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### Integrals, Force, Work, Old Text Books

07/05/2012 1:22 AM

What is the formula for determining the pressure needed to push sand out of a sand mold given the weight of sand, coefficient of plastic wall provided the plate fits snugly around the roof of the mold. Does the length of the attached rod have anything to do with this? Perhaps the rod could be shorter than the mold.

In my old physics book it goes into temperature of liquids and gas. I guess the formula for force is F equals ma. To lift a trunk vertically requires work equal to wh. But here calculus would probably be needed since the mold is gradually being lifted and less force is needed.

So, work and force need to be related in a formula.

Time to do the dishes, read a book. I have some good pictures of my excursion to the beach a long time and could send them another day.

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Active Contributor

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#1

### Re: Integrals, Force, Work, Old Text Books

07/05/2012 2:48 PM

First the easy one:

Work = Force x distance or in the case of your trunk, weight x height (distance).

As for the sand mold, I am missing something. At the sizes I am used to, you whack the side of the mold and if that doesn't do the trick, you hit the sand itself so it starts crumbling (and gravity being your friend it all falls down).

What "attached rod" are you talking about? Also, plastic wall? More details might allow us to help.

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#2
In reply to #1

### Re: Integrals, Force, Work, Old Text Books

07/06/2012 2:43 AM

Here is a picture, I hope. I am having trouble with getting the right pictures on. I had better quite while I am ahead.

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#3

### Re: Integrals, Force, Work, Old Text Books

07/06/2012 7:33 AM

Well, what you are looking for resembles the inner pressure distribution in silos. I think it's worth to have a look at the Janssen equation to have an idea of the shear distribution along the inside of your mold.

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#7
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### Re: Integrals, Force, Work, Old Text Books

07/07/2012 1:40 AM

Thank you. Quite a bit of math.

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#4

### Re: Integrals, Force, Work, Old Text Books

07/06/2012 2:33 PM

Sand molds for making sand castles should have substantial draft (taper) so that as soon as release occurs, the mold is effectively entirely clear of the sand, and can be easily lifted off, with the only work required (after release) being that to lift the mold itself a distance just slightly greater than the height of the molded piece. No need to calculate this work, as it can easily be handled by a small child.

If there is little or no draft, then release is harder, and shaky hands can damage the molded sand.

Prior to release, the lifting force will be higher (equal to the weight of the sand and mold), because the sand clings to the mold. The "clinging" is caused by electrostatic attraction, viscosity effects of any liquids and other materials in the sand (salt water vs fresh water, algae, diatoms, etc) surface tension, static friction, and air pressure acting on the bottom of the molded sand piece. Because the mold top is typically closed, this differential pressure can be significant. In the case of a simple bucket shape with an 8" diameter at the open end, the surface area at the open end of the bucket is about 50 square inches. The pressure upward against the sand is 14.7 x 50 = 735 pounds. Thus, if the sand and water seals against the bucket walls, and the sand does not flow, the bucket can be lifted, and the sand will not fall out.

If you model your sand as a cylinder piston, and consider the bucket walls parallel, then no human will be able to pull the piston out. However, most wet sand is porous to air, so that pressure can equalize, given time, even if the interface of plastic and sand is not permitting much air flow. Sand is not a perfect piston, but for a variable amount of time, it can act as a pretty good one.

Often, just lifting the bucket clear of any supporting surface will cause air to slowly work its way into the bucket, along the interface between sand and bucket. Given a few seconds or minutes, enough air enters to allow the sand to drop under its own weight. If the drop is a small fraction of an inch, the molded piece will probably survive.

Sometimes, rotating the bucket will cause a break in the seal, and the bucket can be removed easily. This, of course, cannot work if the molded cross-section is other than round. So your push sticks can help effect a release. The hole for the pushrod also helps "break the vacuum".

The is no single formula that will enable you to determine the force required on a push stick. With some sand formulations, no force at all will be required (the extreme being very dry sand, for which no force is required -- it falls out as the mold is turned over. For other formulations, the release force will depend upon how long you wait with the bucket inverted (with the weight of the bucket supported, but the sand not supported, so it can fall out a fraction of an inch).

If you think of molded sand as being rigid, and you think of the mold as being rigid, then there is no static friction in an inverted, tapered mold, because the sand is pulling away from the mold, not pushing toward it. In practice, neither the sand nor mold is rigid, and you cannot calculate, in any reliable way, the rigidity of either. Watch or participate with kids building sand castles, and you will quickly see the variability involved, with some releases being quick and easy, some requiring twisting of the bucket, some ending up with part of the sand remaining in the bucket, etc.

So, work and force need to be related in a formula.

They are. Work is force times distance. But why do you want to know the work involved in releasing sand from a mold? The calories expended can be easily replaced by a sip of lemonade.

I guess the formula for force is F equals ma.

Yes, but this has nothing do do with your problem, unless you are trying to accelerate the sand to a particular velocity.

I gather there must be something you are trying to get at. Are your pushrods or plates breaking?

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#5
In reply to #4

### Re: Integrals, Force, Work, Old Text Books

07/06/2012 8:58 PM

Thank you. I am trying to submit part of a letter from the person who first made my sand molds. It describes some of the problems he had. I will try to get this out soon. I am sure it would tie in with what you are saying. Again, I should stop when I am ahead. More later.

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#6
In reply to #5

### Re: Integrals, Force, Work, Old Text Books

07/06/2012 9:24 PM

Znoign td Zrrn/op*ent I am not the greatest on working on the computer. Here is what I was talking about on the previous letter. I am going to watch the news.

Riley Lohr
W,J,/o Creative Design and Development Prototype and Engineering Models Parts Made To 0rder
On ttre square sid.ed. tower, it helps to really pat the rim and also to shake the mold up and down so that you can see and feel the sand rise i-n the mold.. Push the sand back down and shake it up-age*a, Doing this a- few times wil1 lossen iL-eeougb--for €he slnd to come out when you are ready. Til1e pistons reallll'help
on these molds.
Ttre eight sided cone, #I- is one of tl.e trardest, especially to get the thin rrbeak, section out ln one piece. Ttre bulk of the sand comes out easily. It is the rtbeakrr that breaks off and stays in the mold. Patting the mold in the area of the 'tb.ek[ helps. Experiment with packing pressures and techniques and also with patting the mold
The cone #3 will also give trouble with t1.e sand breaking off near the tip. ft takes good packing in the beginning near the tip t,o get it to come out weII.
fhe stairs #5 need. to be tapped. on the. side so that the sand actually breaks away from the mold before you try to push it out. They definitely need the piston.
The ring pi-eces, #4 aad the tops for #6 and # 7 come out nicely if you pack them wellr orld then push them out with the pistons.
You will have to practice with all of them, but f donrt think t+r-afr"Tou wt].l rifilE= Enlr r€al trouble hrith alrly*of them, except the beak on #1.
The d.igging tools for the doors and windows require a light scrapping action toward the centef . Ttre ed.ges will crumble and be rough no matter what you do. Cutting the slits at the top of the turrets is done with many light strokes, using downward pressure.
If you have an

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