What is the Relationship Between Strain and Change in Length in Hooke's Law?

[chriscarson]

Homework Statement

Strain and change in length problem

Relevant Equations

Strain and change in length what is the difference ?

Strain and change in length what is the difference ?

 

[berkeman]

What are the units of each?

 

[chriscarson]

What are the units of each?

strain no units and change of length are in m.

 

[Orodruin]

strain no units and change of length are in m.

So the difference is ...

 

[berkeman]

strain no units

Well, technically the units are "1", but what units are in the numerator and denominator of the fraction that equals that "1"?

 

[chriscarson]

So the difference is ...

No idea

 

[chriscarson]

Well, technically the units are "1", but what units are in the numerator and denominator of the fraction that equals that "1"?

Honestly I need answers not question

 

[berkeman]

Honestly I need answers not question

We don't give answers to schoolwork at the PF. When you look up mechanical strain in your textbook or on Wikipedia (see stress-strain), what units are listed? You can also use Google Images to search for stress strain curves, and a few of them will show you what I'm asking about...

 

[chriscarson]

We don't give answers to schoolwork at the PF. When you look up mechanical strain in your textbook or on Wikipedia (see stress-strain), what units are listed? You can also use Google Images to search for stress strain curves, and a few of them will show you what I'm asking about...

I see, I just want the answer so I can learn nothing special but I understand you have rule.

I try to answer my question by looking for the units of these two .

 

[Chestermiller]

Homework Statement:: Strain and change in length problem
Homework Equations:: Strain and change in length what is the difference ?

Strain and change in length what is the difference ?

What is your understanding of the difference?

 

[berkeman]

I see, I just want the answer so I can learn nothing special but I understand you have rule.

I try to answer my question by looking for the units of these two .

Thank you.

And BTW, the main reason I'm asking for you to look more into this is not just because of the PF rules. Understanding the units of stress and strain is an important step in your education. The fact that the strain is "unitless" is not trivial -- there is a reason for it. It's s good step in your continued learning to figure this out, IMO.

 

[chriscarson]

What is your understanding of the difference?

Because in the formula strain = change in length over length , I always thought that strain is the change in length .

 

[chriscarson]

Thank you.

And BTW, the main reason I'm asking for you to look more into this is not just because of the PF rules. Understanding the units of stress and strain is an important step in your education. The fact that the strain is "unitless" is not trivial -- there is a reason for it. It's s good step in your continued learning to figure this out, IMO.

Well it s true that it s better to see why things are there not just write because are just that way .

 

[haruspex]

Because in the formula strain = change in length over length , I always thought that strain is the change in length .

Right, strain is the fractional change in length.
If a 3m bar is subjected to a longitudinal strain of 1/1000 it extends by 3mm. If we think of the bar as three 1m bars end-to-end, each is subject to the same strain, so each extends 1mm.

 

[Orodruin]

Right, strain is the fractional change in length.
If a 3m bar is subjected to a longitudinal strain of 1/1000 it extends by 3mm. If we think of the bar as three 1m bars end-to-end, each is subject to the same strain, so each extends 1mm.

Just to kick the dead horse a bit:
Change of length is what we call an "extensive" property, it means that if you add up change of length from each part of the bar, you get the change of length of the entire bar. This is true regardless of how you split the bar up.
Strain is what we call an "intensive" property. It is a property that does not add between different parts of the bar and (assuming equal stress and material properties) is the same everywhere on the bar regardless of the size of the part you select.

Other examples of extensive properties: mass, momentum, force
Other examples of intensive properties: density, pressure, temperature

 

[chriscarson]

Right, strain is the fractional change in length.
If a 3m bar is subjected to a longitudinal strain of 1/1000 it extends by 3mm. If we think of the bar as three 1m bars end-to-end, each is subject to the same strain, so each extends 1mm.

good explanation , thanks

 

[chriscarson]

Just to kick the dead horse a bit:
Change of length is what we call an "extensive" property, it means that if you add up change of length from each part of the bar, you get the change of length of the entire bar. This is true regardless of how you split the bar up.
Strain is what we call an "intensive" property. It is a property that does not add between different parts of the bar and (assuming equal stress and material properties) is the same everywhere on the bar regardless of the size of the part you select.

Other examples of extensive properties: mass, momentum, force
Other examples of intensive properties: density, pressure, temperature

thanks

 

[Chestermiller]

Because in the formula strain = change in length over length , I always thought that strain is the change in length .

So if I have 2 bars of lengths 1 cm and 10 cm, and I stretch them each 1 cm, the strain in the smaller bar (which is now 100% longer than its original length) is the same as the strain in the larger bar (which is now only 10 % longer than its original length)?

 

[chriscarson]

So if I have 2 bars of lengths 1 cm and 10 cm, and I stretch them each 1 cm, the strain in the smaller bar (which is now 100% longer than its original length) is the same as the strain in the larger bar (which is now only 10 % longer than its original length)?

Is it like that ...

I give 2 dollars to a man that have a 100 dollars in his pocket and
I give also a 2 dollars to another man that have 200 dollars in his pocket ,

they both benefit the same amount from me ?

 

[jbriggs444]

Is it like that ...

I give 2 dollars to a man that have a 100 dollars in his pocket and
I give also a 2 dollars to another man that have 200 dollars in his pocket ,

they both benefit the same amount from me ?

The value of money is way too complicated to be usefully applied as a physics analogy.

I particularly like the value of a bag of grain as discussed here.

 

[Chestermiller]

Is it like that ...

I give 2 dollars to a man that have a 100 dollars in his pocket and
I give also a 2 dollars to another man that have 200 dollars in his pocket ,

they both benefit the same amount from me ?

They don't benefit the same amount. One guy makes 2% on his money and the other guy makes only 1% on his money.

 

[chriscarson]

They don't benefit the same amount. One guy makes 2% on his money and the other guy makes only 1% on his money.

I agree compared to their sum in their pocket but as for me that the 2 dollars have the role of the strain remain the same value .I think ..

 

[jbriggs444]

I agree compared to their sum in their pocket but as for me that the 2 dollars have the role of the strain remain the same value .I think ..

2 dollars has units of dollars. It'll buy a couple hash browns at McDonalds. Strain is unitless. Like simple interest.

 

[chriscarson]

The value of money is way too complicated to be usefully applied as a physics analogy.

I particularly like the value of a bag of grain as discussed here.
[/QU

2 dollars has units of dollars. It'll buy a couple hash browns at McDonalds. Strain is unitless. Like simple interest.

Mmm. I see

 

[Chestermiller]

I agree compared to their sum in their pocket but as for me that the 2 dollars have the role of the strain remain the same value .I think ..

Well it’s not the same. The percentage changes are the same as strain.

 

[Orodruin]

A buy off €2 will affect a €10 economy more than it would a €1000 economy.

A length change of 2 cm will put more strain on a 10 cm rod than it would on a 10 m rod. In terms of the material stress, strain is what matters more than change in length. Compare to the extension of two (or more) springs in series to that of each individual spring. The total extension adds up, but the strain remains constant regardless of how many strings you add.

 

[chriscarson]

Well it’s not the same. The percentage changes are the same as strain.

but

Well it’s not the same. The percentage changes are the same as strain.

A buy off €2 will affect a €10 economy more than it would a €1000 economy.

A length change of 2 cm will put more strain on a 10 cm rod than it would on a 10 m rod. In terms of the material stress, strain is what matters more than change in length. Compare to the extension of two (or more) springs in series to that of each individual spring. The total extension adds up, but the strain remains constant regardless of how many strings you add.

It s close to the the job of Force for me .

 

[chriscarson]

Well it’s not the same. The percentage changes are the same as strain.

So there is two things that changes when force is applied strain and length.

 

[Chestermiller]

So there is two things that changes when force is applied strain and length.

Of course.

 

[chriscarson]

Of course.

ok thanks

 

[Orodruin]

It should be noted that Hooke's law relates stress $\sigma$ (i.e., the applied force per area) to strain $\epsilon$ as $\sigma = E\epsilon$, where $E$ depends on the material. Thus, from force and cross-sectional area, you can know the strain, but not the change in length (for that you also need to know the original length).

 

[chriscarson]

It should be noted that Hooke's law relates stress $\sigma$ (i.e., the applied force per area) to strain $\epsilon$ as $\sigma = E\epsilon$, where $E$ depends on the material. Thus, from force and cross-sectional area, you can know the strain, but not the change in length (for that you also need to know the original length).

Actually I have the hooke s law in my notes to study , but not easy to understand that part either.