The 0.5 factor is multiplied not divided. The tension on the rope is the resultant from the vertical component (weight) and the horizontal component (pulling the trees together). So at 30 deg the tension on the rope is twice the vertical load (half the weight on each end).
I wouldn't think the dynamic component is that great unless you are in earthquake country. Otherwise let me point out that the rope is rated at the breaking point (for new undamaged rope). Rope accessories are generally rated at the recommended work load, which is around 1/3 of the breaking load.
Last edited by hitchman; 05-31-2007 at 16:42.
I hate math.
"Every day above ground is a good day"
Math is hard.
I have that on a t-shirt...nobody gets the joke, though
"Physics is the only true science. All else is stamp collecting." - J. J. Thompson
There are two kinds of math : easy math, and hard math.
Easy math is the kind you understand, hard math is the kind you don't.
Also a joke that most don't get, or at least don't think is funny.
I've got a degree in the stuff, my wife's joke is that I double majored in math, and more math. However my courses ran to the crystal tower variety, and not the useful stuff like elementary engineering.
Not to belabor the point, but if you take half the weight (W/2) and if
then that's (W/2)*0.5. But these are just words...I now understand the physics of the situation by your descriptionThe 0.5 factor is multiplied not divided
So I gather that the way to think about this is that the known force is W/2, understood to be the vertical projection of the (unknown) total force T on the rope. The ratio of the vertical projection to the total component (hypotenus) is the sine of the angle theta between the hypotenus and adjacent side, so sine(theta) = (W/2)/T. With sine( pi/6 ) = 0.5 we solve for T in 0.5 = (W/2)/T, which is T = (W/2)/0.5 = W.The tension on the rope is the resultant from the vertical component (weight) and the horizontal component (pulling the trees together).
When you say that the 0.5 factor is multiplied and not divided, I guess you mean 0.5*T = (W/2).
so all is clear now.
Grizz the occasionally obtuse
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy
For those of you who do math so well, I have but one thing to say. I hate you. Just kidding, thanks for the science to back up the hanging, I appreciate it.
"If you play a Nicleback song backwards, you'll hear messages from the devil. Even worse, if you play it forward, you'll hear Nickleback." - Dave Grohl
Is that too much to ask? Girls with frikkin' lasers on their heads?
The hanger formly known as "hammock engineer".
"multiplied by 0.5" = "divided by 2"
Maybe the confusion was stating the same thing two different ways.