…
a single peice of rope that is,
fold the same rope in half.
Doubling the rope spreads the load across both strands. The strength of each strand isn’t increased, but the load is cut in half.
a. If you tie one end to your anchor and then load the free end until failure you’ll get some ultimate load, call it “X”.
b. If you loop the rope over a pulley and tie your weight to both free ends you will still only get the same ultimate load X.
c. If you fold the rope in half and anchor it below the fold (that is, so you are anchoring both halves of the rope independently) and then load both free ends you will get an ultimate load of 2X.
The difference between (b) and © is in whether the two “legs” of your doubled rope are acting independently. In (b) the entire load is still being carried in tension through one piece of rope (you can always find a single cross-section of the rope that is holding the whole thing). In © the two legs are carrying their loads seperately from one another.
I’m assuming those college physics items like massless rope and no friction on the pulley in (b). Introducing that stuff will change the answer.
Bending the rope in any direction will reduce its strength. When you tie a knot in a rope - any knot - the ultimate strength is reduced. The figure-8 family of knots has the best strength retention, but at best these still only allow 80-85 % of the rope strength to be maintained. These factors aside, doubling a rope will double its strength, provided some method of equalization is provided so that each half carries the same amount of load. If you take two parallel runs of rope and tie them to an anchor on one end, and a load on the other, if they are not equalized then one rope will carry all of the load until it fails.
Sheaves (pulleys, etc.) do reduce rope strength slightly, but generally this strength reduction is minimal in comparison to that presented by a knot, since the radius is much more gentle. Consequently, one of the highest strength anchors you can establish is the “no knot” anchor, which entails wrapping the rope around an object (tree, bollard, drum, etc.) several times so that the rope friction against the object holds the rope in place (after wrapping, the tail end is usually tied or clipped off to the standing part to prevent unravelling, but this end is loose and not carrying any part of the load).
I disagree. I don’t think it matters how you attach the rope to the ceiling, all that matters is the number of strands coming down. If you cut the ropes at some point between the attachments and the weight you get Y number of strands. The tension in each strand of the rope will be Weight/Y no matter how they are attached.
It matters how many INDEPENDENT strands are coming down; I think we agree that whether you tie one end to the ceiling and hang a weight on the free end versus looping the rope over a pulley and hanging weights on both free ends, the ultimate capacity of the rope will be the same, since the rope will be in continuous tension.
However if you double the rope and attach it such that each “leg” is gripped independently (that is, tension cannot be transmitted from one leg to the other) then you’ve just got two strands of rope and you’ll have double the load capacity.
Listen to treis. You can hang X off of both sides of b., and the tension in the rope will only be as much as in a. (excepting the losses mentioned above), so you’re wrong.
Equalized meaning equal length? One would have to be quite a bit longer than the other. If it were only a small difference, the shorter rope would soon stretch to equal the longer, and then they would stretch together.
This confuses me. Let’s say I have a rope that fails when loaded with 100 pounds. If I anchor it to the ceiling, I can only load with with that 100 pouinds. But if I wind it through a pulley that is anchored to the ceiling, I can now hang 100 pounds on each end? Wouldn’t that mean that my 100-pound test rope was supporting 200 pounds?
Then again, each half of the rope would be distributing that 200 pounds evenly, so each half – taken separately – would only be holding 100 pounds. That I get. But what about that little section that was actually resting on the pulley itself? Isn’t that section carrying the full 200 pounds?
By hanging the rope from the ceiling, with 100 pounds off the bottom end, you induce a force on the ceiling of 100 pounds–and the ceiling pulls on the rope with 100 pounds. The rope has 100 pounds force pulling on both ends. Same for when it is wrapped around a pulley, with a 100 pounds hanging off both sides. That’s essentially the principle behind a pulley.
The pulley is holding up 200 pounds, and must be firmly fastened to the ceiling, of course.
Picture the weight in your mind and then cut off the rope a bit above that. Something like this:
Ft^ Ft^
| |
_|______|_
| |
|..weight |
|__________|
Basically you have two tension forces pulling that weight up. Since that system shown isn’t moving or rotating the two tension forces must be equal at Weight/2. If you had Y strands then each tension force would be Weight/Y. That picture is accurate no matter how you attach the ropes to the ceiling.
Yes it is true that whatever section of the rope is touching the pully is holding up 200 pounds. However that is compressing the rope axially not putting it in tension. In other words it is squeezing the rope compared to the weight pulling it apart from the ends. The rope can bear a much higher compression force before failing than a tension force.
Thanks, treis, that makes sense to me.
And nice weaving of the quotes into a coherent narrative.
The real world isn’t that neat. Ropes may be calculated to fail at 100lb but it really means they fail at 90 - 110lb +or- 3 standard deviation. This means that say you have 1000 ropes suspending a 900,000 lb object, 3 of those ropes will snap, which will increase the total load on the other 997 ropes which may cause additional ropes to snap which may cause the entire system to collapse.
Somehow, that doesn’t sound like the real world to me
the statement does sound strange to me; it is an interesting theory to apply to other mediums though, the human psyche.
What I was trying to say was that the strength of two ropes is actually double the strength of the weakest rope, not the average rope. The more ropes you have, the weaker your weakest rope is so you can’t guarentee that all your ropes will hold in a simple linear fashion.
Great screaming duh. You are of course correct as a simple diagram would have shown me. Misremembered the same question from back in college (where oddly enough I was quite good at physics, statics and dynamics).
Time to send that diploma back 