Why is Young's modulous in Pascals?

[richard9678]

Why is Young's modulous in units of Pascals? I mean 200 GPa for steel.

 

[AdityaDev]

Young's modulus is the ratio stress/strain.
dimension of stress is same as that of pressure since stress = F/A and strain is dimensionless since strain = change in length/initial length

 

[richard9678]

If Young's modulous was simple a number, like 200, I would not think about it. But the modulous is not a simple number, it's in units of Pascals. But, I cannot see why it's Pascals. Stress is in Pascals. I get that. Stress in Pascals is not dimensionless. Why did the engineer have to say Young's modulous is in Pascals, why not just the ratio stress/strain?

 

[richard9678]

Have we got a dimension (stress in Pascals - F/A) divided by a dimensionless number (strain - delta l/l). And the result is in Pascals which has a dimension?

That would mean, if you take a number representing a dimension, and divide or multiply it by a number that carries no sense of dimension, the result is a number with a dimension?

 

[Raghav Gupta]

Have we got a dimension (stress in Pascals - F/A) divided by a dimensionless number (strain - delta l/l). And the result is in Pascals which has a dimension?

That would mean, if you take a number representing a dimension, and divide or multiply it by a number that carries no sense of dimension, the result is a number with a dimension?

Yes to both of your questions.
The engineer might have said only pascals thinking that you might know what modulus is.
Why elaborate when no one is asking in details. This might be most of people's thinking.

 

[brainpushups]

That would mean, if you take a number representing a dimension, and divide or multiply it by a number that carries no sense of dimension, the result is a number with a dimension?

Yes.

Look at the simple model of kinetic friction: f = μ N where f is the force of friction and N is the normal force. μ is a dimensionless number.

Dimensionless numbers crop up all the time and are often useful for characterizing some aspect of a system. The Reynolds number is another example - it is related to the ratio of viscous and inertial drag which means that it is a dimensionless number that characterizes the type of flow.

 

[richard9678]

So, in the equation for Young's modulous, we have a number that has units and a dimension (stress), divided by a unitless number (strain). Now, if I subject a 10KN tensile force to bar of 1cm² area the stress is 1 x 10⁸ Newtons. I can sort of visualise that, visualise the bar under stress The steel bar has an elastic modulous according to the tables of 200 GPa. But that has no meaning to me, I cannot see anthing apart from a number. It might as well be a dimensionless number.

200 GPa would mean something if there was a standard strain, and with steel it took 200 GPa to get the standard strain.

 

[Raghav Gupta]

I suggest you to read wikipedia for further
clarifications.

 

[AdityaDev]

Go through The example given in post 6.
Also the dimensionless strain is not useless. Imagine a spring. As the extension increases, the force increases. A steel wire is also like a spring.
Assume the force exerted is F.
now $Y=F\Delta L/AL$
So $F=\frac{AY}{L}\Delta L$
This looks familiar like F=kx
now you see the quatities L and ΔL have a meaning. The force constant of a spring is AY/L.

 

[richard9678]

"Young's modulus is the ratio of stress (which has units of pressure ) to strain (which iis dimensionless), and so Young's modulus has units of presure. It's SI unit is therefore the pascal (Pa or Nm2 or m−1·kg·s−2)"

That is the extent of the explanation as to why elastic modulous is measured in units of Pascals "and so...". There is no more reasoning. For all practical purposes it is just a number of a value that is required by the equations. And gives one the insight as to the relative stiffness of a material. But, if you talk about practicalities, there are non, except as mentioned to indicate relative stiffness. So, 200 GPa which is the Young's modulous for steel - it's just a figure that you come up with when doing stiffness tests on steel. I don't think it's even related to some kind of standard displacement, where you could say, steel would have to be put under 200 GPa to achieve the standard displacement. It's just a number that fits with the equations.

 

[AdityaDev]

A measure of stiffness that is independent of the particular sample of a substance is the Young modulus E.
The value of Y is constant for any given sample.
Its just used for finding the extension for a given force.

 

[richard9678]

You see, when you use formulas, one tends to put in numbers that reflect a physical situation. Like 10A flowing, 10KN foce pressing, 100m length, 1 second of time passing. It could be a test condition, where you could say the figure you are given in the table tells you that you would need to achieve that pressure to get a standard movement (say).

But, as far as I understand Young's modulous, you never see the values (from tables) reflected in any physical situation ( test or otherwise). When you put in the equation your 200 GPa, that does not reflect a physical situation of any description. It's a pure number really, despite it's having a dimension and being Pascals, a measure of pressure.

 

[Dadface]

If I told you that the speed of a particular object was eleven that wouldn't mean much to you. If I included the units and, for example, told you that the speed was eleven metres per second or eleven miles per hour then it would mean something. Units are needed for a complete description. Youngs modulus for steel has the units GPa because of the units we use to make the other relevant measurements. If we used a different unit for one or more of those other measurements then Youngs modulus would have a different value and a different unit.

 

[Dadface]

I think you want to get a better feeling of what Youngs modulus stands for. Suppose you asked me how much copper wire stretches by when you hang a certain weight from it. I wouldn't be able to give you an answer because the stretch depends not only on the weight but also on the length of the wire, its thickness and on the structure of copper itself. Long thin wires stretch more than short thick wires. I would be able to use a data book and look up the Youngs modulus of copper, this being a property of copper which is independant of its dimensions. Knowing the weight and the length and cross sectional area of the wire you could calculate the sretch.

 

[nasu]

So, in the equation for Young's modulous, we have a number that has units and a dimension (stress), divided by a unitless number (strain). Now, if I subject a 10KN tensile force to bar of 1cm² area the stress is 1 x 10⁸ Newtons. I can sort of visualise that, visualise the bar under stress The steel bar has an elastic modulous according to the tables of 200 GPa. But that has no meaning to me, I cannot see anthing apart from a number. It might as well be a dimensionless number.

200 GPa would mean something if there was a standard strain, and with steel it took 200 GPa to get the standard strain.

No, the stress is 10⁸ N/m² or 10⁸ Pascals.
The stress is not a force. This may be the reason for your confusion.

If you go 100 km in 1 hour, your speed is 100km/h and not 100 km.

 

[sophiecentaur]

Why is Young's modulous in units of Pascals? I mean 200 GPa for steel.

Why shouldn't it be?
I think there is no need to look for anything significant about the fact that two quantities happen to share the same units. It doesn't mean that the two quantities are in any way 'equivalent' or the same thing. Stress when tension is responsible is the same as stress when compression is involved and they both have units of Pascal. We happen to have a separate name for compressional stress - Pressure, which is the first time we come across the Pascal.
Any quantity that involves Pressure and any other dimensionless quantity will have the same units of Pressure.

 

[richard9678]

F/A which is stress, pressure, in Pascals, has a practical connotation. Young's modulous, (In Pascals simply because of F/A in the formula - it seems), has a different connotation, which is not really practical, but mathematical. I mean, the value 200 GPa, which is the Young's modulous for steel, is to be treated more like a "mere" number, wheras say 100 MPa stress in a beam member isn't just a mere number. It means more than a number - it's a phyical state of affairs.

Young's modulous is in Pascals, because of F/A in the formula, but that's the only reason why it has anything to do with the concept of pressure. I think. Real concept of pressure is in F/A. I muse.

 

[russ_watters]

Without trying to pass judgement on whether considering Young's Modulus to be actual units of pressure on not is valid, it isn't the only example where more than one different quantity shares the same units. See: torque and work.

 

[DocZaius]

F/A which is stress, pressure, in Pascals, has a practical connotation. Young's modulous, (In Pascals simply because of F/A in the formula - it seems), has a different connotation, which is not really practical, but mathematical. I mean, the value 200 GPa, which is the Young's modulous for steel, is to be treated more like a "mere" number, wheras say 100 MPa stress in a beam member isn't just a mere number. It means more than a number - it's a phyical state of affairs.

Young's modulous is in Pascals, because of F/A in the formula, but that's the only reason why it has anything to do with the concept of pressure. I think. Real concept of pressure is in F/A. I muse.

It has quite a lot to do with the concept of pressure. You can look at it as Young's modulus answering the question "How much pressure must I exert on the end of this thing to make it twice as long as it is now?" (assuming we stay in Hooke's law regime throughout). To me that has more meaning than a mere number with units tacked onto the end as you seem to imply. Could you imagine if it didn't have units of pressure? It would be meaningless.

 

[Dale]

When you put in the equation your 200 GPa, that does not reflect a physical situation of any description.

Sure it does. It could mean for example that you strained the steel by 1% so a 2 GPa pressure was wsed

 

[256bits]

When you put in the equation your 200 GPa, that does not reflect a physical situation of any description

And also, it is the stress in a material elongated to double its length.

Here is a typical stress - strain curve for a ductile material.

The elastic modulus, in this case Young's Modulus for tension, is just the slope of the line in the elastic region. The slope has units of stress / strain and is then usually expressed as Pascals for the SI system, or in psi for the English system. Depending upon which system of units one uses, Young's modulus references a 1 meter length of material, or a one inch length of material.
Since we are dealing with stress, the area of the material become irrelevant.

 

[A.T.]

I don't think it's even related to some kind of standard displacement, where you could say, steel would have to be put under 200 GPa to achieve the standard displacement.

The "standard displacement" is a strain of 1, which means doubling the length. Obviously, not all materials can be stretched that far and their maximal stress is less than their Young's modulus, so you won't be able to observe the stress value given by the Young's modulus in every material.

 

[sophiecentaur]

Sure it does. It could mean for example that you strained the steel by 1% so a 2 GPa pressure was wsed

Exactly. One shouldn't get hung up too much on Dimensional Analysis. It is a tool and not your Master.