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        riddles >> medium >> stacking bricks curve
        
(Message started by: Noke Lieu on Feb 1^st, 2012, 8:45pm)

Title: stacking bricks curve
Post by Noke Lieu on Feb 1^st, 2012, 8:45pm

So, reading through this (http://mathdl.maa.org/images/upload_library/22/Robbins/Patterson1.pdf) I got to thinking about making a curve- essentially stacking infinitely thin dominos- that overhangs in a similar fashion.

Assuming I cut that curve out perfectly, will it stand up, or will it topple? Where's the structure's centre of gravity?

Title: Re: stacking bricks curve
Post by towr on Feb 1^st, 2012, 10:05pm

I think that stacking infinitely thin domino's in that way gives you a horizontal line of infinite length, which isn't what you want.

If you take the stack of normal dominoes and cut off the rough edges on the right and add them to the left, then it would obviously stand up (because you shift the center of gravity for the top to the left at each level).

Title: Re: stacking bricks curve
Post by rmsgrey on Feb 2^nd, 2012, 7:59am

on 02/01/12 at 22:05:36, towr wrote:

...unless you cause the left edge to become unstable.

Title: Re: stacking bricks curve
Post by towr on Feb 2^nd, 2012, 8:46am

How would it become unstable? You're removing mass from the side that would tip and add it to the side the prevents tipping, so it should become more stable if anything.

Title: Re: stacking bricks curve
Post by rmsgrey on Feb 3^rd, 2012, 9:00am

on 02/02/12 at 08:46:40, towr wrote:

How would it become unstable? You're removing mass from the side that would tip and add it to the side the prevents tipping, so it should become more stable if anything.

It depends which of the various structures you're looking at - many of them are symmetrical (which makes a certain amount of sense - to provide the maximum moment from the counter-balance, you want to have it as far to the left as possible)

And whole-structure topple isn't the only failure mode - there's also the problem when a brick acts as a lever, lifting at one end so the other end can fall.

Title: Re: stacking bricks curve
Post by towr on Feb 3^rd, 2012, 11:59am

I don't think I quite understand what sort of objection you're trying to make.

In the attached image how would B not necessarily be more stable than A?

Title: Re: stacking bricks curve
Post by Grimbal on Feb 6^th, 2012, 1:52am

Maybe rmsgrey was refering to the multi-layer structures (fig. 4 to 6).

Title: Re: stacking bricks curve
Post by SWF on Feb 7^th, 2012, 7:20pm

Using a coordinate system with y pointing downward and x toward the right. The equation of the left side of this shape should be:
x=w/2*ln(b*y)-w/2
and right side oft he shape is the curve:
x=w/2*ln(b*y)+w/2
The shape runs from y=0 to infinity, and w and b are postive constants that can be used to scale the dimensions of the shape.

No matter where you cut this shape with a plane y=Y, the centroid of the area between y=0 to Y lies at x=w/2*ln(b*y)-w/2, which results in no moment for it to tip over the edge of the portion from y=Y to infinity. This can be verified by doing the integral.