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Binary Weight Set
Minimize equipment investment; optimize range and precision of combinations | |
For home users especially, the goal of a weight-lifting set
should be to optimize the range and precision of the
combinations of weights while minimizing the total
investment. Binary numbers happen to satisfy this
requirement. With 7 weights, any combination between 1 and
127 can be achieved.
(In base 3, achieving everything
between 1 and 127 would take 8 weights, and in base 10, it
would take 19 weights.) Even the pseudo-counting system of
1's and 5's would require 11 weights to achieve everything
between 1 and 127 lbs.
Bowflex SelectTech adjustable dumbbells
http://www.amazon.c...-Pair/dp/B001ARYU58
Turn the dial to select your weight. [Freefall, Mar 26 2013]
[link]
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For balance, you need an extra single-pound weight. That way, for example, you can put 64lbs on each end of a barbell. Or 32lbs on each end, or 16lbs on each end, etc. |
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If you are just lifting a vertical stack, then only 7 weights are needed to make any combination from 1 to 127, as described in the main text. |
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But if you want to lift a balanced set weights, you need at least 1 extra, and as many as 7 extra (a duplicate full set), for all combinations of balancings. |
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Oh come on [Vernon], you don't need very many extra weights, you just need a longer bar so you can lift it from the center of mass, not the center of the bar. You could have little marks on the bar to tell you where to hold it for each weight combination. This is the half-bakery you know :) |
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Or just grow one arm bigger than the other. |
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Incidentally, didn't this get covered by the minimum-
types-of-coins-and -notes-required to-make- any-
payment post? |
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Technically, with 7 weights (technically, masses) any combination from 0 to 127 can be achieved. We nerds need to take these things slowly. |
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Wouldn't the empty bar count as 1? |
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The bar has helium balloons tied to it to give it zero weight (not zero mass, of course, oh no, siree). |
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If your weightlifting studio was in a centrifuge then you could have just a single mass but turn a dial to adjust the speed and therefore the weight. |
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(what is the proper name for the place one does weightlifting?) |
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I like the centrifuge idea. Bun in advance. |
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well yeah, but how many stories feature centrifuges used on Earth to avoid having to change the weights on a barbell ? |
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Excuse me, for MY proposed use. Thankyou! |
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If the centrifuge was fast enough, you wouldn't need any weights... |
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The centrifuge concept could be useful for creating an auto-spotting device. Now I don't claim to be an expert (or even an novice) on weight lifting, but I think I heard that when someone is stuggling with the weight, the spotter should apply some upward force to help lift the weight, but not just pick the weight up. |
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Since the centrifuge can adjust the wieght in real-time, this seems like a natural synergy. However, simply reducing the angular velocity when the user is in distress is probably a bad idea because they will feel a sideways force on the weight being lifted. So in addition to having adjustable angular velocity for the weight room, the weigh bench should be mounted on a track to move closer or farther from the hub. If the weight being lifted needs to be reduced, just release the brake (slowly) to allow the weight bench to be centripuged away from the hub. As the bench moves, the rate of rotation of the room should be slowed using other movable masses to minimize forces in unexpected directions. |
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