# Why is it easier to break a tightened or stretched string than a loose one?

I want to know, why is it that it is easier to cut through a string which is tightened then a loose one?

The question arose when I was watching - "What Happened Next?". In a part, they showed two clips, each one demonstrating the crash of rotor blades of a helicopter with a cable horizontally hanging in air.

Clip 1:

Cable is of something like brass (I can't remember exactly what material that was...) and it was stretched. Helicopter rises, the rotor blades crash with the cable and the cable vanishes out of sight. The giant vehicle is perfectly alright.

Clip 2:

Cable is of steel. It is loosely hanging. Helicopter rises, the rotor blades crash with the cable and cable only dances a bit and comes back to its position. The flying machine gets devastated.

Reason:

According to the show's narrator, the difference arises from the point that the materials were different, and, due to the difference in tension of the cables.

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The tension adds stress which brings the cable closer to the breaking point. With the additional stress of the rotor blades impacting it can reach the breaking point easier.

In the case of string cut with scissors the tension on the string helps prevent the string from riding in between the blades separating them.

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Thanks for arriving more close to the point and a common example. But how would tension on the string helps prevent the string from riding in between the blades separating them.? – Awal Garg Mar 23 '14 at 15:39
The tension keeps the string horizontal and perpendicular to the scissors blade motion. Without tension the string turns 90° and becomes parallel to the blade motion. – ja72 Mar 23 '14 at 15:41
That it, thanks for the quick answer... Marking as solved. – Awal Garg Mar 23 '14 at 15:43

Materials snap when their fracture stress is exceeded. When a material is under tension, it has a stress applied to it. The higher the tension, the higher the stress. So a very tight cable is already close to it's fracture limit and any additional stress may exceed the limit. When it's loose, the additional stress may not be enough to exceed the fracture limit and so it may not break.

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Ok, just one thing; in the aforementioned example, do you think the difference in the tension would be enough to cause the devastation of the helicopter? – Awal Garg Mar 23 '14 at 15:36
It is energy conservation of the impact. When the tight cable breaks it takes away momentum and energy, when it does not break it is worse than hitting a wall, the blades bounce back and the cable gives a return bounce from its elasticity (the pillars on which the cable hangs must rock to conserve momentum). – anna v Mar 23 '14 at 15:43

When a string it cut, it is not fracturing. There is a shear force applied to the surface of part of the string that interrupts the fibers by cutting. If you had a perfect pair of scissors where the blades had 0 gap even under load (e.g. trying to cut the string), then the tension on the string probably has little bearing.

One thing that could result in fracturing in this case would be if the cut was slow. At some point the remaining string would not be able to handle the load and snap - if you looked at the string cut end, you'd notice a clean cut up to a point and then a fracture. This is also important regarding the copter blade cutting the wire. Consider the time it takes for the blade to engage the wire if it is taut vs loose. If loose, the mass of the cable and its elasticity have more time to slow down the blade thereby spreading out the impulse. If the cable is taut, the helicopter blade has a more effective force transfer.

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+1 for the more time to slow down the blade thing... – Awal Garg Mar 24 '14 at 10:36

All these answers are correct and describe reasons for the easier breaking of tightened string, but there's one more which contributes and arises from purely geometric considerations : consider a string from A to B and a force F applied in the middle. If the string is loose, you get this:

If it is tight, that:

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This is actually well known from rock climbers setting up a belay, Wikipedia – Joce Apr 3 '14 at 8:17

In the case of a loosened cable string being struck, as opposed to being cut (as @Craig pointed out) is the effect of the momentum of the object striking the cable/string being lost as the loose object dissipates this energy. You see this in car races along the edges that use hay bails, or barrels of water, and behind those highway trucks that carry rows of plastic barrels filled with water to absorb the energy of an impact should you run into one.

All of this happens, or not, before any concern for snapping the struck material. So simply put, the blades did not have enough energy left after putting a loose item (string) in enough tension (as described above) to break. In the case of a taut cable/string, more/most energy of the striking object is put into cutting through it-as the cable/string would take more energy to make "tighter" than the blade has in it's momentum.

If the taut cable/string needed more energy to snap than the blade had in momentum at the point of contact, the blade-not the cable/string-would have to absorb all of the momentum/inertia of dropping to a speed of zero! What is worse (for the blade) is the fact that this energy needs to be absorbed at the very small point of contact/impact. Meaning that all that energy would be focused on the blade at a very small point (think lbs/sq.inch), resulting in maximum stress to the blade material at that point.

The larger the contact area, the less any one point has to absorb, and less damage will occur to the blade.

Sorry for the non-academic explanation.

pat :)

"I'm no physicist, but I know what matters!" ~Popeye

P.S. In the case of scissors, the same principle applies, actually, in that a large amount of force is being applied to a small area (where the blades meet). There the energy is the same, but applied slowly. In other words, where energy is mass x speed, you can raise either one to get the same result. This is why bolt cutters have more 'handle' toward you, and only a little bit where the cutter is.. :)

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A quote comes to mind: "It's not the fall that gets you..." :) – Pat Trainor Mar 24 '14 at 16:58
Brilliant explanation; a much needed one for such a question. Thank you very much... – Awal Garg Mar 25 '14 at 5:11