we'll discuss loss if there's an
acceleration
i'll start with something simple
i have a
motion of an object along a straight
line
nicolette one-dimensional motion
and i'll tell you that the object is
here at twenty one at time t two words
here at time t three ads there
bunty forty year and a twenty-five it
back read what at the wall
and you know you see the
positions in acts
located at that moment in time
i will the fine this
to be the increasing value over acts
it's my free choice but i've chosen this
now
null
we will into juice
what we call the beverage for the loss
of three
i put a bar over it
expense forever etched
we've been talking to you want to try to
keep cool
that we define in physics
at x s ninety two
martin is acts at a time you want
divided by
detoured
minus the warm
that is
art definition in our case
because of the way that i defiantly
increasing value of acts
this is larger
and zero
however
if i take
the average
velocity between team on a key files
that would be zero because they are at
the same position
obsessive zero
if i had
chosen to four and keep to average
velocity between twenty to twenty four
it would have seen
is negative because the upstairs
notice that are haven't told you where i
choose my zero on my tax axes
completely
unimportant forty average velocity it
makes no difference
however
if i had two children
this to be d
directional increasing tax
then
of course the signs reflect
then this would be negative
and this would have been positive
so that iraq's in that you were free to
choose
the germans the science
location where you put your zero
is not important but signs
in physics do matter
signs are important
whether you owe me money or i'll call
you money
the differences only minus sign
but i think it's important for you
now i will give you
not only
the positions
as i did hear
on the x-axis at discrete moment in time
but i'm going to
tell you exactly where the object is at
any moment in time
here you see an axe to diagram
so you see that if you want the object
is a position
exp one
this is the road of the object this is
the straight-line reds moving it starts
here
and it goes to this position
goes to this one that comes back to
p_-forty comes back here
i will tell you now
every
moment in time in between
where it goes
this is now information that is way more
you have the information at any moment
in time
notice
that i know did juries
actually call zero
i'd shows it somewhere here
but i could've chosen id of any other
points
whatever force you will see that it
makes no difference so i have chosen
zero point so that i can make a graph
and now
we will look at the average velocity
in a somewhat different way
say i chose my time tito
history i draw here now this line
tsd
and the angle iveco all fine
and this
or here
michael delta x
and this year
is delta t
and so you could right now
if you're careful about you sign
convention you could write down now that
the average velocity
equals delta x
divided by twelve thirty
the careful
if the angle is positive light gold is a
positive angle
the average velocities positive
but if i
have a negative angle
average velocity would be negative for
instance
between t four mt five
if i draw this line
then this angle here
negative
and so the average velocity between t
four mt five
again if i had
change the zero point
you would have found the same values
forty average velocity the only
difference would have been
the position all of the curve
there's a very big difference in physics
between speeds
philosophy
the average velocity between twenty one
twenty five
is zero
but the average speed
is not
the average speed
is defined
as
the distance travels
divided by the time that it takes to
travel that distance
a lot of the distance
that the object reveled between
fine g_-one and twenty five
well the object
started at a position here on these
x-axis
and that it went up
reached the highest point here
so i'll make a drawing for you here
reached the highest point here
and it went down
net management here
it went up again
comes down again
and its back
and in order to find the average speed
you would not have to know exactly what
this distances
head of this distance
evidence-based int and dismissed
added that distant altogether we're for
instance three hundred meters
and if
the time between
ki wo ninety five we're three seconds
than the average speed would be three
hundred meters
divided by three seconds
that would be hundred meters per second
thirty at that speed would be humbled
meters per second
yes in average velocity
zero
if you look at the location
three three
aunty too
and i bring d three
closer and closer
tito
then days angle of all hell will
increase
and i can go to the extreme that i bring
t_-three
almost like that
the n_ double also i will then be
and gentle
with this point
students will then be
fighting the local
and now you will understand
how we define
instantaneous velocity
at time
which is different from
and average velocity between sometime
intervals
instantaneous
velocity
the and i think a random time t
equals the limiting case
forex
measure at that time keep was dealt a
key
minus acts
measure peptide t_
divided by delta t
and i do that for delta qty
from zero
so saying this
single digits being history on this list
t_-two i'd bring t_-three
closer and closer and closer to keep
tool
and the time between them then goes to
zero
and this
is something that you undoubtedly
recognize
that's the first derivative
opposition forces fine
and i'll continue creation
which is one of the very few
that i want you to remember
extent ada wong
equals
the axe eighteen
mrs wong
must remember northerly ada wong but for
the rest
of your time at m_i_t_
and this could be larger than zero
this could be zero
and this could be smaller than zero
if the angle of all fire
the conventional is positive
and it is a positive value
if it is negative however
when you hear
than it is the negative philosophy
and if the angle of all plays zero
the velocity zero
so it would not look at the spots
we can search for the times that the
velocity zero
so we have to look forward to derail it
is being zeroed it means the
angle alltel being zero
clearly here
reportedly is euro
right here at the starting point
let me tell you object is here with a
zero
when the object is healy's again zero at
this moment in time
mt angola zero
and it is again zero he has a book by
the client's that the velocity is zero
one of the times that the velocities
positive
positive here
velocities positive here still positive
positive becomes negative
negative positive zero
so thats
the definitional the instantaneous
velocity
why is the instantaneous speed
well
speech is not signed sensitive
suppose that the velocity here
just cycle that he wound supposedly
apples plus thirty meters per second
i'd just grabbed his number
out of the blue
and suppose here somewhere
it was michael that veto
suppose doubles minus hundred meters per
second
is is negative
and this is positive
then we would have to say in physics
whether you like it or not
not very pleasing
but you would have to say that this will
all city is lower than that one
because mine is hamlet
is lowered interest thirty
but the speed of course
is higher here because the speed
magnitudes off
velocity
and he's not
signed sensitive so this has the highest
be two hundred meters per second and
this has a lower speed
but this has but what was philosophy
indulge a break game but very important
when you make your calculations
i have always
wondered
what's d
ever to speak with the average velocity
is awfully
now i want you to realize i'm not a fan
of guns at all
but it always intrigued me
how can i measure
the beverage speed
offstage
and i've discussed at this time
people here and we came up recent
easy way to do that
have a wire
goes into the blackboards
y_-one
and we have another wider goes into
blackboard
wider tool
and the separation
is
meets we have to measure that's
setup is here
so this is
why our number one
and this is wider
number two
so you will see d
coming and like this
so i'll make that one
and i'll make this a tool
six to eight setup
and re
fire aboard it
with break this wire at that moment of
time starts
and then did break this wire and that's
when the
pharma stocks
now
i told you
a measurement is meaningless without
knowledge of the uncertainty in your
mission
ordered to uncertainty simple
the distance
and the timing and city
these patients
idle measure for you
d
i have here a large
here's one-liner
use the other wire
i cannot do it any better really then
maybe even office i mean either because
situation is not all that stable i don't
know what happens when the border to hit
the wire
so i would say
it is from the forty eight and a half
centimeters
i cannot guarantee to better then
office centimeter
hundred forty-eight and a half
plus or minus
oprah winfrey centimeters
i wanted to appreciate
that business
of very small percentage ever
he's only five points out of fifteen
hundreds
that is one out of three hundred but
that is only along clear this endeavor
that's very small
that's what we call the relative
then i asked myself the question
i want to measure the accuracy of the
speed of the bullets
to about two percent
that was my goal
how accurate to lead to the timing
i have to make an estimated there with
roughly
how fast a speed of the bolivians and
i would think it is probably lower than
the speed of sound the speed of sound
extreme forty meters per second
i don't know whether it's two hundred or
three or not but it got to be somewhere
in that ball park
off the kind of bullets that we have to
one hundred three hundred meters per
second
let's assume that the speed of three
hundred meters per second just
a wild guess
then it will take five milliseconds
forties bullets
across from here to view
and if i want to make a measurement two
percent accuracy
i have to know this timing
who about one-tenth over many seconds
because one-tenth
over many seconds
is about two percent
so let's check the accuracy
that i need to make the time missions
and so we do have a timer is about
accurate to about
the kind of a millisecond and so
i can
measure of that time
so i'm going to have your some time that
we measure
was a minus
all point one
and we'll do the whole thing
many seconds
but our final answer
in meters
for sex
all right
always have to spin cards
when i do this because
when we do is bullets
that is no kid stuff
and i and i said
really no experience firing guns
this is the bolts
ego
use the bolts
there we go
in place
before i go that i want to check check
the circuit i want to make sure that the
electro nic circuits
properly
your seat
the timing here right
so i do a small test
just to see whether the circuit is
working
should be working
here comes the bullets
you're ready i'm ready
while zero
literacy
flashpoint eights
milliseconds
orange eight is that what you see
five point eight million seconds
five point eight
was a minor xo point one
so outcomes the
average
court speed record velocities the same
thing in this case
one forty eight
point five
point eights
and i have to convert it to me just a
second
to bring to the two hundred
and fifty six
plaza wireless
now all you come in here which you plaza
minuses
this is at one point one third percent
their work
is negligible
through this one
one out of fifty eight is about one
point seven percent so this is the only
one we have to worry about thirty
uncertainty in their is about one point
seven percentage less than two that's
what i wanted and it gives me an error
of about port
meters
for second
and so this
is the results
and you see it's only meaningful
because we have
a great year about
the uncertainties
the measurement
just as we
introduced
average excellent average velocity
i'm going to introduce
ever expect generation
noticed that the velocity
changes here
that brings me to do
next part
the logical part namely
that we're going to introduce
at everett acceleration
and was a little bit of imagination you
can probably guess
what that
looks like
the average acceleration
between trying to keep warm and
twenty-two
would then be the velocity at twenty two
mind of the velocity apart if you want
divided by he combines do you want
that i mentioned his legs for seconds
for times square towards meters per
second
this event for one-dimensional
situation
there's number can be larger than zero
can be equal to zero
and it can be smaller than zero
in our case g_-one pretty tool
here
nor does the velocity zero as a start
and he begins to increase because the
angle of all for increases
he paid all that matters
angled increases
so in our case
forty one twenty two
ever take celebration
is larger
than zero
look at the angle
however
if you take the average acceleration
that's what between team moment e five
that is
smaller than zero
because a year
the velocities zero
which do you know the velocity is
negative
so if you substituted in their
you get an average vote acceleration
which is smaller
sort of science in the velocity and the
signs the average acceleration
depend crucially on how i have defined
by increasing value of x
not where i choose my zero point
reverse the direction of increasing x
that all my sons
change
so you can also write down then that
average acceleration if you like that
delta v divided by delta qty
but you must be careful
because the delta he's time-sensitive
obey your sign
convention
i have here
the tennis ball
and i can buy unsustainable
i can throw it down
and letters assume just for simplicity
that it hits the floor at about five
meters per second
and that's
so very very good tennis ball
and that is also bounces back
with a
velocity over about five weeks
i will shows this
to be my increasing value acts
and so it hits
the floor like this
that means
velocity at which it hits the floor is
minus five meters per second
it bounces off
there comes
and it goes up
plus five he was perfect
accord is v one
and i call these the tube
so what now
is the average acceleration well i would
have to know
the time that it takes
for this
changing
direction and it would recall that the
impact time
i would say in this case the impact on
delta t
is probably
about a hundred sort of second
and so my ever check generation
would be needed to
my knees he won't
that is plus five minus minus five
that it's time
divided by ten to minus two and that is
processed
one thousand
for second script
i have all pipe observe carefully the
signs
if now why say aha i don't like this
i want to call this
the value of increasing acts
no big deal this will become close
it will become a minus
and then this will become a minus so
then the acceleration
is minus thousand leaders
the second screen
i have also here
the tomato
and i have here
some eggs
now imagined all the time
throw the tornado down
or for that matter
and that they hit the floor at five
meters per second
i could do that
they would not come back up
they would go
so therefore the changing velocity would
not be ten
apart from the sign that you have to
think about but it would only be fine
these suspect
the impact hein
would probably be
watch longer maybe quarter officer
so therefore
the average acceleration
during the impact
would then be only five
divided by one-quarter
would be something like
meters per second square
now whether you call it plus or what do
you call it minus twenty meters per
second square the pendulum
your convention of what you call
increasing x
but the eggs and the tomato don't care
what you called mine is and what you
call plus
where the acceleration is minus twenty
meters per second script or plus twenty
meters per second correct
you better believe it
the ad will break
so is only in your convention that it
matters
but of course the physics
not change
the eggs
gordon care less
what you have chosen
sign convention
something breaks because the magnitude
of acceleration becomes too high
that's why
something breaks
a few days ago
i saw a short homes moving
and there was a guy
who felt on the floor
marble floor
benefit
was lying there motionless
he was watson
watson temperature recalls what happened
protocols walks over to the car
touches him
he says
he crushed her skull
he looked very intelligent i must say
what he said
he crushed is cool
and i said to me
that's really physics connections to
eight along all the way
a modest a really most small city when
he hits the floor
he hit the floor like a billiard ball
the guy was bolts for wanting
and so we in fact i was a very short
and when in fact i was short even if you
hit the floor is a modest beat the
acceleration is high
was too much
that's right
is school
was crushed
sold what matters is this
changing velocity and the impact on
now i want to make won't last
stepped from hemorrhage acceleration
we want to go
acceleration any moment in time
just the way we did that
velocity
and that now is the natural step
the acceleration at any moment in time
limits
for bill clinton
goes to zero
measure closed out the people
miners vp
divided by
help
is instantaneous
acceleration
and this
you were recognized is the first the
redacted of philosophy
versus time
which is also
seconds heredity
opposition to a suspect
and so here comes the second equation
i really want you to remember
forever
and ever
than ever
that the acceleration
d_d_t_
which is also
two x
in conflict
weekend
go to our plots
and we can ask ourselves the question
though
where is the acceleration zero where is
it larger than zero and where is it
smaller than zero because this value
candy
larger than zero equal to zero
and smaller them
and no
you have to be
very careful
when you try to the right that from this
plot
have to be very careful
because you and i have no good feeling
for second derivative
velocities easy all you have to do is
looking at all-star
but when it comes with the secondary if
you have to see how old place changing
right here
the velocity is not changing
saudi acceleration everywhere you must
be zero
panama city is increasing
tortilla acceleration must be larger
than
zero here
here
the velocity is almost constant is
almost a straight line
or does that mean
forty acceleration
zero
exactly
here why did make this rattling perf
the velocities positive here but we
decided to negative
forwarded me forty acceleration
naked if you got it
and so you can now roughly finds
the what
acceleration is positive whereas
negative
and where
that's due
a straightforward for example
the way
that you could expect that on an
assignment
if you were extraordinarily lucky
you might even get something like that
on exam
very straightforward i'm going to give
you
the position acts
as a function of time
and then ask you
lots of questions about it
thought his example isn't working
example
x
equals eight
minus sixty
philosophy square
solis tells you whether pat ready object
this any moment in time
and that is being meters
what now is the velocity
at any moment in time
well that's weird
the relevant to the exp t
and i use
the following
x
peeked through the power and
most of you
should not be executed
you can and times p with apollo and mine
as well
that's all i'm using
sold innovative over eighteen zero
i get here minus six
i gave you plus
booty
it would be needed for a second
and the acceleration
i have to take the derivative off the
velocity
i get flustered
so notice that that acceleration
response and in time is not changing
but the velocity
is changing
well at time t equals zero
i've started
probe a little bit i want to get a
feeling for what is all direct is doing
at time people zero
axis prostates
the velocity is minus six
meters per second
any acceleration
equals plus group
i could also ask myself at what time
is actually pull zero
what i the times that x's zero
well i have to solve this second-order
equation which is something that you've
all done
in high school and you will find that
that's the case
when the time
is plus two
and when the time is plus four
take the postal
that makes this
for clues eight
twelve
minus six times too
you see the two were can you check that
that
four also works
just for my curiosity when is the
velocity zero
all that easy
that's when this equation easy road over
that's when people straight
what's is at that moment the position
all i substitute
people freezing here
in addition we minus one
except equals
so no
i'm ready
and plots acts as a function of t
it's of course rattler
and i use this information
that we have just
right
comes my fault
that this big
increasing value x
let this be eight
and that is b_-minus wong
this is the time axis
iva zero here
and so i want to cover about saving
about six seconds
so i have
through
four
now i'm going to use this information
in order to
give you a court which is similar to
that one except this is a simple one
which is just that
so i know that uh... trying to you call
zero
the object is it
position eight
i know that exit zero
that exit zero
at the time
through at the time four thirty object
is here
at this time
and at this time
and i know that time people three
it is a position might as well
but all that is here
that also noted the velocity zero
so we can check that
and so if i make
this plot no
then we will get a corporate sort of
like this
and then delete notice the velocity uid
zero
yang golfarb
equal zero
you objects starts out at do you call
zero
reason negative philosophy
you can see that
the object of people here which here
this is ready object is i hope you read
i thought you object is never here
this is the rotated the one i mention
will track on with the object is sitting
the object is here and it starts going
in this direction
if it starts going in this direction the
velocity must be less than zero and
indeed it is it's minus six
there is the acceleration purchase plus
two design action
the acceleration says i don't want you
to go down
i wanted to go up
well velocity says sort all i can do is
slowly slowly change
and that's what it's doing
is slowly changing the velocity
and there comes a time that the velocity
is zero
thirty old echoes donk
the velocity changes
and when it is that position minus one
that has come to a grinding halt
and now it is returning
these positive value of a is now
increasing
the velocity
and that's what you see
i_d_f_ will bet you wouldn't nickel
that if you substituted that equation
equals four
that the velocity better be positive
it has changed from a mine assigned to
plus sign
because of the positive acceleration
i bet you a nickel
equals four
what is next
avoids the we want to know him
eight my mistake
plus two meters per second
physics work d is now plus two meters
per second
so all that information is in their but
i wanted to be able
two also
digestive don't look at that correct
adjust some bill uh... parabola some
dunkirk
flight to imagine what is happening
and only then
do you get some insights then you really
begin to
in your brains
i know i would like to write down
eight most general forum
the equation
fort the position
and the velocity as a function of time
four-to-one dimensional motion
rabbi t acceleration is constants
so it's going to be one that mention it
again
and we have a great
is going to be a constant
zodiac regime that i write down these
the most general way that i can write it
down
so we going to get acts
equals some number c_-one
plus something too
feinstein
course on fees three
constance crayons
and notice all over it erased my example
my example is gone
that you would see this wasn't a forward
and here we had
uh... what did we have minus
we have minus sixty and we have plus
wonky squid
so you recognize these three
i can now
thank you
derivative
and so i get
situ
plus
t_-three
feinstein
and then i get the acceleration
equals
and now we get some insights
into
qua these quantities
clearly x one
assy rom
the position
of except kind people zero
for which we often right
an ac zero
identi
is zero
that is where axes
c_q_
is really the velocity
a concave equal zero because mintier
zero
t_-two
and the acceleration
is not changing respond
is do
c_-three therefore c_-three
the acceleration
but it gives you some insight into
meeting all of these quantities
and you can see you can read now some
some physics in there
c_-one c_-two and c_-three
an independently b even zero
larger than zero or negative
makes no difference each one of these
combinations
of alex possibility in physics
when we have gravity
object
influenced by
the gravitational acceleration
and the gravitational acceleration
is a constant
every right often for that
gravitational acceleration
the leather g
when i drop in object
or throw it vertically up
or throw a totally balanced all
one-dimensional
it comes to a man who when i throw it at
an angle
i keep it one eventual
the acceleration is always the same
and that the genie
gravitation acceleration
in boston
nine-point eight zero
meters per second square varies a little
bit for different places
this gravitational acceleration
is independence
of the mass of the object
that are dropped
of the speed of the object
of the chemical composition of the
object
the size of the object love the shape of
the object
assuming
that we have no edta rec assuming that
these experiments are done
in vacuum
you did all of these that the
gravitational acceleration
is independent of all these quantities
by no means
is it true
we think so
i want to do appreciate that it is not
obvious and it cannot be proven
from first principle
remember last time
we dropped an apple
from three meters andrew drop another
one
one-and-a-half leaders
and in your second assignments
which i haven't seen yet i'm asking you
to calculate the gravitational
acceleration for me
using these both
experiments and of course
i want you to also tell me what you
uncertainty is in your final answer
and i'd like to help you
a little bit
to set it up
and also
to get these equations
in terms of
gravity
whenever we deal with gravity
we get
the g_m_ there
so suppose
you are the object
a time people zero
with the apple
and i
call deposition x zero article that zero
i'm free to chose might zero position
and i drop it
zero speed i just let it go because
that's the way
we did it in class
the old it goes down
and it hits the floor
the general equations now
which clearly gravity if i call this the
increase in value over x
you can choose it differently
this is my choice today
the following
x
equals
x zero
lesbian zero key
plus long-haul
piece graham
and you know
zero
meters per second
the velocity
at any moment in time
equals the zero
plus
g_t_
any acceleration
is constant it's anthony g
uh... in my case i have chosen people
zero x zero
zero and i've chosen this zero
so these co
and so you see
many object is here which is
three meters below this point
and you know the time i would talk to
get there
but you cannot calculate
x would be ten three meters that's when
it's here
we made a measurement in class how long
it took so you know the time
and so you can come up with a value
g_e_ and you can do that for both
measurements
and of course i want you to tell me
also what the uncertainties
those measurements
remember that we derived
last time nazi
at the time that it takes forty apple to
full
will see crimes that square root of
eighty over g
and we never knew what that cmos
i get a demonstration to show you that
the time is proportional to discourage
never knew what that she was
now you know because now you have the
equations here
and you'll see
that that's the
clear greek was the scream too
i could not be arrived at from my
unanswerable analysis
now
i won't you too
relaxed
and at the same time
yet a little bit alerts for change
look at this situation vehicles ji ki
that means when i drop on apple and i'm
going to drop another one today
that need a lost city increases with
time
so a fight
stroked his apple what it was falling
i would see the separation
strokes to increase with time because
the velocity
brought up was fun
i have here an apple or i'm going to put
up a lot
about three meters from the floor
three nevis
soul the heights history needs
approximately
we know from last time remember we did
it that was about seven hundred eighty
million seconds to hit the floor
i will just around at all but i think
about it about
a tenth of a second
just to get an idea
if i can
fresh maestro beats
twice per second
to hertz
so much strobe
is three times per second
i'm sure hit that ball but it's falling
twice maestro polite
i don't know where it is though
because when we stroll bits and ran at
the apple go the two are not
synchronized so maybe the first time
that bill
like brings it may be here
and the second time it may be here
but it's also possible that the first
time it's here
and the second time is there
and so depressing i want to do is to
test your own witness
we will blink
you will tell me where you see them
we will take a picture
we will take picture which will show is
exactly where those two balls were
but that's the first witness this
so get ready for this
and then
we will do a second one
which is even more
intriguing
so now i have to first
lower this albert
so that we get a nice dark
background
there we go
fingerprints on it it's not so
black-and-white
earliest
that's the background
what am i doing i need to do everything
i could wind up up
fight is always a bad day for me
and i'm going to bring up a lot
there's a
for metal gear
electro magnets
and so i
there were six years with the
electromagnetic activate it
very similar to what we did
last time we have to putting up a lot
and apple
will
but now i have to start the year
probe
that's about
towards that's about to flesh is seconds
and i'm going to make it
it's black
pitch black
white school
i will come down three two one zero
and bob bear was behind the camera open
the shutter when i say one
and when i say zero to bowl will fall
so
you mail always see the bowl in its
highest position that may not combat of
course because
it makes the flesh is in the time
but the shutters open and that i drop it
ordained purity
i'm reading make it as dark as we can
well be ready
everyone ready
you don't look ready
the four zero
so let's look at it again
in slow motion
resonable
local boy that's the boy you tried at
two ten times you never
through that again
sold now we have developing that picture
and
i would like you
to tell me where you saw the bull
where were they were up late
where was the first one how much how
much hot below two highest point
what it is much
the first one
and then the second one was pretty low
then
sounds interesting
will take a look
well the pictures
developing
i'm not going to test
you real lives
i'm going to
stroll reacts
wasn't unknown frequency unknown to you
i will tell you what secret it's a
higher frequency
you're going to see more balls
on the way down
i'm not going to ask you
where they are exactly all i wanted to
tell me afterwards
how many russell
condom
as its polls you know we have only hope
ornate seconds
well part of the picture come out
while you're good
your good was very high actually first
uh...
first-class very high
misleads
you did very well
we're going to start now was the second
is the audio restored
so i uh... activated the magnet began
charities
okay thank you both
okay bob
if you're ready
i'm ready
going to make it is dark as we can
so i wanted to tell me how many
balls will you see all well aware have
to change your mind witness
come up with our might lead
what do you think
blythe ready
well be okay
one
well
who saw three
four eleven oh four
five he has a five there's a five
notified
withdraw stakes
wow seven
nine
who's just cellmark
one at a real rhetoric like it
well i'll tell you what standards
tended to dole point eight seconds
depending upon where you had its are
lucky you are a love so u
your leaders the
or maybe eight
bolts
it was a good test
and for those of you
thought that it was only
that only sulphide
there you see them that's count them
let's count them together
isn't one
through three for five six seven this is
about
so for those of you who sulfides i would
take take some rest this weekend you'll
need it
but i'll need it to see you monday
