Surprising Physics: Falling Flat Boards & Chimneys

[Integral]

No, not pi feet high. pie feet high!

pie should always be rounded and never squared.

Oh... now it is clear, tell me, did your wife object to pie tracks arcoss the floor when you were done?


I have always pondered the obvious error in the statement pie are square!

 

[honestrosewater]

So, without using big words, can anyone tell me if you think the places where the chalk breaks are determined by inconsistencies in the structure of the chalk (it breaks where it's weakest) or inconsistencies in the forces it undergoes (energy becomes more concentrated in some areas) or a combination of both or other factors?

 

[cronxeh]

I think the chalk is too strong to start breaking apart in the air, and it breaks right when it hits the repulsive forces on the ground. The forces are not equally distributed due to the structure of the chalk and depending on the angle, force of collision, area and position of the impact, chalk structure and chemical makeup, it will break along the stress points

 

[PerennialII]

... yeah, it'll be a complex display of fracture considering the 'macroscopic' large cracks appearing in sequence, the smaller 'spalling' etc. with all the redistribution of stresses during the fracture process.

 

[Integral]

In my view I see the shock wave from the impact traveling through the chalk at the speed of sound in chalk and interacting with the stresses induced by the sudden greater then g acceleration of the still falling tip.

Of course this assumes that one end of the chalk strikes first causing a rotation of the stick about that end. Of course the energy of the impact will have a major effect, thus I am restricting this to falls from about $\pi$ feet.

 

[Moonbear]

What flooring material does it have to drop onto? Concrete, tile, linoleum, wood, carpet? Especially wood and carpet will likely cushion the fall and lead to a different fracture pattern than on concrete or tile.

 

[εllipse]

What if a piece of chalk drops in the forest, and there's no one there to see it break?

 

[Integral]

What flooring material does it have to drop onto? Concrete, tile, linoleum, wood, carpet? Especially wood and carpet will likely cushion the fall and lead to a different fracture pattern than on concrete or tile.

My experiments where done on hard classroom floors. I cannot say anything about carpet or cushioned surfaces.

Do I need to specify the brand of tile?

 

[BobG]

My experiments where done on hard classroom floors. I cannot say anything about carpet or cusioned surfaces.

Do I need to specifiy the brand of tile?

Don't do it on carpets - it'll land butter side down.

 

[brewnog]

So, without using big words, can anyone tell me if you think the places where the chalk breaks are determined by inconsistencies in the structure of the chalk (it breaks where it's weakest) or inconsistencies in the forces it undergoes (energy becomes more concentrated in some areas) or a combination of both or other factors?

Certainly not because of any inherent weakness in the chalk. I'm going to use some big words now, because I'm qualified to use them!

When thinking about this problem, we assume that the chalk is isotropic (material properties are the same in any direction), and homogeneous (material properties are constant at all locations within the material).

While there may indeed be some weaknesses in the chalk, and it's impossible to guarantee that there aren't, on a macro scale the chalk is the same at any point along its length.

 

[Integral]

Certainly not because of any inherent weakness in the chalk. I'm going to use some big words now, because I'm qualified to use them!

When thinking about this problem, we assume that the chalk is isotropic (material properties are the same in any direction), and homogeneous (material properties are constant at all locations within the material).

While there may indeed be some weaknesses in the chalk, and it's impossible to guarantee that there aren't, on a macro scale the chalk is the same at any point along its length.

Agreed, those are certainly underlying assumptions. Any micro cracks could completely change the out come!

 

[Integral]

Don't do it on carpets - it'll land butter side down.

Humm... perhaps the butter would reduce the screeching of chalk on board?

 

[brewnog]

Agreed, those are certainly underlying assumptions. Any micro cracks could completely change the out come!

Ahh yes, I wasn't merely informing HRW, I was instructing her on how to introduce SCFs into your chalk collection to make the sticks shatter into 7 pieces instead...

 

[honestrosewater]

Ahh yes, I wasn't merely informing HRW, I was instructing her on how to introduce SCFs into your chalk collection to make the sticks shatter into 7 pieces instead...

Hm, I should have said no acronyms either. (System Control Factors?)

I thought it made more sense that Integral's chalk was partially broken before the drop. It could easily happen during shipping and handling. But fine, you're the experts.
So what types of stess are you guys talking about? Can you infer anything about the types and locations of the stresses from the locations and characteristics of the fractures?

 

[brewnog]

Hm, I should have said no acronyms either. (System Control Factors?)

You got the F right! Stress Concentration Factors. Things like cracks, corners, or sudden changes in geometry will concentrate the stresses, so that they are much higher around those areas. Think of Sellotape being easier to tear if you put a nick in the edge.

I thought it made more sense that Integral's chalk was partially broken before the drop. It could easily happen during shipping and handling. But fine, you're the experts.

Absolutely, and damage would indeed make the chalk break more easily. It needn't even be damage caused by transport or handling, - many manufacturing processes leave imperfections in the product which can cause local weaknesses. However, since we're observing that the chalk breaks at roughly the same places each time, it's unlikely that this is caused by damage.

 

[honestrosewater]

Absolutely, and damage would indeed make the chalk break more easily. It needn't even be damage caused by transport or handling, - many manufacturing processes leave imperfections in the product which can cause local weaknesses.

Yeah, but I didn't feel like looking up how chalk is made. Does anyone already know? I'll check later when I have time to kill.

However, since we're observing that the chalk breaks at roughly the same places each time, it's unlikely that this is caused by damage.

Oh, I didn't know they all did break in the same places, but I thought of that too. If you set a box of chalk on a table and gave it a "karate chop"- you know what I mean?- wouldn't that usually cause similar damage to all or many of the pieces? The "karate chop" could be caused by the corner a heavy box falling on it.

 

[brewnog]

Yeah, but I didn't feel like looking up how chalk is made. Does anyone already know? I'll check later when I have time to kill.

I would imagine it's just compressed in a mould. Part of me thinks that it could be extruded, before being chopped up, but at the moment I'm tempted to say that it's just moulded. Either way, there are no inherent flaws as a direct result of manufacturing.

Oh, I didn't know they all did break in the same places, but I thought of that too. If you set a box of chalk on a table and gave it a "karate chop"- you know what I mean?- wouldn't that usually cause similar damage to all or many of the pieces? The "karate chop" could be caused by the corner a heavy box falling on it.

Yeah, but I think that Integral's spent so many hours on the empirical side of his theory that it's probably more general than just one box of chalk. I imagine him to have sourced different brands of chalk from all over the world, under strictly controlled conditions, before testing them all to destruction in his secret underground lair.

 

[honestrosewater]

Yeah, but I think that Integral's spent so many hours on the empirical side of his theory that it's probably more general than just one box of chalk. I imagine him to have sourced different brands of chalk from all over the world, under strictly controlled conditions, before testing them all to destruction in his secret underground lair.

Hm, I guess his secret underground lair isn't so secret anymore.

 

[BobG]

Hm, I guess his secret underground lair isn't so secret anymore.

During dry spells, you can just follow the trail of chalk dust.

Oh, wait. He lives in Oregon.

Integral, dry spells have nothing to do with witches. They're prolonged periods without rain.

 

[honestrosewater]

Integral, dry spells have nothing to do with witches. They're prolonged periods without rain.

I thought witches were women who practiced sorcery and had magical powers.?

 

[BobG]

I thought witches were women who practiced sorcery and had magical powers.?

Which witch? The ones that wear black hats or the sand witches that hang around with dust devils?

 

[Janus]

During dry spells, you can just follow the trail of chalk dust.

Oh, wait. He lives in Oregon.

Integral, dry spells have nothing to do with witches. They're prolonged periods without rain.

Oh we know what those are here in Oregon, sometimes we get them that last as long as a WEEK!

 

[honestrosewater]

Which witch? The ones that wear black hats or the sand witches that hang around with dust devils?

It could be either- I only know they always carry brooms.

 

[honestrosewater]

Oh we know what those are here in Oregon, sometimes we get them that last as long as a WEEK!

Do yours carry brooms?

 

[Integral]

I would imagine it's just compressed in a mould. Part of me thinks that it could be extruded, before being chopped up, but at the moment I'm tempted to say that it's just moulded. Either way, there are no inherent flaws as a direct result of manufacturing.



Yeah, but I think that Integral's spent so many hours on the empirical side of his theory that it's probably more general than just one box of chalk. I imagine him to have sourced different brands of chalk from all over the world, under strictly controlled conditions, before testing them all to destruction in his secret underground lair.

My testing was done sporadicly over my 15 years in academia, if front of many different black boards in many different class rooms. Most of the chalk I have dealt with has been of very similar dimensions, but I have allowed dimension as a critical parameter.

Now as for tracks into the secret lair, it is not clear? Are those $\pi$ tracks from Bobs $\pi$ feet or dusty chalk track?

I am sure that broom carrying lady was just the janitor sweeping up the chalk tracks (which are much easier to clean up then $\pi$ tracks) and not a witch!

As I write, I notice that something strange is happening outside, there is some unusual form of energy pouring through my windows, and the clouds all seem to be blue?
Janus, what is that big yellow thing in the sky?

 

[Janus]

Do yours carry brooms?

Sure. They use them to keep the storm drains clear.

 

[Janus]

As I write, I notice that something strange is happening outside, there is some unusual form of energy pouring through my windows, and the clouds all seem to be blue?
Janus, what is that big yellow thing in the sky?

I don't know, But I bet you is has sumptin' to do with one of dem der' "dry spells" cast by a "sand witch".

 

[Integral]

I don't know, But I bet you is has sumptin' to do with one of dem der' "dry spells" cast by a "sand witch".

That sounds reasonable... Now I am hungry! A sandwitch and some round $\pi$ sounds real good.

 

[Janus]

That sounds reasonable... Now I am hungry! A sandwitch and some round $\pi$ sounds real good.

Round $\pi$? I thought $\pi r^2$?

 

[Integral]

Round $\pi$? I thought $\pi r^2$?

That is a common myth. When was the last time you ate a square $\pi$?

 

[Janus]

That is a common myth. When was the last time you ate a square $\pi$?

It was a Shepherd's $\pi$.

 

[honestrosewater]

I like to fit square $\pi$ into a square meal; It's more efficient that way.

 

[Crosson]

This chalk business is reminiscient of Feynman's conjecture: If you grasp the two ends of a dry spaghetti noodle and break the noodle by bending, it is almost impossible to break it into any less then 3 pieces.

 

[Mk]

That is a common myth. When was the last time you ate a square $\pi$?

I usually encounter it in a triangular prism form.

http://www.rockfield.co.uk/images/chimney_collapsing_real.gif
This chimney broke into $\pi$ pieces.

So tomorrow I'll settle this - if I remember to buy chalk. I'll try and get the sidewalk form as well. I don't have a highspeed camera.

 

[Mk]

I bought the chalk today, but I'm going to do it tomorrow. I'm confident it will break into pi pieces. Happy trails!

-Mr. Smith