# Do we now express mm as the letter m with a superscript?

1. Nov 29, 2014

### richard9678

Hi. I'm looking at a stress/strain graph. The vertical axis is marked Stress/MN m-2. Is this saying that the figures on the axis have been calculated using KN for force, and cm2 as area? Thanks.

2. Nov 29, 2014

### Doug Huffman

No, it is saying that the vertical axis label is unity, to be multiplied by the figures.

3. Nov 29, 2014

### SteamKing

Staff Emeritus
MNm-2 means stress is measured in mega newtons per square meter.

And for anyone who doesn't realize it, m-2 = 1/m2,which is not the same thing as a centimeter, which is 0.01 times a meter.

There are 104 cm2 (100 cm * 100 cm = 10,000 cm2) in 1 m2.

4. Nov 29, 2014

### richard9678

Stress, I know is very often given in Giga Pascals. I suppose then, where it says 1000 on the graph, that is indicating 1GPa? Still not sure what m-2 is about.

5. Nov 29, 2014

### SteamKing

Staff Emeritus
1 pascal is defined as 1 newton per square meter, or 1 Pa = 1 Nm-2.

1 kPa = 1000 Pa = 103 Pa = 1kNm-2

1 MPa = 106 Pa = 1 MNm-2

1 GPa = 109 Pa = 1GNm-2

If you are having trouble interpreting a graph, why don't you post the graph and let us take a look?

6. Nov 29, 2014

### richard9678

Where the axis reads 1000, that I believe should be taken as 1000 MN. That is a very great force. However, the graph is also indicating that the area associated with that force is 1m2, or 1 square metre. When you take these things into account, you calculate the stress to be 1000MN / 1m2, which is 1Gpa. Okay. but I still don't get why the graph says MN m-2, rather than MN m2. I understand the latter, but not the former.

7. Nov 29, 2014

### SteamKing

Staff Emeritus
The stress should be in units of MN/m2 (the '/' is very important here).

If you don't understand how exponents work, here is a short lesson:

x * x = x2

1 / (x * x) = 1 / x2 = x-2

I know MNm-2 looks odd, but this is how MN/m2 is sometimes written.

8. Nov 29, 2014

### richard9678

It's the notation I don't get. Area is measured in square meters. So, if I calculate the area of something that is 3m x 3m I'd give the answer as 9m2. I would not give the answer as 9m-2.

Lets say my tensile test set-up involves a steel bar with an area of 1 m2. And I applied force in Mega Newtons. In such circumstances to get any meaningful strain results I would be applying force in the hundreds of MN. Indeed, I would easily be required to apply 1000MN to get an adequate indication of strain. Okay, so, stress, which is a ratio of force / area is being expressed in terms of force in MN and area in square meters, or 1m2. So, to my mind, if I annotated the stress axis, to indicate the nature of the values on the stress axis, I'd write stress/ MNm2.

I'd be indicating to the reader that where the axis indicates 1000 on the stress axis, that is to be read as 1000MN per metre squared.

Of course if area is 1m2 this is the same as 1/m2 which I think equals 1m-2.

Is m2 the same as m-2 is the same as 1/m2? If not, why not?

What am I missing?

9. Nov 29, 2014

### richard9678

Okay, I'm beginning to see this I think. Stress is N/m2. So the value of stress is a function of the reciprocal of m2. Or 1/m2. The minus figure in m-2 is, I think just saying reciprocal of m2.

10. Nov 29, 2014

### SteamKing

Staff Emeritus
Nor should you. Area is measured in square units.

[Note: corrected this expression]

It is, which is why you must either write the units of stress as MN / m2 or as MNm-2. A unit of MNm2 is not stress. It is 'mega newtons times square meters'.

This is where you are getting mixed up. Stress is the ratio of applied force to the area on which it acts. A ratio of two quantities implies the division of one quantity by the other, so the ratio of a to b can be expressed in several ways:

a : b

$a \div b$

or a / b, where the '/' stands for 'is divided by'

The units for calculating stress in the SI system are the force in N divided by the area in square meters.

These units are abbreviated N / m2, which is read as 'Newtons per square meter'. Some people prefer to replace the division of force by area instead with multiplication of the force by the reciprocal of the area, which is the same as saying force × 1 / the area.

Because the reciprocal of X2 is the same as 1 / X2 is the same as X-2, then

N / m2 is the same as Nm-2. Notice, the latter expression has no ' / ', and because the two units N and m-2 are written next to each other this implies multiplication.

11. Nov 30, 2014

### Staff: Mentor

I think that SteamKing missed one of the things you said. m2 IS NOT the same as m-2. However, m-2 IS the same as 1/m2.