I use ridgelines when hammocking and have various ridgeline cordage with varying breaking strengths. I'm trying to find a basic general formula for calculating how well a particular cord might avoid breaking given a falling object's mass and starting height. For the purpose of this exercise I think we can ignore the lashing knots that suspend the ridgeline and also assume there are no kinks, damage and inline knots on the ridgeline either.
An example is: A cordage with breaking strength of $250\,\text{lbs}$ is rated at $1.13\,\text{kN}$ (unsure where this $1\,\text{lbf} = 4.45\,\text N$ comes from).
Say a $10\,\text{kg}$ object (maybe a branch) falls $10\,\text m$ onto the ridgeline, I calculate the energy of the object to be $$10\,\text{kg}\cdot9.8\,\text m/\text s^2 \cdot 10\,\text m = 980\,\text N$$
Without further consideration, since $980\,\text N < 1130\,\text N$, the ridgeline should not break. However I read that you also need to divide by distance traveled during impact. I suppose this relates to how much the cordage stretches. Since this cord doesn't stretch very much, let's assume given the ridgeline length that the total distance moved during impact is $20\,\text{cm}$ or $0.02\,\text m$. Then it follows that $980\,\text N/0.02\,\text m = 49000$? This is where I'm stuck because $49000$ (not sure what units this is) seems quite large.
Best Answer
If I understand correctly, this question is asking for a general formula to determine whether a cord will break because of a falling object. You've given a breaking force, $1.13\,\text{kN}$ or $1130\,\text N$, and you've given the object's mass, $10\,\text{kg}$, and falling height, $10\,\text m$. The issue is that we also need to know the stopping distance. The impact force on concrete will be much greater than the impact force on a trampoline. This is because work is equal to force times the distance that force is exerted over, and the work done on the object by gravity is equal to $$mgh=Wh$$ where $m$ is the object's mass, $g$ is the acceleration of gravity, and $h$ is the height it falls from. $W$ is the object's weight. In order to stop the branch, the rope will need to do the same amount of work on the object.
The work done on the object by gravity is equal to $$10\,\text{kg} \cdot 9.8 \,\text m/\text s^2 \cdot 10\,\text m = 980\,\text J$$
In order to do the same amount of work on the object without breaking, the stopping distance must at least by $980\,\text J / 1130\,\text N = 0.87\,\text m$.
Let me know if anything needs clarifying.