# B Stretching (tearing) of string

1. Jul 8, 2017

### DesertFox

Hello everbody!

I found the following representation: F = 2ρdl(d²l/dt²)

F - the maximum stretching force (force at which the string tears);
ρ - density;
dl - random differential section of the string;
t - time.

This is some kind of parallel between WAVE and STRING?

I cannot find information in the world biggest search machine, so every single explaining comment will be highly appreciated...

Thank you!!

2. Jul 9, 2017

### davenn

if this formula is from the same author as in your other post, then that is likely the problem

typing "determining the force required to break a rope" into google, here's one site on the subject
http://www.digipac.ca/chemical/mtom/contents/chapter1/ltw_001.htm

there are many others

3. Jul 9, 2017

### DesertFox

Yes, it is the same author. But in this case: I think his formula is correct.

4. Jul 10, 2017

### Ibix

Who is this author? Please note that PF rules require you to provide a proper reference when asked - and you already ignored that once on your Newton's third law thread.

The formula you quoted isn't valid, let alone correct. Even assuming that the force on the left should be a stress, which would at least make the units correct, you have a differential (dl) on the right and not on the left.

You are talking about tensile strength. I don't think there is a formula for the maximum stress a material can stand. Certainly not a simple one. It's dependent on the way you prepare the material as much as anything else, which is a very complex subject.

5. Jul 10, 2017

### Vanadium 50

Staff Emeritus
It's not correct. It's not even wrong,

6. Jul 10, 2017

### DesertFox

I think the formula is valid. I will give my argumentation....

According to me, this is just another form of F=ma. This is an equation which determines how a string stretches dynamically assuming it has zero stiffness (i.e. its spring constant = 0). I suspect that in the equation, density, is in units of Kg per meter of length of the string, not Kg per cubic meter which is how it's normally defined. With this understanding the units work out!

Now, consider a differential length of string, dL.

By Newton's Second Law: Force = mass x acceleration = density x dL x acceleration.

So, stress in the string = density x dL x acceleration.

But force does not break a string, stress does. The string will break when the maximum stress reaches the breaking stress. I think the factor of 2 has something to do with the fact that the maximum stress (or load) is twice the average stress (or load).

We can also say: d2l/dt2 = (F/2) / (ρdl) = F/(2m) (m - mass)

This is my explanation of the quoted equation.... I will appreciate every comment. Thank you!!

7. Jul 10, 2017

### davenn

did you not read V50's response ?

I wouldn't argue with some one so well educated ... if he say's it's incorrect, you would do well to believe that

as has been said to you a number of times now, across several of your threads, you need to start reading and learning some real physics
and forget about books written by philosophers, otherwise you are just going to be led further and further astray

did you go to the link I gave you and study the info there ?

8. Jul 10, 2017

### Vanadium 50

Staff Emeritus
You've gone from reading a poor text to defending a poor text; you've gone from confusion to crackpottery.

You have a choice - accept that you've been led astray by a poor book and start afresh, or to continue to hold an incorrect view and never learn. Up to you.

9. Jul 11, 2017

### Staff: Mentor

We will not discuss this book further at PF

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