Would a hemp rope with a 30mm diameter break if a 100 kg object is attached to one end and dropped from a bridge (free-fall). The other end of the rope is attached to a pole on the bridge. The object would fall 4 meters, after that the rope would stretch completely. Bridge height is 6 meters, so after the 4 meter fall from the top of the bridge the object would still be in the air.
It all depends and there are many variables that we don't know exactly like the earlier comments mentioned, but it sounded interesting to try an estimate. And thanks in advance for any corrections to my math (its been 40 years since I took this class).
The velocity at 4 meters of free fall can be found from:
v² = u² + 2as
where s = displacement; u = initial velocity; v = final velocity; a = acceleration;
v² = 0 + 2x9.81m/s^2x4m
This link provides the stopping force, I made a couple guesses on rope stretch and got the following
0.01 m.. 396 KN
0.1 m .. 40 KN
This link manilla rope strength provides what I would think of as an estimate of magnitude for the rope strength where it lists the Minimum Breaking Strength of 30mm at 54 KN.
So depending on how much stretch you get, rope breakage is possible, and there is a good chance that some other part of your anchoring or attachments will break.