Why Do Cables Use dx for Distributed Loads and ds for Weight?

[Cyrus]

First, on an unrelated note, I would like to share an anwser I think I found to be correct on a question I posted here a while back. I asked about how a smooth collar that was Not Pinned could prevent a moment. The problem I was faceing was the fact that in order to have "play" so that the collar is loose, there had to be some physical gap to allow for sliding. But if there is a gap, then when a moment is applied to the collar, it will move due to this gap a minute amount, which will result in some horrible complications. I think my resasoning in my gripe was correct, and if you actually did know the amount of gap/play or slop (whatever you want to call it) between the materials, you could calculate a moment and force that is prevented more accurately. (The amount of error in reality would depend on the geometry of the collar and the amount of play between it and the journal.) But the little devil here is the fact that there can be literally NO space between the collar and the journal, and yet it can still have the ability to slide, provided that the frictional force is zero! What a tricky little devilish detail! I guess that's why they call it an IDEAL CASE!

Anywho, My question is on distributed loads on cables. Why is a distributed load on a cable with respect to dx, but a distributed weight of a cable with resepct to arch length ds? (Oh yeah, and I've got a lot more questions on this subject to come!)

 

[Cyrus]

Im 100% positive that someone here has dealt with statics of distributive loads on roaps.

 

[ravenprp]

Thank you for sharing your thoughts and insights on the topic of statics of ropes and cables. It's always great to see someone actively engaging and finding answers to their questions.

Regarding your first point about the smooth collar preventing a moment, your reasoning seems to be correct. The gap or play between the collar and the journal can definitely affect the accuracy of the calculations. This is why it's important to consider all factors, including the geometry and frictional forces, when analyzing a system.

As for your question about distributed loads and weights on cables, it's important to note that these two terms refer to different types of loads. A distributed load is a load that is spread out over a certain length or area, while a distributed weight is the weight of a cable that is distributed along its length. The reason for using different variables (dx for distributed load and ds for distributed weight) is to account for this difference in the type of load.

I hope this helps clarify your question and I look forward to hearing more of your thoughts and questions on this subject. Keep up the curiosity and enthusiasm!