Built on Facts

First day of the semester yesterday. Wide-eyed undergrads were flocking to their physics classes in our brand new and completely beautiful building. I’m not so sure they were thrilled about it; doing physics is not something that naturally appeals to most denizens of the university. I admit I’m feeling a few pangs myself for entirely different reasons – though in a lot of ways teaching (and grading!) is a massive time sink, as a research assistant I do miss being in front of a blackboard and helping teach the next generation their physics. Maybe I’ll volunteer to do some tutoring now and then…

What are they learning this week? If I had to guess, probably linear motion in one dimension for the first class and static electric fields for the second class. Via Swans on Tea, we can see a great demonstration of one form of 1d motion. It’s high-speed photography by artist Alan Sailer of liquid-nitrogen-frozen objects being perforated with a pellet rifle. I’ll just sample one, you can view the rest at the link – this one is a plum meeting a pellet at some 200 meters per second:

There’s lots of freshman physics in this scenario. There’s finding the average acceleration of the pellet in the object by looking at the speed before and after. There’s finding the force the pellet exerts by using the acceleration and the mass of the pellet. There’s conservation of momentum in the way the fragments fly. There’s electrical currents in the flash that makes the photograph possible. There’s the energy and power involved in the light itself. There’s no end to the problems you can pose.

I propose we do an open-ended question to stretch our minds, since this one not a cut-and-dry numerical answer: why do frozen objects have a greater tendency to shatter than warm ones, even in the absence of an overt water -> ice phase change? Think about what temperature is on the atomic level, and you’ll be on the right track.

Comments

#1 Eric Lund
January 20, 2010

The warmer the material, the larger the thermal vibrations of the atoms therein. That means an improved ability to withstand shocks, even when there is no phase change. If the temperature is too low, the thermal vibrations may not be enough to prevent brittle failure of the material. If you are in a place like Fairbanks where temperatures can drop below -40C, this leads to things like timing belt failures–your car will then overheat because one of the systems that depends on the timing belt is the coolant pump. (I’ve had occasion to observe this firsthand.) That’s one reason why anyone traveling by road in rural areas of Alaska in winter should convoy if possible: if the timing belt fails on one vehicle the others can pick up the people who were in the car and bring them to a place with a telephone (cell phones being useless most places outside Anchorage/Fairbanks/Juneau).

A more famous historical example, but one that IIRC involves a phase change, is the organ that Peter the Great ordered constructed in St. Petersburg. The organ pipes were made of tin, which, unbeknownst to the organ builders, undergoes a phase change to a more brittle state around -40C. When during the winter the temperature inevitably fell that low (we are talking about Russia, after all), the pipes fell apart.
#2 Ramdic Hellbane
January 20, 2010

Your car wont get a chance to overheat. Without a timing belt the engine wont run.
#3 rob
January 20, 2010

how exactly do larger thermal vibrations at high T improve the ability to withstand fracture?

my guess is that at low T the reduced atomic motions means when interatomic bonds are broken, they don’t reform on timescales fast enough to resist propagation of cracks in the crystal. although, this doesn’t quite satisfy me cause i assume bond formation takes place on time scales much smaller than time scales for cracks to propagate.
#4 complex field
January 21, 2010

At the macroscopic level, cold temperatures make most things brittle. A sudden shock, eg, pellet vs frozen plum, simply shatters the plum.

“Drilling” a little further down, and looking at the hydrogen bonds (in this case), those bonds act as springs obeying Hooke’s law. Like any spring, there is a limit to the elasticity of the material from which it is made. Once that limit is breached, the spring fails and breaks. Lower temperatures “shorten” the springs, giving them a larger K, and lowering the limit of elasticity.

Down to the atomic level: no clue. I got a “D” in my quantum theory class.
#5 complex field
January 21, 2010

I should note that in my spring model, most springs after breaching the limit of elasticity simply deform, causing a permanent change in their K constants. The same would apply here, in that the change equates to a catastrophic failure of the bond.
#6 Eric Lund
January 21, 2010

Your car wont get a chance to overheat. Without a timing belt the engine wont run.

Maybe your engine won’t start without a timing belt, but if it is already running it will continue to (try to) run. As I said, I’ve seen it happen–the rapid rise in engine temperature is typically the first sign visible to the driver that the belt has failed. Note that in a stationary car the belt only feels thermal stresses, which aren’t by themselves sufficient to produce a problem any more than a frozen rose held in your gloved hand has a problem. It’s the additional stress (for the timing belt, the fact that it actually has to move around its loop) that does it in.
#7 complex field
January 21, 2010

Eric Lund,

I think you are referring to the serpentine belt or, on older cars, the fan belt.

The timing belt acts as a clock for the “car system”. The ignition will not spark the plugs without an in-tact timing belt, but it can try to go on without the serpentine belt. Or the fan belt.

Just like no clock = no computer, no timing belt = no running engine.
#8 Uncle Al
January 21, 2010

Tin pest, the white (metallic)-grey tin transition, occurs around 10-14 C in pure tin. It is catalytic in grey tin. A bit of blown dust is rapidly lethal to a pipe organ.

Shattering depends upon elasticity, shocks, and energy dissipation mechanisms. Ballistic gels will enormously dilate then return, as captured in uncountable high speed videos. Mythbusters firing high velocity slugs down through water into a slab of ballistic gel in a Plexiglas tank is eloquent. Bullets were slowed by the water, or zipped into the gel, or quickly disintegrated upon water entry. Then Jaime fired a deer slug with his 12 ga. rifle. The tank shattered.

“Frozen” isn’t enough. Mythbusters froze wet wood pulp or plied wet newspaper versus block ice, then fired bullets. Ice shattered. The frozen composites’ surfaces chipped.
#9 Anonymous Coward
January 21, 2010

I love simple physics explanations, but I’m skeptical that there’s one here.

Metals become stronger (as in higher yield strength) as they get colder, with only a small amount of increase in crack propagation effects. I don’t think cold ice is noticably more brittle than warm ice (although the conditions under which the ice formed can have huge effects on its mechanical properties).

The materials that exhibit very large embrittlement effects are those that undergo a phase change (as mentioned by Uncle Al – that tin stuff is weird and true – or in the original post with water/ice) or with very long molecules (like rubber, various other hydrocarbons). If you’ve got a good explanation, I’d love to hear it.
#10 fatima louise
March 4, 2010

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March 15, 2012

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