# F = -kx

http://ouhos.org/
http://ouhos.org/
http://phys.wordpress.com/category/classical-physics/
http://www.leancrew.com/all-this/2010/07/bathroom-scales-and-robert-hooke/
http://www.leancrew.com/all-this/2010/07/bathroom-scales-and-robert-hooke/
F = -kx
Hooke’s Law
It is beautifully simple. If the
spring extends by distance x
on application of mass m,
It is beautifully simple. If the
spring extends by distance x
on application of mass m,
then according to Hooke’s
Law it will extend by 2x if a
mass 2m is applied
http://commons.wikimedia.org/wiki/File:14_Robert_Hooke._Pencil_Drawing.jpg
http://www.le
ancrew.com/a
llthis/2010/07/
bathroomscales-androbert-hooke/
http://blogs.nature.com/london/2007/10/
SLIDE 11: THE CASTLE OF KNOWLEDGE
(RECORDES, 1575)
What happened can be seen on the title page of
Recordes' book &quot;The Castle of Knowledge,&quot; the
first science book in English, published in 1575.
The wheel of fortune is turned, not by the
wisdom of God, but by the ignorance of man.
And, as the role of God, the final cause, was
taken over by human knowledge, the whole
notion of causal explanation came under attack.
ll rely on Hooke’s Law.
Robert Hooke was a brilliant 17th century English
scientist/engineer/architect whose name is not as well known as it
should be because:
He was a contemporary of Isaac Newton’s, and anyone working at the
same time as Newton is likely to be overshadowed.
He got on Newton’s bad side, which was not the right side to be on, as
Gottfried Leibnitz and William Chaloner could attest. Hooke claimed
that some of Newton’s work in gravitation was derivative of his own, an
affront Newton never forgave, even after Hooke’s death in 1703. When
Newton supervised the Royal Society’s move from Gresham College
in 1705, Hooke’s portrait and some of his experimental instruments
were conveniently lost.
Still, Hooke’s name is well known among engineers because of his law of
linear elasticity, a cornerstone of much civil and mechanical
engineering analysis. Amazingly, Hooke first published his law as an
anagram. It wasn’t until a few years later that he published a proper
paper on the subject, “De Potentia Restitutiva, or Of Spring.”
Here’s his explanation of the anagram:
About two years since I printed this Theory in an Anagram at the end of
my Book of the Descriptions of Helioscopes, viz. c e i i i n o s s s t t u
v, id est, Ut tensio sic vis; That is, The Power of any Spring is in the
same proportion with the Tension thereof: That is, if one power stretch
or bend it one space, two will bend it two, and three will bend it three,
and so forward. Now as the Theory is very short, so the way of trying it
is very easie.
The usual translation of Ut tensio sic vis is As the extension, so the force:
there is a linear relationship between force and deflection. In
mathematical terms, Hooke’s Law is typically written like this,
F=kx
where F is the force, x is the deflection, and k is the constant of
proportionality, usually called the spring constant.
“Of Spring” goes on to give several examples of springy things and
describes experiments that prove the linear relationship. His claim to
universality comes in this paragraph:
From all which it is very evident that the Rule or Law of Nature in every
springing body is, that the force or power thereof to restore it self to its
natural position is always proportionate to the Distance or space it is
removed therefrom, whether, it be by rarefaction, or separation of its
parts the one from the other, or by a Condensation, or crowding of
those, parts nearer together. Nor is it observable in these bodys only,
but in all other springy bodies whatsoever, whether Metal, Wood,
Stones, baked Earths, Hair, Horns, Silk, Bones, Sinews, Glass, and
the like. Respect being had to the particular figures of the bodies
them.
You could make a very good argument that this paragraph is just bullshit.
Of these materials, only Glass and baked Earths (assuming by the
latter he means ceramics) follow Hooke’s Law reasonably well up to
their breaking point. The others exhibit distinctly non-Hookean
behavior over some range of loading. They either don’t spring back to
their original position (metals stressed above their yield point) or aren’t
linear in their elasticity (sinews).
Hooke must have known this. One of his prime examples is the coiled
spring, made by bending a metal wire into a helix. While the finished
spring certainly follows Hooke’s Law up to some load, the wire itself
just as certainly didn’t follow Hooke’s Law as it was being bent into the
coiled form in the first place—if it had, it would have sprung back to
What was important to Hooke, and what is still important to us, is that
many materials are linearly elastic over the range of loading they are
typically subjected to in the finished product. Yes, you can bend a
piece of wood beyond the linear range, but you don’t build a house out
of wood stressed that highly. The wood joists in the floor below me are
bending slightly under my weight, but they will spring back when I
leave the room. Most manmade structures and devices are built to be
used within the linearly elastic range, and that’s why Hooke’s Law
works.
So, back to load cells. The simplest load cell is an old-fashioned spring
fish scale. Here’s a handsome example whose photo I nicked from
Malolo Blue Water Tackle.
The pointer moves along the body as the coiled spring inside deflects
under the weight of the fish. The weight markings are uniformly spaced
because of Hooke’s Law: As the extension, so the force.
But Hooke’s Law tells us that we don’t need to used coiled springs to
measure force. Any structure that isn’t overstressed will display a
linear relationship between force and deflection; we just have to be
able to measure that deflection. Most structures don’t deflect visibly
when lightly loaded, but we can still measure their deflection by
drawing on a little knowledge from electrical engineering.
Tryalls and tribulations
At times, transcribing the Hooke folio was exhausting, taking
hours to decipher a single scrawled word, and I felt that my
frustration mirrored Hooke’s own. He increasingly records
unreasonable obstructions to his theories including the
principle, later expressed in Newton’s first law, that ‘a body
once put into motion would move perpetually if it met with no
resistance’, the decrease in motion being proportional to the
amount of resistance. However, the Society were
unconvinced, as Hooke complained, ‘instead of hearing
grounds and reason, experiments were always called for and
all loaded with objections little to purpose’. Eventually, to
demonstrate that resistance decreases motion, Hooke
showed the Society something that I gradually realised was a
http://blogs.nature.com/london/2007/10/
http://phys.wordpress.com/category/classical-physics/
Hooke manuscript is returned home
May 18, 2006 BBC News is reporting about a lost and
The hand-written notes are thought to contain a “treasure
trove” of information about the early endeavours of the
hidden in a house in Hampshire, was rescued from a
public auction after a fundraising effort pulled in the
&pound;940,000 needed.
As you probably know, Hooke was famous (among other
things) for his frequent disputes with other physicists
(most notably Newton and Huygens) on the priority of
various discoveries, and this new manuscript could help
in settling (a bit late) some of them.
http://phys.wordpress.com/category/classical-physics/
Hooke manuscript is returned home
May 18, 2006 BBC News is reporting about a lost and found Hooke
The hand-written notes are thought to contain a “treasure trove” of
The document, which had lain hidden in a house in Hampshire, was
rescued from a public auction after a fundraising effort pulled in the
&pound;940,000 needed. As you probably know, Hooke was famous (among
other things) for his frequent disputes with other physicists (most notably
Newton and Huygens) on the priority of various discoveries, and this new
manuscript could help in settling (a bit late) some of them.
http://phys.wordpress.com/category/classical-physics/
Hooke manuscript is returned home By Rebecca Morelle BBC News science
reporter
The manuscript will be preserved and analysed
More details
The long-lost manuscript belonging to pioneering scientist Robert
Hooke has returned to the Royal Society.
The hand-written notes are thought to contain a &quot;treasure trove&quot; of
A digitised version of the notes will eventually be available on the web.
The document, which had lain hidden in a house in Hampshire, was rescued
from a public auction after a fundraising effort pulled in the &pound;940,000 needed.
The &quot;white knights&quot; have been revealed as the Wellcome Trust, which gave
&pound;469,000, and 150 donors who came forward after the Royal Society
appealed to its fellows and the general public.
The manuscript will now be rebound, transcribed and carefully analysed; and
infrared scanning will be used to reveal some notes that have become
illegible over time.
http://news.bbc.co.uk/1/hi/sci/tech/4990266.stm
A polymath
Robert Hooke, who died in 1703, was a polymath whose many contributions
included coining the term &quot;cell&quot;, devising a law of elasticity, creating spring
regulators for time pieces; and designing several major buildings, such as
the Monument to the Fire of London.
In 1662, Hooke became curator of experiments at the Royal Society, and he
was later elected a fellow in 1664.
The fragile pages of the manuscript contain Hooke's notes of Royal Society
meetings that took place in the 17th Century.
They are scattered with sketches and marginal observations, which the
society hope will give insight into the man whose work crossed so many
fields.
http://news.bbc.co.uk/1/hi/sci/tech/4990266.stm
Professor Lisa Jardine, a historian from Queen Mary, University of London,
and biographer of Robert Hooke, was the first person to alert the Royal
Society to the existence of the document. She will be working with the
society to analyse the notes. &quot;These are the records of what happened at
the Royal Society between late 1677 and late 1682. There could well be a
Newton experiment in there that nobody knows about,&quot; she said. &quot;Hooke
was a colourful, controversial character. These minutes are more likely to tell
us about his interactions with other people. For a biographer like me, they
will give us a much fuller picture. &quot;I think, in terms of modern science, they
will tell us about the origins of laboratory science, research team interaction,
and how controversy and competition fuelled discovery. They will reveal the
mechanics, the machinery of scientific discovery.&quot;
http://news.bbc.co.uk/1/hi/sci/tech/4990266.stm
Scientific disputes
Hooke was involved in many disputes with scientists who he accused of
plagiarising his ideas - the most famous being his feud with Isaac Newton,
who he accused of stealing his ideas about gravity. Professor Jardine said
the manuscript might shed light on some of these disagreements. &quot;There
are four pages which may tell us whether Hooke really had beaten Christian
Huygens to a balanced spring watch for measuring longitude.&quot; Martin Rees,
president of the Royal Society, added: &quot;The manuscript is significant to both
scientists and non-scientists, and covers pioneering experiments relating to
astronomy, gravity and microscopy. &quot;The descriptions of his experiments are
the closest one could get to an original experiment without actually being
there. We hope that scientists and non-scientists alike will soon be able to
appreciate how exciting this discovery is.&quot; The papers will also go on display
to the general public at the Royal Society's Summer Science Exhibition in
July.
http://news.bbc.co.uk/1/hi/sci/tech/4990266.stm
http://www.leancrew.com/all-this/2010/07/bathroom-scales-and-robert-hooke/
ll rely on Hooke’s Law.
Robert Hooke was a brilliant 17th century English
scientist/engineer/architect whose name is not as well known as it
should be because:
He was a contemporary of Isaac Newton’s, and anyone working at the
same time as Newton is likely to be overshadowed.
He got on Newton’s bad side, which was not the right side to be on, as
Gottfried Leibnitz and William Chaloner could attest. Hooke claimed
that some of Newton’s work in gravitation was derivative of his own, an
affront Newton never forgave, even after Hooke’s death in 1703. When
Newton supervised the Royal Society’s move from Gresham College
in 1705, Hooke’s portrait and some of his experimental instruments
were conveniently lost.
Still, Hooke’s name is well known among engineers because of his law of
linear elasticity, a cornerstone of much civil and mechanical
engineering analysis. Amazingly, Hooke first published his law as an
anagram. It wasn’t until a few years later that he published a proper
paper on the subject, “De Potentia Restitutiva, or Of Spring.”
Here’s his explanation of the anagram:
About two years since I printed this Theory in an Anagram at the end of
my Book of the Descriptions of Helioscopes, viz. c e i i i n o s s s t t u
v, id est, Ut tensio sic vis; That is, The Power of any Spring is in the
same proportion with the Tension thereof: That is, if one power stretch
or bend it one space, two will bend it two, and three will bend it three,
and so forward. Now as the Theory is very short, so the way of trying it
is very easie.
The usual translation of Ut tensio sic vis is As the extension, so the force:
there is a linear relationship between force and deflection. In
mathematical terms, Hooke’s Law is typically written like this,
F=kx
where F is the force, x is the deflection, and k is the constant of
proportionality, usually called the spring constant.
“Of Spring” goes on to give several examples of springy things and
describes experiments that prove the linear relationship. His claim to
universality comes in this paragraph:
From all which it is very evident that the Rule or Law of Nature in every
springing body is, that the force or power thereof to restore it self to its
natural position is always proportionate to the Distance or space it is
removed therefrom, whether, it be by rarefaction, or separation of its
parts the one from the other, or by a Condensation, or crowding of
those, parts nearer together. Nor is it observable in these bodys only,
but in all other springy bodies whatsoever, whether Metal, Wood,
Stones, baked Earths, Hair, Horns, Silk, Bones, Sinews, Glass, and
the like. Respect being had to the particular figures of the bodies
them.
You could make a very good argument that this paragraph is just bullshit.
Of these materials, only Glass and baked Earths (assuming by the
latter he means ceramics) follow Hooke’s Law reasonably well up to
their breaking point. The others exhibit distinctly non-Hookean
behavior over some range of loading. They either don’t spring back to
their original position (metals stressed above their yield point) or aren’t
linear in their elasticity (sinews).
Hooke must have known this. One of his prime examples is the coiled
spring, made by bending a metal wire into a helix. While the finished
spring certainly follows Hooke’s Law up to some load, the wire itself
just as certainly didn’t follow Hooke’s Law as it was being bent into the
coiled form in the first place—if it had, it would have sprung back to
What was important to Hooke, and what is still important to us, is that
many materials are linearly elastic over the range of loading they are
typically subjected to in the finished product. Yes, you can bend a
piece of wood beyond the linear range, but you don’t build a house out
of wood stressed that highly. The wood joists in the floor below me are
bending slightly under my weight, but they will spring back when I
leave the room. Most manmade structures and devices are built to be
used within the linearly elastic range, and that’s why Hooke’s Law
works.
So, back to load cells. The simplest load cell is an old-fashioned spring
fish scale. Here’s a handsome example whose photo I nicked from
Malolo Blue Water Tackle.
The pointer moves along the body as the coiled spring inside deflects
under the weight of the fish. The weight markings are uniformly spaced
because of Hooke’s Law: As the extension, so the force.
But Hooke’s Law tells us that we don’t need to used coiled springs to
measure force. Any structure that isn’t overstressed will display a
linear relationship between force and deflection; we just have to be
able to measure that deflection. Most structures don’t deflect visibly
when lightly loaded, but we can still measure their deflection by
drawing on a little knowledge from electrical engineering.