- Jan 17, 2019
Thanks, it seems to trade seconds for distance and abstracts away from the work concept towards momentum. I believe that the work equation is interchangeable with kinetic energy (m*a*d = 1/2 m*v*v....if we neglect energy at start).I think you're on the right track. The biggest difference between static and dynamic rope in a fall is the amount of time that it takes to resolve the momentum and end the collision. Dynamic ropes buy you more time to resolve the forces by extending their length.
A dynamic rope that extends the collision time in a fall will reduce forces on the body compared to a static rope. How much reduction is the big question and there are so many variables that lab testing with some high tech dummies/equipment would be needed before we could come to any data driven conclusions.
The equation used to express the collision is derived from newtonian physics (f=ma). It's the impulse-momentum equation if you're interested in researching more on it.
The useful bit (F*change in time OR seconds) expands to mass * m/(s*s) *s, I believe.
So, the more seconds (rope stretch) to decelerate from free fall to zero (hanging on rope) then the less the deceleration has to be at any single instant in time. Even if you only increase the rope stretch time from 0.1 seconds to 0.2 seconds, you've still cut the force of deceleration in half. I think this happens so quickly in real life that it steps around our common sense (we don't see collisions and their aftermath closely enough to notice this and incorporate into our daily understanding).
Sound about right?
If I get time, I'll work a toy problem both ways and see if the answers compare.