Re: [Phys-L] real-world physics

[brian whatcott <betwys1@sbcglobal.net>]

On 6/6/2012 2:39 PM, John Denker wrote:
> On 06/06/2012 11:28 AM, LaMontagne, Bob wrote:
> > Stuntmen also use big air filled bags with flaps that can pop open
> > when the pressure reaches a certain level.
> Yes.
>
> > The idea is to keep a
> > fairly constant force over the distance that the bags or boxes are
> > collapsing.
> Exactly so.
>
> This can be understood at the high-school level by drawing the force
> versus distance curve and considering the area under the curve.
>   -- There is a constraint on the distance, namely the available
>    stopping distance.
>   -- There is a constraint on the force, namely the maximum tolerable
>    force.
>
> Assignment:  What is the optimal shape of the force versus distance
> curve that satisfies these constraints?
>
> Also:  Where does the energy go?  That is, identify the specific
> place(s) in the system where energy dissipation must occur.
>
> =========
>
> The same force-versus-distance graph applies when selecting a rope
> to use for belaying a rock climber.  Similar considerations apply
> to bungee jumping.  Ideally, you want the graph to look like this:
>
>                    _____________________
>                   /
>                  /
>                 /
>         _______/                        _____________
>
>     (slack)    (NS)    (S)               (broken)
>
>
> where NS indicates the non-stretchy regime:  You want the effective
> spring constant dF/dx to be a large as possible in this regime, for
> a number of reasons.  For one thing, you don't want to do work against
> the rope, stretching the rope if you are trying to climb up the rope.
> Secondly, you want to maximize the area under the curve.
>
> Meanwhile S indicates the stretchy regime.  You want the effective
> spring constant dF/dx to be as small as possible in this regime.
> That's because you want to maximize the area under the curve,
> subject to the constraint on the maximum tolerable force.
>
> Last but not least, you want the ultimate breakage to occur as far out
> as possible ... but you do *not* want to express it in terms of breaking
> strength.  You could express it in terms of maximum elongation, but it
> would be even better to express it in energy units.
>
> Note that you could buy samples of several different kinds of rope
> including good climbing rope (from the sporting goods store) as well
> as junky rope (from the hardware store).  Measuring the force versus
> distance curve is entirely doable, even at the high-school level, if
> you take care of the obvious safety issues.
> _______________________________________________
Hmmm...I think a veil might well be drawn over these rope ponderings: 
they appear to be an uneasy mix of Alpine rules and OSHA rules:
Briefly: an alpinist wants a rope which will stretch (at most)  40% of 
its loaded length when dynamically stretched : this allows his belay to 
hold  and minimize the force applied when he falls.
 His static line is preferred to be stiff for hauling up and rappelling 
down. Under 5% stretch for a steady (165lb) load.

The OSHA rules prefer very robust stiff ropes or tapes where the fall is 
cushioned by progressively breaking stitched accordion tape.

Brian W