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12-04-2012, 05:06 PM #1
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How many Lego bricks can be stacked until the one at the bottom breaks?
It's a question that has exercised the greatest minds on the internet, but until now there has been no definitive answer.
How tall can tower of Lego be built before the bricks at the bottom buckle under the strain?
Now engineers at the Open University have finally come up with the solution to the conundrum and, here's a clue, its probably going to be bigger than you think.
The question was initially posed on social news site Reddit, where it ignited a burning debate that attracted nearly 1,200 comments.
But it is thanks to the BBC that the answer was found after Radio 4's More or Less programme asked academics to get into their labs and test it out on a hydraulic press.
Dr Ian Johnston, an applied mathematician and lecturer in engineering, told the broadcaster: 'It's an exciting thing to do because it's an entirely new question and new questions are always interesting.'
It's already known that Lego is extremely resilient, with the company this Spring enlisting 4,000 South Korean children to erecting a record-breaking tower in Seoul measuring a dizzying 105ft high.
But every building material has some theoretical limit beyond which it cannot be used and, before even higher Lego towers can be built, it would be sensible how much the plastic bricks can suffer.
To work out how tall a tower can be built before it crushes itself, researchers need to find out two things: the total mass of the building material used and its yield strength.
This latter factor is how much pressure a material can take before it breaks. To find it out Dr Johnston's team took a vulnerable-looking 2x2 Lego brick and placed it on a metal plate atop a hydraulic ram.
Across the brick they placed a second plate attached to a load cell to measure the force pushing upwards. Then they put on safety glasses and slowly backed away.
Ratcheting up the pressure on the hydraulic testing machine, they sailed past 3,500 Newtons of force, which is the equivalent of having 350kg (a third of a tonne) pushing down on the brick.
Eventually the load reached a phenomenal 4,240 Newtons - equivalent to 432kg - and the brick slowly began to deform after reaching what Dr Johnston explained was its 'material failure'.
'The material is just flowing out of the way now and it's not able to take any more. We're getting a plastic failure,' he said.
'It means the brick keeps on deforming, without the load increasing. Metals can be plastic, and this plastic is being plastic.'
Repeating the experiment showed again that the average 2x2 Lego brick, each made of ABS plastic, can carry a mass of 432kg. Once that figure was known, working out how high a Lego tower could be was easy.
With an average 2x2 Lego brick having a mass of 1.152g and the total mass a single brick can carry being 432kg, dividing the former by the latter gives the grand total of bricks a single Lego brick can support: 375,000.
Multiply that by the height of the brick - 9.6mm - and it turns out that, theoretically, a tower of Lego 3.5km (2.17 miles) could be built before the one at the bottom has any problems.