Is the maximum ability of a rope to withstand the tension force constant?

Suppose, I have a rope which has a length of 10 meters. I know that it can handle up to 100 N centrifugal force in circular velocity condition. Then I attached a 10 gram spherical object to the end of the rope and I started rotating the object at 10 revolutions per second without the rope breaking.

If I want to rotate this again with the same angular velocity and object but change the rope length to 100 m. Will the rope be strong enough?

• Have you calculated the centripetal force for the 10 m length of rope? If you then increase the length to 100 m, how does the force change? – Mick Dec 3 '18 at 12:23
• The strength or the rope is related to the total number of twists, and not the rate of twisting. – ja72 Dec 3 '18 at 23:28

1 Answer

A rope is not stronger than its weakest point. The longer a rope is, the higher the probability that it will have a weak point, that will break under a smaller force than a shorter rope would. Conversely, a shorter rope has a lower likeliness of having a weak point, and will on average withstand higher forces.

Example: Let's assume that the probability that a $$1$$ meter rope is having one or more points that will break at less than $$10$$ N is equal to $$p$$. This would mean that the same probability (of having at least one point which will break at less than $$10$$ N), is going to be $$(1-(1-p)^{10})$$ for a $$10$$ meter rope.