshmallow gun.

More views of money and politics in Nova Scotia

When information is presented in a format computer programs can read, as opposed to a static, telephone directory-style list, fresh insights spring from the data. Contrarian friend Gus Reed prepared a compendium of revelations arising from Elections Nova Scotia’s annual political donations report—once we liberated it from the cloistered format favored by the former Chief Electoral Officer.

Some examples:

  • Does Nova Scotia have a party of the rich? Not according to the donations made in 2010. When Gus plotted the proportion of donations against their size, all three major parties showed a remarkably similar distributions:

  • Vote tallies for the three major parties in the last several elections have shown sharp geographical variations. Is the same true of people who donated to political parties in 2010?  Here’s a list of the top 10 cities and towns whose residents contributed to each party.

Draw your own conclusions. Gus’s report has more of this, including a list of everyone who gave more than $1000 to a Nova Scotia political party in 2010. Download it here.

Elections Nova Scotia plans to release the list of 2011 political donations today [Update: Or not]. Wouldn’t it be great if the new Chief Electoral Officer could find his way clear to releasing the data in a format that makes searching for insights easy rather than hard?

A Contrarian map of politics and money in Nova Scotia

In a series of posts last September, Contrarian revealed that Nova Scotia’s Chief Electoral Officer had degraded the format used to report political donations over $50. For the first time, she released the file as a scanned PDF that cannot be searched or readily copied to other formats.

Helpful Contrarian readers promptly hacked* McCulloch’s degraded files, enabling us to republish the data in the searchable, text-grab-friendly format used in previous years’ reports. Today’s long overdue follow-up provides the data in two new, even more useful and interesting formats:

  • An Excel spreadsheet readers can view, parse, and re-use in ways limited only by their imaginations and programming chops.**
  • An interactive Google Map showing every donation to a registered Nova Scotia political party in 2010.

[Direct link to map] Dots on the map are color-coded by party: orange for NDP, red for Liberal, blue for Tories. The larger dots stand for donations over $1,000. Clicking on an individual dot brings up the donor’s name and address, and the amount of the donation. Use the + and – slider on the left side of the map to zoom in and out; click and drag the map to focus on a particular town or neighborhood.

Over the next day or two, I’ll post some other useful ways of visualizing this data, produced by a particularly creative Contrarian reader.

Google is not perfect. It has trouble geo-coding rural route addresses and post office boxes, so these sometimes appear in odd places or even as overlapping donations sharing a single location.***  The optical character recognition (OCR) process required to decode Elections Nova Scotia’s deliberately degraded file may have introduced a few errors into the data. If you notice any, please use the comment link at the top of this page to let me know, and I’ll try to correct them.

I expect political junkies will find playing with the map mildly diverting. Is it also important (as I maintain) or dangerous (as Election Nova Scotia professes to believe)?

Chief Electoral Office Christine McCulloch, since retired, contended that crippling her legally required disclosure report was necessary “to protect contributors from ‘data-mining.’” In fact, Nova Scotia law contains no such requirement, and the one judicial precedent runs counter to her policy. In a moment of hyperbole this week, an Elections Nova Scotia official offered the preposterous suggestion that  the spreadsheet I am releasing today could even be abet identity theft.

About the worst that could happen is that someone could — could, but probably won’t — use the spreadsheet to develop a direct mail solicitation list. A company wanting to do that probably has access to more sophisticated OCR tools than Contrarian. As a practical matter, the Elections Nova Scotia’s lockdown only impedes ordinary Nova Scotians seeking to use the data in creative, citizenly ways.

Earlier this month, the President of the United States issued an executive order directing all federal departments to implement application programming interfaces, commonly known as APIs, to give software developers direct access to their public data. This will lead to creative, entrepreneurial uses of public data that enhances its value to the people who paid for it.

In Nova Scotia, we’re moving in the opposite direction, responding to overblown privacy concerns by locking up data that used to be freely available. This is a recipe for turning our province, which overflows with digital programming talent, into a information age backwater.

I hope Nova Scotia’s new Chief Electoral Officer will reconsider this policy with an open mind. More importantly, I hope cabinet ministers and senior officials will consider the economic and cultural benefits that will accrue if their departments ease their grip on the many kinds of data they gather.

[UPDATE II:] Elections Nova Scotia plans to release the 2011 political donations data Friday.

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* Many readers contributed time and skill to this effort. Hearty thanks to JS, PGH, WF, NMK, and most especially, mapping guru WCR.

** The spreadsheet only lists donations to registered provincial political parties. It does not include donations to individual riding associations or to candidates in the 2010 Glace Bay byelection. The manner in which Elections Nova Scotia tabulates these simply makes it too much work.

*** An interesting example is the large orange dot just south of TransCanada 104 east of Antigonish. Clicking it sometimes brings up John “Nova” Chisholm’s $2,500 donation to the NDP (!); and sometimes Carl Hartigan’s $1,000 donation to that party. The two men have post office boxes and very similar postal codes. You may have to zoom in and out to different resolutions to see both donations. [UPDATE I:] Hartigan, I’m told, is a close associated of John Nova’s.

 

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