oh for pete's sake

[John Paul Sanborn]

Mathmaticaly challenged.

 

[ramanujan]

thanks for making those corrections Joe.. it was too late and I was in too much of a hurry

Stumper I didn't use the same values that others did in their calculations if that explains why my values differ from others.

I agree with you that the potential energy of the saw before it is dropped must equal the energy expended when it has stopped but I think that the original question was what regarding what a breakaway lanyard will take before it breaks. ie, not total energy but peak force.

also someone mentioned that the energy disappates in the form of heat. this is incorrect, only a very small fraction of the energy will be transformed into heat, most will be used to move the climber and the tree and maybe tear the lanyard etc.

 

[Stumper]

ramanujan, What values did you use? You had a bunch of fomulae and figures but where did you start? The discussion had been centering around a 7 pound saw dropped 4 feet. The figures you show would match up to a fall of over 12 feet. I wonder if there is an engineer lurking out there laughing at all of us (myself included) for going on and on about things we obviously don't fully understand.
Despite our dismal math performance I think that most of us know what we can do safely in the trees.:angel:

 

[Joe]

Originally posted by Stumper
I wonder if there is an engineer lurking out there laughing at all of us (myself included) for going on and on about things we obviously don't fully understand. Despite our dismal math performance I think that most of us know what we can do safely in the trees.:angel:

So what if there are engineers, mathematicians, and physicists laughing at us. We still need to learn the stuff, right? Are there any engineers, mathematicians, or physicists speaking up? No. So what is going to be done to fill in the blanks? I wouldn't waite for an engineer, a mathemtician, or a physicist to show up and explain things. Remember, these guys have spent a lot of time, money, and effort
to learn what they know. Don't expect any of them to give it away for free.
Forget about them and focus on what needs to be done.

Joe

 

[Joe]

http://www.motionmountain.org

I think the guy who put this link together is an amateur and enthusiast.

Joe

 

[hillbilly]

Ramanujan, thanks for your post, it makes sence in many ways!
However:
"In this case the acceleration is in fact deacceleration as the saw is slowing down, and we'll assume it's at a constant rate"

Maybe the assumation that the deacceleration (and in turn
the force) is linear is a too big assumtion. Would expect
the force to be smaller in the beginning of the stretch and larger
at the end of the stretch.

"also someone mentioned that the energy disappates in the form of heat. this is incorrect"

What I meant was that energy is never destroyed, if the
potential energy is reduced and the kinetic energy is to
be 0 at the end of the fall, that "lost" energy must go somewhere.
If it be the tree, the climber, the saddle and the
lanyard that gets heatend, it still must happen.
This energy transfer might very well be negliable when
calculating the force on the lanyard, but it still must
take place.

I studied mathematics 1,5 years at the university, sadly
it is very theoretical and if not combined with other fields,
pretty useless. However if anyone were to have any mathematical
questions, I will be more than happy to help you. Just send
me a PM.

 

[CJ-7]

Ok, I am really asking for it here, I am an engineer, but 34 years since my last physics class, and I don't use dynamics (that is what you are talking about here) in my work. I am a civil engineer not a mechanical. Here's my interpretation out of a book provided by a colleague, who refuses to get involved in this discussion (many of these formulas have already been given in prior posts):

F=force (pounds, force (lbf) as opposed to pounds, mass)
m=mass (pounds, mass (lbm))=7
a=acceleration (feet per second per second)
g=gravitational constant (feet per second per second)=32.2
v=velocity (feet per second (fps))
Ek=kenetic energy (feet-pounds force(ft-lbf)
s=distance (feet)=4

Saw weight = 7 pounds
Drop = 4 feet
assume no friction and initial velocity = zero
assume lanyard evenly stops saw over the distance of 6"

v=sqrt(2as) =sqrt(2x32.2x4) = 16 fps (here g=a)

after falling 4 feet the 7 pound saw has gained kenetic energy

Ek=((m/g)(v squared))/2 =((7/32.2)(16x16))/2 = 27.82 ft-lbf

now how much force, evenly distributed over time, is required to decelerate the saw in 6" (0.5 feet)

first calculate the acceleration (actually deceleration) needed to stop the saw from 16 fps over a distance of 6".

a=(v squared)/(2s) = (16x16)/(2x0.5) = 256 ft per second per second

F=(m/g)a = (7/32.2)x256 = 55.6 lbf not that far from the force noted in other posts.

I have made some simplifications here to get some of the basics across.

 

[TheTreeSpyder]

i've been searching for some kind of table that says something falling from 1' has a 'fall factor' of........, from 2' of....... to 10. Seems that we could use such a table for a lot of things and understandings. Seeing that 2 things fall to earth at the same speed from the same height; and that speed x mass = force would be pretty simple for many examinations.

i have found these 4 calculators that may help, but are even a bit beyond my confidence as they present more functions, many leaning towards the energy absorbtion properties of the lines etc.

Fall Calculator

The Splat Calculator

Terminal Velocity Calculator & Graph

Climbing Fall Calculator

Again and again, minimizing force by minimizing acceleration seems to bear out, bringing me back to tight lines and meaty hinges, minimizing fall etc.

 

[Joe]

Here's my personal favorite.

http://www.glenbrook.k12.il.us/gbssci/phys/class/BBoard.html

Joe

 

[Jock]

Just dont fall