when we take a spring
something that we are so familiar with
now
and a spring as length rallying a
relaxed state
spring constant k
aiken extent
the spring
with some force that i apply
the spring then
rail counterweight switches bring forth
and it will be an equilibrium there
a chorus
zero position and that school is now
delta aol
instead of exports we have done before
if i
doubled the force
delta al will double
what's what's that about the poorest
maybe it was built
unit was dealt a al
is proportional repair
nothing new
as long as hopeful holes
if i make
the spring twice as long
i would get the double b_ extension
because when i have to us
spring since errands
each one on the in front of this force
we'll get longer by this amount
things i have to springs in series i
will get twice
delta l
so delta alpha
is also proportional
of mine
if i take 'til
springs
parallel
one like so
and one like so
relax lang al both the same spring
constant k
and it now i apply
enforce on it
then each wong of these three forces
is only
hospice wong
gennady counter this force
in other words
extension delta bill that i hope came
from this external force
is now only hoppers much as it would be
which won't spring
and if i had three springs parallel all
identical i would only get one-third
often
extension
forgiven force
in other words
delta l
is also
inversely proportional
who don't know more
off springs that i have assuming that
they are
identical springs
now i'm going to
usually wrong
or wire
which has cross-sectional area really
eight
and then to help
and i'm going to apply
the force here
as a result of that forced
it will get longer by certain amount
delta alpha
exactly like that
and clearly
when i make this force
stronger delta hell will increase and as
long as well slow holds
baptist reports
provided by the wrong
balance it without
provided this spring forces they really
proportionate was dealt a l
i have again the delta l will be
proportional with the force double the
force
i kept white belt that out
if i bought
two of these roads
together so i'd double the length of the
rollet
and clearly i will get
twice delta l because it
means roth will experience the force he
trough will get longer by delta aol and
so
who are thrilled that will be quite o
dot o
so again delta alice proportional with
al
suppose now i have to abuse rob's
next to each other
noticed a parallel
parallels brings here
and i apply
before xep
then the spring sports
on each one of them if i called at the
spring force
well we have to be hot
to counter the sports
sordid both haven't cross-sectional area
a b
and so now we've got all the
cross-sectional area
i could only hop
of delta l
and so now we have a situation that if i
may be wrong
well by this whilst doing it
just one rolled
just completely equivalent of this
situation
i'm only getting half delta l forty
given force
and so now we have the delta l
is proportional inversely proportional
for cross-sectional
so now we can make up the balance
and we can say hot
delta l
is proportional
hutu forces
proportional to help
an intricate proportional
riviera the cross-section where
so after divided by eight
is then proportional
del file
overall
and that proportionality constants
we give a name
and that is covered the white
and that is cold
young's modulus
is young
wanderlust
f over a week as did i mention of
pressure
force unitarian
is what we call stress
and delta allover al which is
dimensionless
recall that strain
if we compare tour all of these
different values all too
domes margolis
the one with the
smaller value
why forty same stress
we'll give you
a larger strain in there with you to be
here
to make it longer
young's model is is very high
the royalties extremely states
than it is
delhi difficult to make the
ralph longer
i have here for you some numbers which
of course i on the web so you don't have
to copy them
and you have young's monitors there
for various metals and i also headed
down there
michelman today we will
work was that quite extensively
first there were simple example
you get a feeling
what is at stake here i can take a year
we're all there is a radius are
wichita board five centimeters
that would give me
a cross section where are you
or eight spots
simpleminded spikes
graham eaters
o_j_ thick the roads
i make a very simple i make their legs
one leader
and i hang on the role of
at the bottom
and master m
let's let's say five hundred democrats
and i won't buy from the fewer guns yes
i won't quite welcome
in the midst of course
which i plan on the rolls
is about five thousand mtrs
so i can i ask myself how much longer is
israel going to be
so we're going to have the delta at all
going to be f
provided by any
funds al
divided by young tomatoes
and we don't know what at this
we know what alice and we know what case
so in our case
this number is six point three
content of this evidence
for the numbers
that we have
and for now we can look at spiegel as an
example
so we take steel
white
twenty content of depends mutants per
square meter
and we substitute that in here
and we find that we get an extension
delta l
i believe is only a third of a
melanie indeed
or point three millimeter
think about this
still overall
centimeter fic
and it has a length of one leader
and i think five hundred kilograms on it
and only gets one the bike contend that
the melanie that you couldn't even see
that
however if you go
and make the royal which would be really
a rope
if you make it out of my own
which hasn't
young's modelers
always bollocks fifty five times lower i
don't have to use that number
about fifty five times lower
soda delta l
will then be fifty five times larger
and so instead of a third of a
millimeter
i will get something like seventeen
evidence
and that you can see here is your naked
eye
i think a rope
they fake
not on identify from the pentagon
bullets
and i will see it gets long about one
point seven centimeters
you can see that
infront
of your eyes
if i start adding more weight
on these boris
very interesting things are going to
happen as we will discuss
today
one thing which is all beautiful
ultimately happen if you keep floating
down keep adding mask it will break
and the breaking point
is getting dare into third column
and recall that the
ultimate pencil strength
so n_f_l_ over eighty
wendy's value well
becomes too large
that's what it comes down to
then it will simply break
if we
make a case that we have here steel
ralph
for weeks after over eighty is six point
three times sent to the seven th because
i was one remember
then you can look there on the steel
that it will break we will be very safe
because it will break until after over a
becomes
five content to be a so we just factor
of ten away from that there's no problem
even my own will be very safe
because that wouldn't break until
the stresses three times
ten thirty eight
however
if we chose aluminum
if we make the bar out of aluminum
that you're very close food is number
six point three content of this evidence
and so
if you had a little bit more mass and
fight on the programs
your aluminum bar
would break
you see the properties of these medals
are very very different indeed
now before it breaks
reaches situation
that this training is no longer
proportional to distress
in other words we abandon hoops wallets
i will show you also today
was a demonstration
the material begins to before
he begins to
flow inouye
an ailing you take the weights all it
will no longer
have its original likes it will not
return to regional banks but it will be
much longer
and i will try to schedule here
their career
off
stress versus strain
typically looks like to hear i'm going
to plot delta l
over health
and here
over eighty
so this is distressed
and this is the strength
in the beginning
you will see apportioned
that is really a
that's hopeful
when you keep adding force which we will
do by gravity be with his hand weights
on it
bennett stocks to bend over
but the point here
which we called the gillespie limits
and cleveland oh
this portion is no longer linear so even
though small no longer holds
still
if you take the weight off
the wire off the wild
it will still come back to zero
once you have past this point
that is no longer the case
you will not see also that
a small increase or stress
will give a huge
straight
so don't rolled through that that's the
wrongful death
very long all of the southern
little bit of extra stress
i didn't know you were too
the weight off the roads it would not
come back to zero but it'll come back
somewhere to hear sorts prominently
before
in general that
robb gets hot
andy work that you have done
goes into heat
and goes into
the deformation often
of the rock
so it goes like this
and that it goes like this and he would
breaks
this value four f already
which is that
third column there
it will bring
i'd like to discuss richard is
horizontal portion
but have locked we may actually be able
to see that with my demonstration but
it's hard to get exactly at that point
part of the current is horizontal
it means that without any increase
over eighty
the y_o_y_o_ continued to get longer and
longer
and recall that
plastic flow
so this whole portion here
is plastic flow
almost becomes like a liquid
and then by right here
there's something very strange that is
happening
then but it breaks
the stress here is actually lower than
there
this is something i can ever show here
in class
but i can explain to you why that
happens
when your past this point here
the rocks
begins to pinch
you get this
unpredictable rental pigs but somewhere
and will start to pinch
but have you ever use a prime
with the cross-section remuneration
eight
and so act
divided by a prime
will be larger aneta provided by a
if you could do this experiment in a
controlled fashion
and their machines designed to do that
then you could actually law work
f over eighty
sold at the stress actually goes down
but that at all for a private still go
up
and therefore
delta l
no increase
and their machine to a specially
designed to test these
medals
and what they do is they go up in space
small steps or perhaps
so dick tracey is holczer
led by the time they get into the
plastic flow every year
date before they increase
before they decrease its first
delta al gets larger with a decrease in
they continue to decrease it
and so that's the way that they can map
out also this portion
but we will not be able to do that
their metals which are extremely brittle
until he even though to curve would look
very similar has all these correct
teristics
this point then
light
all the rain here so this whole proof
then
squeezed into
small parameter space offbeat
off the street
and so i want you to see most of this
use some of this
and we do that with a demonstration
which we have there
and i will make a
drawing of the basic idea
we have a couple wider you'll get the
dimension comment very shortly
we attached to the copper wire
a wrong
a solid rock
and at the end of the solid brought
is america
whenever
and we're going to hang rates on here
with his network
is a little platform
and candidates at this point
but cannot lower itself platform
is fixed
for those of you who are very close
this is where that platform is that is a
fixed platform
and sort of american only kilts
but cannot go down
and so now
opal's show you
what happens
is wider gets
longer here is the white hat
and it is really
this line here
now the why it has become longer
so the wire is no longer
bipin amount
knocked out
this is not the point
where this
lawrence
his royalties effect
and stored in their work
and i'll be like this
it celtic than ever
refill kit in the roman angle
delta theta
this link
is pal
and we're going to load it down
with a mass and
which we're going to increase
and then we have a
the laser beam
which we shot onto the mirror
baeza been comes in like so
visit the normal premiere work
uh...
but has angle here is dealt a traitor
laser beam
bounces off
and returns
like so and a single of course is also
delta theta
uh... property
and it's been
this is the base of the view that which
i need to the mirror
use the laser
goes into the new york
and thus ballplayer
all that returns although we did on the
wall
so we're going to show you where this is
belt is on the wall
and the law is very far away
distance capital l
up on the wife
and you'll see very shortly
we do it that way
let me first give you the dimensions
orbits
instrument l
the thirty-six enemies
it is pop art
is bart
which has links d
is seven in the house and the news
the distance of the wall
is about sixty meters
radius off the
while you were actually did i get out of
the wife of the papa larger
twenty arkansas buddies
i give it in terms of the diameter
because that's the way that the
manufacturer
gives it to us
and that translates into a
cross-sectional area
all that why you're off two point zero
understand to do my best seven meters
great
all right
noticed that
delta state up
that angle
angle here delta theta
is delta l divided by d
delta theta
equal telltale
divided by t
the light that returns
hits the wall there at a distance l
so why at the wall i can call it delta
why that is at the wall i call that
displacement of delta y
divided by l
will be told alpha theta
uses it small and an approximation it's
a very good approximation
they tied to hang in in radians
it's not help but they don't because you
see here
at the changes over an angle to go
and so delta y
equals two l delta fade out
to al
delta theta
uh... delta l
divided party
and look what we have done i'll
we have converted something that is
imaginable
delta l
which is fractional millimeters
we have convert that to something
on the wall that we can measure
because there's ratio to well over p
you know a case for did i mention that i
have chosen
is about four hundred
and twenty five to psych and
magnification factor
so
if we see this placement of that laser
beam on the wall
or forty centimeters
which is the easy to see
it means that the white live longer
by only one millimeter
so forty centimeters bear translates to
one millimeter there
i think we would see
that laser beam go up four meters it
would mean that the why it would only
have
become wants an even longer
sort is a wonderful way
to magnify the effect in to measure it
so i will not make an attempt
lowdown d
copper wire
or we can actually here
they can he get hurt
so we started airways
we will of course popular brands
we'll write down then how much that lays
a spot goes up on the wall
and then inbetween
increasing
the weights increasing the force we will
take
the masses off
to see whether they've returned with the
length of the
rolled returns to
erection elect
and you will see after a while to get
permanent deformation
and it no longer comes back which
original
length in other words
the basis for will not return to zero on
the wall
stay high
so wrong
if you are
there are wally were hiding behind
maybe we want to move the hugh grant out
of the way
for that
so here is that copper wire which will
be hard to see for some of you with tony
twenty thousand opening stick
and here is that mirror which can
significant tilt
and one is going to boot
rates on here
and then we will take the weight off in
between
and we will try
constructs
stress versus train except
that it is practical for me to book it
is the mass how many kilograms we have
on the air
let me know what a
s you calculate evoke wait it's not so
important now
and he i simply have delta y the keep in
mind
the delta lines always four hundred and
twenty-five times larger
then don't l so we're going to florence
we're going to see
come up with a curve that is somewhat
similar to that point
so wrong if you put on the first
popular graham
the mir always start to also made a
little bit
and so we have to be a little patience
and in the beginning
you may be bored because
we're going to get me a part of the car
so it goes a very slowly very gradually
we have um...
five centimeters
for the first popular graham quit your
weather remove the health care reform
it returns practically to zero
maybe it's a little higher but thats
not very significant
quick to make it one kilogram
oc
unifier
all it off
poets about nine centimeters
nine-tenths of using it in the living
apart
nine to ten centimeters
can you remove the optimal graham wrong
that one can print that was one kilogram
on
have to just wait let them talk a little
it's also leading
it's possible that you already begin to
see
a small the formation
maybe one or one and a half centimeters
a quick question their question mark
there possible
cable what i have to
you know i think it is
or what we moved the question mark
so now we are at
one-and-a-half
so it is strictly linear you would
expect something like fifty
that's what it is fifty sold still doing
quite well can you take them off
one-and-a-half
all that you see no longer
wants to return
its original exits
khalili long than operable deformation
has already approved
and so we're now something like six
enemies
and you won't make it to kilograms
two kilograms
it is linear
you would expect
near twenty
still amazingly linear
discloses i can't see it differently but
all these readings on electric no more
accurate than office any proposal
okay he removed two kilograms
all or a look at that place khalidi of
the formation of a
no longer returns
zero what it is uh...
or call and and all
okay you make a two-and-a-half
you know slowing approaching depart and
what they were going to see
and everybody's going to take off like a
rocket
that was a little bit of extra weight
it'll start
to move substantially
we haven't reached that point yet
but we're close to it
winnow
twenty six twenty five twenty six
still looks quite linear and you take it
off the wrong
no need to take it off anymore because
it's clear that we uh...
that we have permanent deformation no
sense in following that so butter to
make it three kilograms
but what will that will did i say of
course
was the number listed
twenty what
twenty five or so
so we have to riyadh
all that is why it is hanging in there
must tell you
thirty-two dot you make it uh... for it
what about what's going on the wall
the drop my is about to start now
wielded by three thirty
ice at thirty two
still moving
still moving
fifty two
pedals at fifty three
now don't look at
the board now look at at this spot now
can you add remember the number are
fifty-three
you had one kilogram now
look at them
pepin almost twice as long and it is
still moving
still going
still going
hope it will settle going right up my
fifty-three
five kilograms
ratified right
ninety-seven awkward on six ninety-seven
by the nineties
ninety-seven now what's this point
ang
now you can really add that plastic flow
portion
by adding one kilogram look what the
point is it still moving
what will suffice
ninety seven
so we're not six kilograms
all actually that is still waiting for
me to estimate i would say
it's about
double the length of that
stick that we have on the wall and this
tickets two meters long
moving up still more than a little bit a
little more than four meters
forty for me it's just for the right
here
for the rest of his four hundredths
would on seven
go both ways feeling now
but was it
but what i want to do now
i want to get to the breaking point
we can no longer measure the
displacement
but we are very close to the breaking
point now
so we're going to open up to the point
that will break
that allows us to better the
ultimate tensile strength
we're at seven oh
he put it on
overrunning thoughtful uh...
are clark
you because you can't and it was put on
the check you look at the wire
okay to a great kilograms
great
okay that's out for pizza
number of india
so we have one-and-a-half opa kilogram
we have bikes enemy
let me do it is a caller
or give me a point here
and then that while we have about ten
ended one-and-a-half
we have about fifty
and had two we have about twenty
and at two and a half
we have twenty five
i was a little bit
okay idea perhaps when we were little
bit more carefully
causes a great terrific data
kw
food is love it
it
and then we have a two-and-a-half we
have twenty five
all
maisie well hold any of that is
three we have to be true
quarrel
uh...
oc
folks like incompatible
before we have fifty three
no question all
uh... or not
and then byproduct ninety
strata
response
ninety seven
it's here
and then our last point that was always
even have a four hundred here
well that's great
yours four hundred
and what do we have there
six
want to report though i think
last point
event
we don't have the rest
but the problem before this incident
seasons of the great kareoke
buried in the beginning
and start to bend over
over
uh... you draw that line
anywhere you want him
and then it breaks
and so we can all actually make an
attempt
to calculate
you don't want to loose
from the date of course you have to
select portion
where you think that the data i
reasonably linear
so we don't want to list
itself
equals
divided by eight
you have you you creation don't want to
lose
because after vided by eight times l
divided by delta l
we know it's been a whatever works
still on the blackboard there
and so now it's a matter of
where do we think that
foxhole still holds
i think this whole portion would be fine
so we could take this point is not at
this point
because anywhere on the straight line
you'll get the same value priyanka model
is
so i'll do is two kilograms
and twenty senate because i would use
this point
equals two hundred newton's
we have delta y
equals twenty centimeters
threatening self-help
equals
twenty
divided by four hundred
twenty percent
so this is f
by the body
and then we have here delta y
platform font
alexi with us
so at least two hundred
that's right
by this
twenty google rembrandt that we call
them simultaneously
so without working
twenty new tunes
that's right
every
is true
unscented minus seven hundred bite by
gary
unoccupied i don't think switches point
three six
i multiplied by four hundred and twenty
five
edye divide by delta y the tiny delta y
in seven years
so india so its point two
and i got seven point seven times tend
to be
he's not that at all
because i think from what i remember is
that it is eleven
content to defend
that's what it is
soul that is quite amazing for such a
crude measurement that we do here
we can also measure
the ultimate pencil strength
letters weekend
measure the value for f over eighty
when it broke
happened i think but let eight kilograms
but it'll be eighty
divided by
the area that we know
and so it gives me a d
divided by
to times divided by ten to two minus
seven
and that is four times ten thirty eight
morton's
precipitator
this is also
newton's
whisk-broom either
and that's not that
it's a little higher than we have their
but it's a very crude measurement and
don't forget
we were unable
to follow the portion when it was going
down
we only wind up in mass in in in weight
and so that value there
takes into account the decor of comes
down
something we could not
do we didn't have the means of doing
that
percentage strain
is actually extremely low
eighty portion that the corridors linear
you can ask yourself the question that
was dealt a l
provided by l in terms of percentages
during this portion to you
well
we don't know length
openly three six
and when we take the case
where we should have reached the end of
the workflow
ram into space
we have a delta l which is four on the
twenty five times lower than this
so we have twenty
divided by four twenty five
and that is done
four point seven
absent or minus two
but that is in terms of
centimeters and we wanted to improve
meters
so
we have to multiply
by not affect the tentative
lines too
exported since mine's too
divided by point three six
and that gives me
one point three
constantin combine this three jones of
percentages that would put or point one
three percent
for the wire
when it reaches the end of its
books lol parameter space
has only become longer by four point one
three percent
and when the wuyda blake's
in general for medals
it's maybe fifa ten percent longer
than it originally that's a typical
value for medals
barcelona citing the linear portion of
the curve
i can generate
a simple
harmonic motion
want to show you that
wipro
i think it may be a portion of the cover
of rebel strongholds
i could penetrate waits on the ropes
orders on the road and i could but it
also made her
sort of force
if you have
people who live
find eight
uh... delta help
funded by l
that's the force that i applied
soda springs forces opposing that
thirty spring forth as a minus sign here
indicate the direction
and so this
is similar to az gold miners kate that
you have seen richest
spray
at this now
is archaic
and they'll fill these are x
and so you can predict that it will
start to also made it
wasn't angular frequency
omigod
spirit of k divided by m and his
appearance
which is to part
to five
uh... spiro of emal okay
and is now to match that i'm hanging
if we take our coca wire
we know what life
if i take the value eleven instead of
the one that we found that it's very
close anyhow
severed a car or wire
and i'll find depending upon the maps
that i can't wait
applied in any case for cape with his
value k
afaik by constantly before
groupings
so it now i have a moment amassing
montero grandpa
i can calculate
the period of one also nation
and one over the period is the frequency
f
and i believe that is something like
thirty acres
source but also late like this
thirty eight times per second
and if i think two kilograms on it
this frequency would become something
like twenty five hrs
was a higher
mascot me a longer period
you it
the speed of sound
also depends
young small business
without proof
people you will see this in uh... if you
have a cake
eight oh three
i will tell you that the
speed of sound
i'm screwed
jones modelers divided by the density of
the material
and i've listed those there
on the giraffe
audited by the up the script
until the higher don't smoke it was the
height of the speed of sound reason that
it intuitively
so rough pleasing
aiken sort of understandable don't screw
it is hard to see
by having a rock
abar
and i get his bar here abbank i hate it
if his bar were infinitely state
let me jump smog repeatedly height
bend the barcode instantaneously
more here
when i hit it big
but at the bar is not infinitely stated
that has a certain amount of usd city
then what happens
that either
mid-year
and i couldn't you
some kind of
local increased pressure
which is going to propagate dissent
like a pressure way
like stop actually
and that takes time
and all our curriculums model is this
the staff of the material is
the fact that that will go
if you don't want it is very well
material is more or less sick
it will take a longer time
for this bulls
to reach these ants
so it's sort of intuitively pleasing to
me that the stiffness of the material
is related to the
speed of sound
i have here magnesium bart
edited museum bar
has a length l
and i can calculate the speed of sound
for magnesium by taking its
young's motorist
which is very divided by role
which is their and i come up with the
speed of sound
which is about five
well just a second
you look at those numbers they willl
substantially higher than the speed of
sound in the air which is only
some three hundred forty meters per
second
the speed of sound
for magnesium eason fifteen times
larger
than the speed of sound in there
if this bar has a leg to help
this pressure
disturbance
will start to move to the left
and that it'll come back here
so it will have to make a complete
security which i called a purely its
may to compete journey in so many
seconds
two l
divided by the speed of sound
and sort of freak until his bar
the frequency admits it would like to
also make
when i get to the bank
is one over three
and that is the speed of sound budd bike
l for those of you who will take eight
oh three in the future
you'll see a much better the revision
these frequencies this is a poor man's
version
the speed of sound
is about five kilometers per second
the legs of the bar
is about one of the twenty two
centimeters
and so that translates
into our frequency of roughly twenty two
twenty one hundred truths
but a preconceived footage magnesium bar
it's about twenty one of them
and you can hear that
beautiful tall
bolded here
i will bring it to you
the
remember during the course battery
work wrestling
wrist this problem
we had a walk
and we have to strings attached to it
you would want string
here is the block
yet another string
and we're going to put on this year
was forced out
nothing was happening
sort attention here
staff
here
very close to four zach
plus the rate will be
object so here you have quality prime
equals and applause and
until we argue if you increase after i
get the strings are
identical
that had to break first year and then
here because the breaking point
ready force is too large for two
straight
boca refers to you that it occurs here
because you have the extra
but yet
when we took on a very fast
it would break here
and when we for very slowly i will do it
again it would break here and all we can
fully understand
because what does it mean that this
spring is going to break
it means that strength has to get longer
by a certain amount belt that help
before it sets story i'd go to going to
break
for the strength to get longer by
certain among delta l
this broadcast to compound
purple here was a certain four slash but
he calls are made
the block will come down with some
acceleration eight
anytime delta t
it move over to the streets a belt but
it's great
which is that delta alpha
that this sprinkle fuel
but that takes time
to reached that delta al that which it
wants to break and so if i called very
fast
i don't get at that time
and that's why then the wild at the
bottom will break
an invite
who very slowly
the one that the focal point we have a
break and why are you can see it very
well in his
want to which it straight and they're
identical
visit might emerge into safety rope
if i pull very fast
you see the bottom won't breaks i kept
it in my hand
and the problem
he still safe
however
if i repeat this
and i
do it's very gently
was hard to get people
there we go
okay so now i'm going to have slowly
increase the force
i get the brought plenty of time to come
down
plenty of time
an article
at a good week and see you monday
