In reply to jimtitt:
> (In reply to cc_10)
>
> Or perhaps the integral of the force X time since force X time is momentum.
It is true that impulse is the intergral of force with respect to time, but it is not true that force x time = momentum.
Force x time = m(u-v) the change in momentum.
This change in momentum will be constant in a lab situation so the only factor to affect the force is time : Force = constant / t.
It is safe to moddel a rope as a spring so in this sittuation of clipping both ropes into the one bit of gear we have 2 springs in parallel.
Hokes law states Force = -kx [ k is the spring constant and x is the ammoun tof stretch in the rope]
For parrallel springs this becomes Force = -2kx.
By combining equations we get constant / t = -2kx
rearrange to get t: time = - constant / 2kx.
In conclusion this means that due to both ropes being cliped into the one piece of gear stoping time has halfed and as such force theoretically doubles.
This is a simplised theoretical situation all donations wellcome to fund a full investigation
[very bored physics graduate, with climbing background]