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I am attempting a project in which a robot needs to carry 5 layers of Jenga pieces around a course, while following a line and without dropping the stacked blocks. Figuring out the static frictional force needed to move the Jenga blocks off of one another requires certain values.

I already have the coefficient of wood on wood, which is 0.35, but I need either the average mass of a Jenga block, or the typical density of the wood used to make Jenga blocks.

Thank you in advance!

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    Can't you just weigh your Jenga blocks? (If you don't have any Jenga blocks, you'll need to get some to test your robot anyway.) – user2357112 supports Monica Feb 3 '17 at 17:46
  • Quick tip: that formula for friction you learned in school? It's a lie. For what you're doing here, it's probably close enough, but don't be surprised if the numbers you get don't match your robot's actual performance. – Mark Feb 3 '17 at 21:39
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Well, it looks like that per Hasbro, an official Jenga set is made of Alder, which apparently has a density of 0.38 g/cc, which when combined with the dimensions of a standard Jenga block from this answer of 1.5cm x 2.5cm x 7.5cm, gives us an average of 10.6875g per block for a 28.125cm³ block.

The margin of error on both the density (one site I found had a range from 0.4–0.7 ×10³ kg/m³, or 0.4–0.7g/cm³) and the dimensions of the block due to manufacturing tolerances are enough to be considered significant, so I'd add a nice fudge factor to that before running further calculations.

  • 0.4-0.7 kg/m3 is 0.0004-0.0007 grams/cc. That fudge factor for a 28.125cm³ block is going to be a miniscule one (~0.0011 to ~0.0197 g/cm³). For a tower of 5 layers (15 blocks) that's an estimated maximum 0.2955g difference in weight based on density alone. – doppelgreener Feb 3 '17 at 17:19
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    Sorry, fixed my unit notation there: it's 0.4-0.7 10^3 kg/m3. That ends up as 0.4-0.7 g/cc, allowing for up to 1.8x the original as a possible value. – David C Ellis Feb 3 '17 at 17:19
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    I've updated the formatting of your notation slightly. Thanks, that makes more sense out of it. – doppelgreener Feb 3 '17 at 17:20
  • yeah, if we can get a density of 0.4-0.7 kg/m3 out of something we can use to build Jenga towers, I think the Space Elevator guys want to have a talk about that... – David C Ellis Feb 3 '17 at 17:23
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    Well that's the density margin of error (from an average density of 0.38g/cm³ or 380kg/m³) rather than the density itself. :) – doppelgreener Feb 3 '17 at 17:32

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