I want to go back to those snap swivels, and figure out if they'll be safe to use. I need somebody to check my math...
NOTE ADDED LATER: Umm, there are some mistakes in the calculations below. Do not trust them! When I get time, I'm going to re-do this, but for now all I have is time to add this warning.
MORE NOTES ADDED STILL LATER: "I thought I was wrong once, but it turns out I was mistaken." My calculations are correct. My friend with a Master's in physics, confirmed I did this right. However, I had made some initial mistakes and corrected them without fixing the changed numbers in a couple of spots. Fixed those numbers, and everything below is now correct and consistent.
OK, I've got a four-ounce rock, that's a quarter pound. My arm is about two feet from shoulder to hand, and my sling is three feet from pouch to grip. Whether doing an Apache style or a figure-8, I'm going to guess that my sling is doing about ten revolutions per second at release (if I could keep it swinging that fast for a whole second...). That guess is based on timing several videos, and seeing how much the sling moved between two frames. Twenty frames per second, as near as I can tell, and the sling moved a half-revolution from one frame to the next.
Centripetal force is calculated as F = v
2/r. Velocity can be estimated from the circumference of the circle my sling is moving in (C = 2*pi*r), divided by the time for one revolution. So v = 2*pi*r/t. Plug that back into the force equation and simplify, and we get: F = m*r*(2*pi/t)
2Plug in the numbers:
m | = | 0.25 pound |
r | = | 5 feet |
t | = | 0.1 second |
pi | = | 3.14159265358979323846 (approximately) |
And I get a centripetal force of about 4935 ft-lbs/sec
2.
The force of gravity is 32.2 ft/sec
2, so divide that into 4935 and I get the effective "weight" of my rock, just when I release it: 153 pounds (for a four-ounce rock!).
Something seems wrong here.
(It may seem wrong, but it is actually right.)
The force pulling on my finger is equivalent to hanging a 150-pound weight from that finger?
(Yes; and a six-ounce rock will pull with a force of 230 pounds. Damn English measurement system. What idiot decided to use "pound" as a name for a unit of mass AND a unit of force??)
Of course, that force is only for a small part of a second...
But it sounds like my 70-pound snap swivels might not take the strain.
(I think I had best buy some heavier snap swivels -- I am quite glad that I have only been slinging tennis balls and snowballs so far.)
Could somebody check my math? My neighbor's windows stand at risk if I bust one of the swivels...
(Yeah ... some 200-pound swivels ... that should be good enough.)