Science question - tensile strength and dental floss

[SpokaneCY]

Not sure "tensile" strength is the right term but physics question for the group...

Is a rope of 100' easier to break apart than a rope of say 1'?

The floss connection... I find when my fingers are further apart (a longer piece between 2 points), it breaks easier than if I have a small piece.

Oh - and accounting major so I can tell you the COST of the floss, but not the value of flossing.

 

[NorthCyd]

Not sure "tensile" strength is the right term but physics question for the group...

Is a rope of 100' easier to break apart than a rope of say 1'?

The floss connection... I find when my fingers are further apart (a longer piece between 2 points), it breaks easier than if I have a small piece.

Oh - and accounting major so I can tell you the COST of the floss, but not the value of flossing.

This is more a weakest link in the chain question. Assuming the material is flawless the length does not matter, but nothing is flawless and the rope will break in certain spots because of the flaws in the material. Because a longer piece of rope will have more flaws in it generally speaking longer pieces of rope will break easier.

 

[cyco2000]

This seems like a plane on a treadmill type question.

 

[JimDogRock]

I would agree that that manufacturing/materials imperfections are the cause for this case.

If the material is perfect and conditions are the same across the entire length and the same force is applied then I would expect the shorter piece of floss to break before the longer piece.
The reason for that hypothesis would be the force required to move the material in the first place. For floss, since it is so light, the difference is hard to think of. But if you replace the floss with braided, steel cable or a long length of chain it's easier to visualize that the force to get 1' of the material taut will be less than the force to get 100' taut.

 

[mj4cy]

tensile strength is tensile strength. It's simply the yield strength of the material multiplied by the area (and if you're in the engineering world you'd add in factors of safety). So rather the floss is 1" vs. 100" it'll break at the same strength. It's just easier to grip as it gets longer.

Now length has everything to do with compressive strength. As something gets taller/longer and you push from both ends, you'll eventually have lower capacities due to buckling failures.

 

[Acylum]

As something gets taller/longer and you push from both ends, you'll eventually have lower capacities due to buckling failures.

It’s like shooting fish in a barrel sometimes on here.

 

[CYEATHAWK]

It’s like shooting fish in a barrel sometimes on here.

Longer rods in an engine develop more torque than shorter rods.....but are more likely to bend at higher rpm.

 

[besserheimerphat]

This is more a weakest link in the chain question. Assuming the material is flawless the length does not matter, but nothing is flawless and the rope will break in certain spots because of the flaws in the material. Because a longer piece of rope will have more flaws in it generally speaking longer pieces of rope will break easier.

This is the right answer. Flaws are typically uniformly distributed throughout the length of material. However, the impact of any given flaw on the cross section will follow some probability distribution. The longer the piece of material, the more likely it is that a cross section with a flaw will have a major negative impact on strength.

 

[BACyclone]

Longer rods in an engine develop more torque than shorter rods.....but are more likely to bend at higher rpm.

In both cases this is because of the longer lever of the length of the rod.

The potential downside could remain that a larger rod would add to the mass of the circulating assembly, which would rob some net power.

 

[ArgentCy]

This is the right answer. Flaws are typically uniformly distributed throughout the length of material. However, the impact of any given flaw on the cross section will follow some probability distribution. The longer the piece of material, the more likely it is that a cross section with a flaw will have a major negative impact on strength.

Which is also why ropes are a bunch of strands that get wound together. Probably gets rid of that problem and gets you closer to theoretical strength.

 

[Sousaclone]

tensile strength is tensile strength. It's simply the yield strength of the material multiplied by the area (and if you're in the engineering world you'd add in factors of safety). So rather the floss is 1" vs. 100" it'll break at the same strength. It's just easier to grip as it gets longer.

Now length has everything to do with compressive strength. As something gets taller/longer and you push from both ends, you'll eventually have lower capacities due to buckling failures.

This. Tensile strength is tensile strength. The only time that overall length would matter would be in a vertical tension situation. Then you get to use the self weight of the floss against itself

The longer piece will elongate substantially more than the short piece. So it may also 'seem' easier.

As for you floss breaking thing, the longer piece is probably giving you a better lever arm or advantage to be able to break it.