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Raise to the power 4

Raise to the power 4

Raise to the power 4

(OP)
Area is metre squared
Volume is metre cubed
Sectional Modulus is metre ???

Is it quadrupled? or does that mean multiply by four?

What is the written description (with superscript) for squaring a square?

RE: Raise to the power 4

Section Modulus is the moment of inertia divided by the distance from the neutral axix to the extreme fiber.
It's units are therefore length cubed.

RE: Raise to the power 4

Moment of inertia of area uses units of length to the fourth power.  Squaring a square gives the fourth power, 4 written as a superscript.

Quadrupled means multiplying by four.  I don't think there is a written term for it like cubed or squared.

Squared & cubed come from geometrical analogies.  The four-dimensional equivalent is a tesseract, but I've never heard of so many meters "tesseracted".

RE: Raise to the power 4

(OP)
My mistake with the sectional modulus, I was working on the moment of inertia.

I thought quadrupled meant multiplying by four which was throwing me, I'd come across it on a web site and wasn't sure where they were going.

I've only ever head of "metres to the forth" which is why I'm asking.

Maybe we should invent the concept and give it a new name, it all has to start somewhere smile smile bigcheeks smile smile

RE: Raise to the power 4

This is an important fundamental of the principal of dimensional homogenity.
All physical quantities are expressed in terms of BASE/FUNDAMENTAL quantities :
L : Length
M : MAss
T : Time
t : temperature

Then there are derived quantities:

Speed : [L][T]^-1 => L /T => m/s = km/hr = mm/s (No matter which unit system you use dimensional analysis renders itself useful.

Force = [M][L][T]^-2 => M * L / T^2 => Nm/s2

Hope this helps.

-vhs

=========================================
2thumbsup Mech Rulz 2thumbsup

RE: Raise to the power 4

(OP)
I don't understand how what you said helps me vhs.

I get dimensional analysis, I'm after the name for raising something to the power of four similar to using squared or cubed.

RE: Raise to the power 4

It's just "to the fourth power" or "raised to the fourth power."  I guess the word maker-uppers never worked on a single word to denote the operation probably due to the fact that there's no physical entity to which it would be applied--squared is in reference to a "square" and cubed is in reference to a "cube."

DB

RE: Raise to the power 4

Squared and cubed are 1-syllable words, so we need something shorter and more obvious than "tesseracted".  I propose "fourpled".  : )

RE: Raise to the power 4

JStephen,

That operation sounds like something that's more fun than you're supposed to have at work. [surprize]

DB

RE: Raise to the power 4

A little spelling issue there on the smiley face.blush

RE: Raise to the power 4

I'd like to second 'fourpled'

Semi-related, does everybody remember what the third derivative of position is?  Hopefully nobody here is too familiar with that term...

RE: Raise to the power 4

The third derivative of position is the rate of change of acceleration which I believe is called jerk.

Timelord

RE: Raise to the power 4

I believe Timelord is correct if you are talking about dynamics.  If you are in the mechanics realm, I think the third derivative of position (displacement) is shear:

EIv''''=p
EIv'''=-V
EIv''=M
EIv'=Int(M)dx
EIv=[more integrals than anyone should care about]+[a bunch of constants]

RE: Raise to the power 4

GBor:

I’m not sure I know what you mean.  I thought that velocity, acceleration and jerk were kinematic quantities, kinematics being the branch of mechanics that studies the motion of a point.  I also thought that shear was represented by the off-diagonal components of the stress tensor.  Can you elaborate?

RE: Raise to the power 4

he's talking about the elastic beam equation, I think. A bit of a 'stretch'.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Raise to the power 4

I was just playing around, but the equations that I cited are beam equations from Applied Elasticity.  "position" can mean many things, so I decided to define it as "displacement", which you can differentiate a few times to get "shear"

Quote:

Mechanics that studies the motion of a point
I think would be described as "Dynamics"...as opposed to "statics".

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
www.borowskiengineering.com

RE: Raise to the power 4

Thanks, Greg...at least I don't feel like a complete idiot.

After we got off on "fourpled", I was trying to hang on to the levity...bad attempt...back in my hole!

RE: Raise to the power 4

GBor:

Nice website.

The difference between kinematics and dynamics is that kinematics studies the motion of bodies irrespective of mass, whereas dynamics studies the forces acting on masses in motion.  Statics deals with the equilibrium of forces.  Velocity, acceleration and jerk are kinematic quantities.

RE: Raise to the power 4

I am going to vote here for a new name for raising to the fourth...

I think we should call it TIMED (not times) as in four timed equals 256

Wes C.
------------------------------
When they broke open molecules, they found they were only stuffed with atoms. But when they broke open atoms, they found them stuffed with explosions...

RE: Raise to the power 4

Thanks, RGasEng...I'm not much of an HTML Guru, but I managed to "hack out" that website...a real programmer would probably laugh.

wes616,

Can you give us a phonetic spelling on that one?  Is it Tie'med or tie-med' or more like timid?  Perhaps tim-ed'?

RE: Raise to the power 4

GBor according to physics the first 4 dims are:

point
area
volume
time - ^4

So it would be TIMED

Like I timed the race, and that horse had the new track record...

Wes C.
------------------------------
When they broke open molecules, they found they were only stuffed with atoms. But when they broke open atoms, they found them stuffed with explosions...

RE: Raise to the power 4

You can have a lot more Freudian fun with forepled though.

DB

RE: Raise to the power 4

Thanks, Wes,

Not sure "timed" would get my vote...doesn't sound technical enough.  Trying to explain it would lead to people misunderstanding and thinking ill of you.  "Forepled" on the other hand...hmmm...

RE: Raise to the power 4

Well, if you really think about it.. Neither Squared or Cubed is all that technical...

But I could be convinced of forepled... big smile

Wes C.
------------------------------
When they broke open molecules, they found they were only stuffed with atoms. But when they broke open atoms, they found them stuffed with explosions...

RE: Raise to the power 4

A square is a 2 dimensional object.
A cube is a 3 dimensional object.
A tesseract is 4 dimensional cube object.

Perhaps "meters tessered"

or "Tessic meters"

RE: Raise to the power 4

That's pronounced "FORP-uld", not "fore-PLED" in case anyone wonders.  Hate to get it wrong from the beginning.

I assume fourple rhymes with "vorpal" if that helps.

RE: Raise to the power 4

   Is there any validity to the claim that very primitive people can only count to three -- once, twice, thrice, and all that?

   For some reason, those Cro Magnon types in France did not work out second moment of area in their cave paintings.  

                           JHG

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