UPSB v3 Archive | [topic][2.5.1] Elastic Weights

Contributors: Eburt
Abstract: A First attempt at making a pen with varying weight distribution durring spinning.

Before even begining this, let me state that I am at my wit's end. I'm pretty sure this idea was a failure, so only bother reading this if you interested in the theory/physics or perhaps interested in continuing the idea. I'm basically posting for the sake of reaserch.

Basic Idea: Use weights inside the pen on elastic strings to create variable weight distribution. As yo uspin the pen faster, centripital force increases, pulling the weights to the ends, and increasing momentum. Then, if a direction change occurs, the centripital force is instantly nullified, causing the weights to spring back to the center of the pen, allowing for a quick change in direction, due to smaller force that needs to be overcome on the ends. (Force=Mass*Acceleration and the pen is spinning much slower at the center, so the force caused by the weights is far less)

Here's what I tried out. I made multiple "vortex" type mods with various weights and elastic materials, but could not get any of them to move the weights effieciently. The best results were using Lead Fishing Sinkers and a small fine Orthodontic Rubber Band (the kind on braces). These were optimal since the weights are dense and small enough to fit in the pen and the bands, when cut, are easily streched to about the right length. This still did not work however, and to further investigate I did some physics reaserch. Here are my calculations:

F-centripital = m*(v^2/r)
FC = .002kg*(v^2/.03m)
Note: This is for a very small increase in the band length, longer ones would be even more unrealistic. Also it uses spins that go on the axis of the pen, like TA, not conal ones like charge.

In order to find the velocity I found the circumfrence of the weight's rotation and multiplied by rotations/second:
Circumfrence = (Pi)2r
C = 3.14*2*.03m = .19m/rev
I found 3 revolutions/second to be about average for my freestyle spinning.
.19m*3 = .57m/sec

FC = .002kg*(.57^2/.03m) = .02166N
Therefore the force exerted by the elastic material must be about .02166N (preferably a bit lower) in order for it to strech, and then be able to return.

Hooke's Law can be used to determine the force and is as follows:
F-spring = kx ; where k = Spring Constant and x = Elongation Distance

FS = k*.01m (the rubber band was 2 cm, unstreached, 3 cm streached for this example, so a change of .01m)
Now plug in your FC for FS to find you necessary k
.02166N = k*.01m : Divide by .01
2.166 = k <- Ideal Spring Constant for these conditions

Now to find the Spring Constant of my rubber band I streched it with a weight:
FS = kx
.005kg*9.8(gravity) = k*.005m(distance this weight streched)
.049N = k*.005m : Divide by .005
9.8 = k <-Spring Constant of my Rubber Band

So basically I need a weight 5 times more dense, or a band 50 times weaker, that will still hold together... or some combination there of. And since I used Lead and the most elastic material I could find... I doubt that will happen. This is largely a failure, but feel free to discuss it/look over my math, in case I missed something.

Edit: Just noticed my math was off by a factor of ten. The difference is only 5 times instead of fifty. Perhaps this isn't as farr off as it seems... I'll keep looking into it.

----
Original Thread

UPSB v3

Pens & Mods / [topic][2.5.1] Elastic Weights