Forces exerted on an anchor point from a falling object

[adiabatic1234]

Hi,

I'm looking at the forces exerted onto an anchor point when a n object is dropped but is secured to that anchor point witha steel wire rope lanyard.

i can find this but not sure if it is relevant or not to my investigation:
Fmax = mg + sqrt(2mg x E x A x fall factor +(mg)2 )

The mass is 69kg, E is 193GPa, A = 15.6x10-6, fall factor 2 (4m rope 8m total drop)

I know the KE and final velocity but I'm not sure of the stopping distance.

any guidance helps!

Thanks!

 

[jbriggs444]

You've given a formula. Can you motivate that formula?

At a guess, that is for a massless wire rope which becomes taut and then stretches under the force the falling object. As you've explained, the "fall factor" is the ratio of drop distance to rope length.

I think the formula you mean to write is:$$F_\text{max} = mg + \sqrt{2mg \times E \times A \times \frac{h}{l} + 2mg}$$
At a guess, E is Young's modulus for the rope and A is its cross-sectional area. I've used h for the fall distance and l for the rope length. m is obviously the object's mass and g is the acceleration of gravity.

In reality, I suspect that you will get also get some cushioning from the "whip" effect as a rope that was not straight rapidly becomes straight when it tightens. It will be hard to quantify that and will require at least the rope's linear density as a parameter.

 

[adiabatic1234]

Thanks, this what i meant

I've got the theoretical value, what I'm trying to ascertain is if this is the correct method to estimate the load on the anchor point.