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## #1 2012-05-08 17:06:33

limpfisch
Member
Registered: 2012-05-08
Posts: 11

### Which spring requires more material to make?

Which spring requires more material to make it, one of radius 5 cm and height 4 cm
that makes three complete turns or one of radius 3 cm and height 4 cm that makes
five complete turns?

i thought i did it right but logically my answer can't be.

Last edited by limpfisch (2012-05-08 17:07:10)

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## #2 2012-05-09 01:44:48

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Which spring requires more material to make?

Maybe someone can do a better analysis as this is very simple.

It might be exactly the same believe it or not, but this is only sketchy calculations and
using 5 rings instead of 5 turns and 3 rings instead of 3 turns, so it is probably not exactly
the same thing.  But let's say there are three springs instead of two and one has no space in the
middle because the spring thickness is double the radius.  Now take three circle areas for an
approximation instead of volumes.  The volume of the r=half and rmax = 1 and rmin = 0, i mean
area of the circle is just 1 times pi, ignore pi just call it one.   There is no center to subtract off for this one.
Now for the donut shape of radius equal to 1 and a half or 1.5 then 2 squared (max radius) minus 1 squared (min radii),
which is 3.  So the r=1.5 goes to 3pi or just 3 if we are doing proportions.
so far we have R=1, SO 0.5:1 and 1.5:3  (3 IS AREA OF DONUT LOOKING FROM TOP)
Now we do donut with r = 2.5 or 2 and a half.  rmin = 2, rmax = 3
3 squared minus 2 squared = 9 - 4 = 5 and 2.5:5 is the ratio.
ratios obtained:
.5:1
1.5:3
2.5:5
Now do a fourth one r = 3.5.
4^2-3^2=16-9=7
3.5:7
So they go up by odd numbers like the squares...
So in this simplification the answer is the same for each spring.

Now we should consider the fact that the spring slants in  a spiral

But I don't know how to do that.

In your example r=5, the perimeter center line of spring is 10pi times 3 turns  = 30.
And in your example the r = 3 perimeter center line of spring is 6pi times 5 turns is 30.
both are 30.
So the answer must be pretty close I think.

Maybe someone can do a better analysis as this is very simple.

igloo myrtilles fourmis

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## #3 2012-05-09 01:54:17

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Which spring requires more material to make?

Okay, get this insprination!!!
If a spring is 300 feet long and has one turn or two turns then they both have about 300 feet of metal as that
takes over.  So there is the answer!!! The 3 turn spring in your problem has more metal in volumej!!!!!!
I am pretty sure.  Do you see why??? It is because the length of the spring takes dominance as shown above in the 300 foot example with only 1 or two turns and a very small thickness like under a foot or an inch.

igloo myrtilles fourmis

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## #4 2012-05-09 02:51:55

bob bundy
Registered: 2010-06-20
Posts: 8,462

### Re: Which spring requires more material to make?

hi limpfisch

Welcome to the forum!

My thoughts on this have followed the same lines as John's.

Ignoring the height (reasonable as compressing a spring doesn't change its volume) and assuming the same cross section

spring 1 = (2 x pi x 5) x 3 turns

spring 2 = (2 x pi x 3) x 5 turns.

They have the same amount of material.

But what of the spiral effect?

Well then you have to know more about the spring since actual cross section will need to accounted for and also there are two ways of terminating a spring.  see picture below.

Does the end taper or is it cut off square across the cross section.  I think for the springs in the question this will have more effect than the spiral.

So on the basis of the information given, I think they are approxiamtely the same.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #5 2012-05-09 04:58:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Which spring requires more material to make?

Hi limpfisch;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #6 2012-05-09 05:23:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Which spring requires more material to make?

Hi bobbym

You do understand that this is a help me question and not a puzzle or an exercise?

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #7 2012-05-09 05:36:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Which spring requires more material to make?

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #8 2012-05-09 14:24:23

limpfisch
Member
Registered: 2012-05-08
Posts: 11

### Re: Which spring requires more material to make?

It's ok i got it after about 2 hours of thinking. I used the formula for a helix and then found the absolute value of it's derivative and went from there. Turns out the 2nd spring does use a little more spring.....i think.

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## #9 2012-05-09 14:37:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Which spring requires more material to make?

Hi limpfisch;

That is what I used the parametric forms for a 3D helix and the arc length formula. The second one is longer.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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