Work (energy) that causes a crack without distance

[jamiek]

If you had a bowling ball sitting statically on top of a perfect rectangluar porcelain tooth, and the bowling ball caused a crack in the porcelain tooth (hairline fracture), but then you immediately took the bowling ball off the tooth... wouldn't there be no work done since the bowling ball didn't move downward any distance from the force of gravity? The tooth is at the same level (height) if it has a crack in it, isn't it? Work requires force over a distance. It seems cracking the tooth is missing the distance part of work.

My theory in this case is that a small movement did occur (in the tooth), but I'm skeptical of the bowling ball movement (which seems to be zero). The crack would virtually not cause the bowling ball to change height, but the tooth would move a hairline sideways. The tooth is still at the exact same level height wise, but the tooth is a hairline wider due to the space in the new crack. The tooth doesn't split into two pieces and break apart completely, it just has a hairline crack. This is not a homework question, I'm simply doing a thought experiment to see if there can be Work done without any distance covered.

Another example would be a hydraulic cylinder that is plugged, you put a lot of force on the piston and the hydraulic cylinder develops a hairline crack in it - but no fluid leaks out, the hairline crack is such a small crack that the fluid remains in the exact same position as it was before the hairline crack. The fluid is so thick that it doesn't seep through the crack at all. The pressure caused the crack since it is a closed system that is plugged up. Again in this case my theory is that a small movement must have occurred - some of the fluid must have budged just a tiny bit, to fill in the tiny new space made available by the hairline crack. If the crack was small enough, it would seem that it would have no effect on the distance the piston moved - because the fluid has nowhere new to go - it can't move any fluid into the crack, and the cylinder remains exactly the same shape and size, it just has a tiny crack in it. The hairline crack may cause the volume of the cylinder to increase just a hairline due to expansion, but I think you could have a hairline crack that is so unnoticeable and small that the cylinder maintains the same volume. If you absolutely must move the piston in order to do work, then it must be a hairline distance via a massive amount of force.

 

[sugeet]

just hold a very heavy rock, for 10 mins, continue it for another 20 mins at the same level.

did you do any work by carrying the rock for such a long time?? but you will surely be tired, is it not?

Is gravity doing work to keep me on earth?? where is that accounted for if it is so??
In any conservative field, without displacement / (change in potential) there is no work done by definition, but how is it that I do work and feel tired when I carry anything for long time.

 

[HallsofIvy]

sugeet, are you responding to jamiek's post or just asking questions of your own?

In any case, the answer is is the same- IF you consider the "porcelain tooth" or your arm to be a single rigid object there would be no work done. However, in that case there would be no "crack" or "tiring".

In case that the tooth cracks, the bowling ball must move downward slightly- the crack itself allows the ball to move lower. That is the work done by the bowling ball on the tooth. Similarly, your muscles are dynamic, not rigid- your arm goes up and down slightly as you are "holding" the rock in place. The work done by your muscles moving the rock the slight distance back up to where you want to hold it causes the tiring.

No, the Earth's gravity is not doing any work just holding you on the earth. That's why it can continue to hold things for eons without losing energy!

 

[sugeet]

HallsofIvy! I understand something, but what if I keep the ball, on my head, I can't stand indefinetly! You mean I am doing no work , then why am i tired

 

[Studiot]

Hello, Jamiek.

In both your examples you mention a crack.

Now the fundamental characteristic of a crack is that the material either side of that crack has moved apart, even if by a small amount.

The work done is the work involved in separating this material, both in the movement and in the energy required to create the new surfaces.

Cracks can only occur in a material in tension. They cannot occur in compression, where the material is being forced closer together.

So how does this arise?

Well if you pressurise or put a heavy weight on any real material it squashes or bulges sideways, at right angles to pressurising or weighting force.

This distorts the shape. Imagine squashing a balloon.

In the case of your weight on a tooth, the tooth bulges very slightly at the sides, causing a sideways tension. This causes the hairline crack.

As HOI said the energy comes from the fact that this bulging lowers the weight slightly.

does this help?

 

[HallsofIvy]

HallsofIvy! I understand something, but what if I keep the ball, on my head, I can't stand indefinetly! u mean I am doing no work , then why am i tired

If you were able to stand perfectly still, literally "without moving a muscle", you would not do any work and would not get tired- like a table supporting a weight. But. as I said before, you can't do that. Just standing upright requires constant motion of small muscles and holding a heavy weight on you head requires still more (think of how your neck muscles are moving to keep your head balanced). That motion involves work and makes you tired.