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# Lever arm length calculation

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I'm working on a project creating "mobiles" or hanging art. I cannot find any resources that explain how to calculate the length of the lever arm or the distance from the moment (I think that is what the point where the leverarm is hinged or attached but I only got a BA and not a BS so my hard science background is not quite as good as it might be) for differing weight loads. Nor can I find any resources that speak the construction of mobiles as an form of art but addressing the physics or mathematical factors. Anyone with an idea or two? Thanks

Gatortrapper

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The principle of leverage can be derived using Newton's laws of motion, and modern statics. It is important to note that the amount of work done is given by force times distance. To use a lever to lift a certain unit of weight with a force of half a unit, the distance from the fulcrum to the spot where force is applied must be exactly twice that of the distance between the weight and the fulcrum.

...

Load arm X load force = effort arm X effort force. If, for example, a 1 gram feather were balanced by a one kilogram rock, the feather would be 1000 times further from the fulcrum than the rock; if a 1 kilogram rock were balanced by another 1 kilogram rock, the fulcrum would be in the middle.

Lever - Wikipedia, the free encyclopedia

as for mobiles, i have found trial-&-error practical. :smilingsun: you might check out pendulums for some equations/ideas/concepts you can use. :smilingsun: >> Pendulum - Wikipedia, the free encyclopedia

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It can be expressed mathematically like so:

$F_e=F_1\left(\frac{d_1}{d_e}\right)$

where $F_e$ is the smaller of the two forces (or weights), $F_1$ is the larger weight, $d_1$ is the smaller distance, and $d_e$ is the larger distance. Wonderfully depicted here:

-

~modest

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Excellent tools! Great help. Thanks. I had rooted around trying to find something and I knew it was there but like a misspelled word in the dictionary, they can be difficult to find.

Gatortrapper

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