How to Estimate Tensile Force on a Pre-Tensioned Rope?

[Glype11]

I figure that there is a connection with how much a given forces displaces the rope in the perpendicularly direction. Obviously the more tension on the rope then there will be less displacement with a given force. I'm not sure how to progress from that point.

Any other ideas on how to estimate the amount the force for a rope in tension?

 

[A.T.]

I figure that there is a connection with how much a given forces displaces the rope in the perpendicularly direction. Obviously the more tension on the rope then there will be less displacement with a given force.

I guess you mean "the more pre-tension ...", because the final tension will be greater with more displacement.

I'm not sure how to progress from that point.

You have to assume some elasticity model of the rope like Hooke's Law and draw a force vector diagram.

 

[anorlunda]

When you say perpendicular direction, are you thinking of a case like plucking a guitar string?

 

[jbriggs444]

I guess you mean "the more pre-tension ...", because the final tension will be greater with more displacement.
You have to assume some elasticity model of the rope like Hooke's Law and draw a force vector diagram.

A simple model would be one where the pretension is large relative to the increase in tension due to a small lateral displacement -- assume that tension is unchanged. Then all you have to deal with is trigonometry.

 

[Glype11]

A simple model would be one where the pretension is large relative to the increase in tension due to a small lateral displacement -- assume that tension is unchanged. Then all you have to deal with is trigonometry.

Simple model indeed. I overlooked it.

 

[Lnewqban]

A force that is perpendicularly applied to a pre-tensioned rope can develop a huge mechanical advantage regarding the pulling tension of that rope.
Pulling vehicles out of mud pits using a rope attached to a tree is a known technique.

Please, see applicable examples and calculations:
https://courses.lumenlearning.com/s...-6-common-forces/#CNX_UPhysics_05_06_StuckCar

Here you can see how the Hooke’s law applies to ropes:
https://www.phys.ksu.edu/personal/m...ing/Belaying/ProblemSpringConstantOfARope.pdf