No Springs--Honest Weight (Speed question)
Daniel P. B. Smith
New York. Evidently the Toledo Scale company must have been a sponsor,
because Toledo Scales figured in several of the exhibits. The huge
Willamette Meteorite was on display, on a platform which was part of a
giant scale, and see how much the meteorite weighed and how very little
the needle moved when you stepped onto the platform yourself.
But the best exhibit was "Your Weight on Other Planets." This was a row
of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
was a standard scale which showed your weight on Earth. Others were
calibrated to show your weight on the Moon, Jupiter, etc.
It really sounds dumb, but actually that exhibit was brilliant. There
was something about it that was instantly appealing to a child's mind.
It was quickly grasped and it made its simple point in an unforgettable
way. And, after all, realistically, stepping on that faked-up Toledo
Scale the closest _I'm_ ever likely to come to walking on the Moon.
OK, the puzzle.
In a burst of nostalgia NASA decides to send another flight to the Moon,
and they decide to conduct a ooperative teaching venture with the Hayden
Planetarium. As well as hitting up Toledo Scale for some
product-placement payola.
NASA decides to weigh an astronaut on the No Springs--Honest Weight Moon
scale at the Hayden, then _ship an actual Toledo Scale to the Moon_ On
arrival at the Moon the astronaut can be weighed there, and all the
schoolchildren can see that the "Moon" scale at the Hayden was telling
the truth.
Quick, now: in order to get the "right" answer, should the scale they
send to the Moon be the Hayden's "Moon" scale, the Hayden's "Earth"
scale, or a scale calibrated in some other way?
--
Daniel P. B. Smith
Preferred email address: dpbs...@world.std.com
Alternate email address: dpbs...@bellatlantic.net
"Lifetime forwarding" address: dpbs...@alum.mit.edu
Visit alt.books.jack-london!
Daniel P. B. Smith
When I was a kid, my mother used to take me to the Hayden planetarium in
New York. Evidently the Toledo Scale company must have been a sponsor,
because Toledo Scales figured in several of the exhibits. The huge
Willamette Meteorite was on display, on a platform which was part of a
giant scale. You could see how much the meteorite weighed and how very
little the needle moved when you stepped onto the platform yourself.
But the best exhibit was "Your Weight on Other Worlds." This was a row
of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
was a standard scale which showed your weight on Earth. Others were
calibrated to show your weight on the Moon, Jupiter, etc. I believe of
them displayed your weight on the Sun, despite the problems involved in
THAT thought experiment.
It really sounds dumb, but actually that exhibit was brilliant. There
was something about it that was instantly appealing to a child's mind.
It made its simple point in an unforgettable and quickly grasped way.
And, after all, realistically, stepping on that faked-up Toledo Scale is
the closest _I'm_ ever likely to come to experiencing a walk on the
surface of the Moon.
OK, the puzzle.
In a burst of nostalgia NASA decides to send another flight to the Moon,
and they decide to conduct a cooperative teaching venture with the
Hayden Planetarium. And to hit up Toledo Scale for some
product-placement payola.
NASA will publicly weigh an astronaut on the No Springs--Honest Weight
Moon scale at the Hayden, then _ship an actual Toledo Scale to the
Moon._ On arrival at the Moon the astronaut will be weighed there, and
all the schoolchildren watching on television can see that the "Moon"
scale at the Hayden had been telling the truth.
Quick, now: in order to get the "right" answer, what scale should NASA
send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth" scale,
or a scale calibrated in some different way altogether?
Daniel P. B. Smith
B. Smith" <dpbs...@bellatlantic.net> wrote:
> When I was a kid, my mother used to take me to the Hayden planetarium...
> The best exhibit was "Your Weight on Other Worlds." This was a row
> of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
> was a standard scale which showed your weight on Earth. Others were
> calibrated to show your weight on the Moon, Jupiter, etc. I believe of
> them displayed your weight on the Sun, despite the problems involved in
> THAT thought experiment....
>
> OK, the puzzle....
>
> NASA decides to send another flight to the Moon,
> and they decide to conduct a cooperative teaching venture with the
> Hayden Planetarium....
>
> NASA will publicly weigh an astronaut on the No Springs--Honest Weight
> Moon scale at the Hayden, then _ship an actual Toledo Scale to the
> Moon._ On arrival at the Moon the astronaut will be weighed there, and
> all the schoolchildren watching on television can see that the "Moon"
> scale at the Hayden had been telling the truth.
>
> Quick, now: in order to get the "right" answer, what scale should NASA
> send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth" scale,
> or a scale calibrated in some different way altogether?
PROPOSER'S ANSWER:
[Spoiler space]
The slogan should be "No Springs--Honest Mass." A Toledo scale is a
form of balance. It indeed has no springs, but it works by balancing
masses. On the Moon, an astronaut would weigh about 1/6th what he or
she would weigh on the Earth--but so would the balance weights inside
the scale.
Thus, if an astronaut steps on a Toledo scale, the dial reading will
always be the same, regardless of the local value of "g." If a
165-pound astronaut steps on a standard Toledo scale on the surface of
the Moon, the dial will point at 165 pounds just as it does on the
Earth. And if the astronaut steps on the Hayden's Moon scale, the dial
will point at 27 pounds just as it does on the Earth.
In fact, the entire "Weight On Other Worlds" exhibit could be set up on
the surface of the Moon and would still be accurate. The Earth scale
would still show what the visitor's weight would be on the Earth, the
Moon scale would still show the visitor's weight on the Moon, and the
Jupiter scale would still show the visitor's weight on Jupiter, and so
forth.
So if NASA wants an accurate reading of the astronaut's weight on the
Moon, they need to send along the Hayden's Moon scale.
Leon Garde
> When I was a kid, my mother used to take me to the Hayden planetarium in
> New York. Evidently the Toledo Scale company must have been a sponsor,
> because Toledo Scales figured in several of the exhibits. The huge
> Willamette Meteorite was on display, on a platform which was part of a
> giant scale. You could see how much the meteorite weighed and how very
> little the needle moved when you stepped onto the platform yourself.
> But the best exhibit was "Your Weight on Other Worlds." This was a row
> of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
> was a standard scale which showed your weight on Earth. Others were
> calibrated to show your weight on the Moon, Jupiter, etc. I believe of
> them displayed your weight on the Sun, despite the problems involved in
> THAT thought experiment.
> It really sounds dumb, but actually that exhibit was brilliant. There
> was something about it that was instantly appealing to a child's mind.
> It made its simple point in an unforgettable and quickly grasped way.
> And, after all, realistically, stepping on that faked-up Toledo Scale is
> the closest _I'm_ ever likely to come to experiencing a walk on the
> surface of the Moon.
but did that make you an expect on toledo scales ?
do you know how that work ?
they are a balance beam that automatically readjusts
the position of the balancing mass and displays that position
on the needle ?
ok so they are truly "no springs" scales.
> OK, the puzzle.
> In a burst of nostalgia NASA decides to send another flight to the Moon,
> and they decide to conduct a cooperative teaching venture with the
> Hayden Planetarium. And to hit up Toledo Scale for some
> product-placement payola.
> NASA will publicly weigh an astronaut on the No Springs--Honest Weight
> Moon scale at the Hayden, then _ship an actual Toledo Scale to the
> Moon._ On arrival at the Moon the astronaut will be weighed there, and
> all the schoolchildren watching on television can see that the "Moon"
> scale at the Hayden had been telling the truth.
> Quick, now: in order to get the "right" answer, what scale should NASA
> send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth" scale,
> or a scale calibrated in some different way altogether?
The moon scales are hopefully accurate.
(although this experiment will not prove they are accurate,
as they will show the same reading as they do on earth whether they are
accurate or not ).
Whether the mass was made 10 times bigger ( or whatever factor
required to adjust for the different of earth gravity to moon gravity. )
or whether the printing on the readout was adjusted, the results is the same.
Factor is Acceleration due to gravity on earth
divided by acceleration due to gravity on moon
This is the only correct way to calibrate balance beams for use
on the moon.
(ie change the printing on the readout, or make the balancing mass(es)
10 times bigger...)
of course, if spring scales (or equivalent) are used
then they do not require any adjustment apart from zeroing.
It is not clear that you rule out any equivalent of a spring
when you say "no springs". I have not inspected every
toledo scale, so I cannot say which mechanisms were used in them.
but i assume that only balance beam principle scales were used.
(It is ambiguous if you included or excluded zeroing,
which kind of answers the question about whether the scales
use the balancing principle ( or hookes law, or equivalent)..
zeroing is only required for a hookes law principle scale,
balance beam principle scales once zeroed on earth are zeroed for everywhere ,
unless complex mechanisms bring air pressure into the equation .. )
leon
Daniel P. B. Smith
> but did that make you an expect on toledo scales ?
> do you know how that work ?
>
> they are a balance beam that automatically readjusts
> the position of the balancing mass and displays that position
> on the needle ?
>
>
> ok so they are truly "no springs" scales.
Scales of that style were enormously popular for many decades and many
are still in use. Not only did they bear the slogan "No Springs--Honest
Weight," but many of them were transparent and visibly showed their
inner workings, or enough to make the principle of operation clear.
The platform is connected by a linkage and a set of gears such that
downward force on the weighing platform forces a pair of weighted
pendulums (pendula?) to rotate outwards from the vertical. At the same
time, the mechanism rotates the hand on the dial. The motion of the
dial is geared-up; I don't know the quantitative details, but say the
dial rotates perhaps 300 degrees as the pendulums are displaced outward
by 15 degrees.
In other words, in principle the scale works by finding the value of A
for which
P = C W sin(A)
where A is the angle by which the pendulums are displaced from the
vertical, W is the weight of the pendulums, and C is a constant
involving the length of the pendulum, linkages, and gearing, and other
factors.
To a casual glance, the scale on the dial appeared to have graduations
at equal distance. I don't know whether that's just because sin(A) is
closely proportional to A for small A, or whether there were clever
features of the mechanical design that linearized the relation.
Matthew T. Russotto
}
}But the best exhibit was "Your Weight on Other Worlds." This was a row
}of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
}was a standard scale which showed your weight on Earth. Others were
}calibrated to show your weight on the Moon, Jupiter, etc. I believe of
}them displayed your weight on the Sun, despite the problems involved in
}THAT thought experiment.
}
}Quick, now: in order to get the "right" answer, what scale should NASA
}send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth" scale,
}or a scale calibrated in some different way altogether?
You haven't described the method of operation of the scale, but I
suspect (given the "no springs" slogan) the "moon" scale should be
sent, as the scales actually probably measure mass.
--
Matthew T. Russotto russ...@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."
Dick Christoph
The puzzle you pose is interesting. What caught my eye was this:
> But the best exhibit was "Your Weight on Other Worlds." This was a row
> of Toledo Scales, each with the slogan "No Springs--Honest Weight." One
> was a standard scale which showed your weight on Earth. Others were
> calibrated to show your weight on the Moon, Jupiter, etc.
So they altered the non-earth scales to report different results and yet
left the sign saying
"No Springs - Honest weight", Wouldn't this raise doubts in the public's
mind about the honesty of weights determined by Toledo Scales?
Just a thought.
--
-Dick Christoph
dchr...@minn.net
http://www1.minn.net/~dchristo
"Daniel P. B. Smith" <dpbs...@bellatlantic.net> wrote in message
news:dpbsmith-0FF659...@news.cis.dfn.de...
John Seeliger
<01dq3t83ea4dtufg7...@4ax.com>...
> Here is sort of a follow-up question concerning scales and balances.
>
> Of course, we are all aware of the digital electronic SCALES available
> today that have no moving parts. My question: Is there such a thing
> as a digital electronic BALANCE with no moving parts?
There might be some type of semiconductors that will change their
conductivity based on the weight I guess. I don't know. I do know that
crystal oscillators in quartz crystal watches work by passing electricity
through the crystal causing it to oscillate at a period determined by the
cut. Furthermore, the inverse effect, piezoelectricity can be generated by
applying pressure to a crystal, of crunching lifesavers with your teeth in
a dark room.
Also, there are pressure sensors, like on the throttle of an F-16 that
sense pressure. I don't know if it's entirely electron or if they have
hydraulics in the sensor. I had a college course "Engineering Measurement
and Instrumentation" that talked about all kinds of sensors (ex. Hall
effect, humidity, metal detectors, etc.). Not sure if we had pressure
sensor. Might have though.
Rich Grise
gauges. It'd be pretty easy to set up a balance with a
strain gauge (or load cell) under each pan - oh wait,
you said no moving parts. So I'm guessing you mean
zero point zero etc. deflection, not 0.00000000001"
deflection, right?
Cheers!
Rich
jbuch1
Because of finite elastic modulu (lack of unobtanium), when force is
applied to any piece of solid, there is motion. But is that then a
"moving part"?
Moving part could be:
the beam in a beam balance,
the spring in a spring scale,
the substrate strain in a strainguage,
the substrate strain in a piezoresistive element.......
It looks to me like it isn't a difference of kind, but is a difference
of degree.
Jim
--
-----------------------------------------------
For a keepsake quality gift for young girls,
a personalized adventure book:
John Seeliger
> Sounds like somebody should define "moving part".
>
> Because of finite elastic modulu (lack of unobtanium), when force is
> applied to any piece of solid, there is motion. But is that then a
> "moving part"?
>
> Moving part could be:
> the beam in a beam balance,
> the spring in a spring scale,
> the substrate strain in a strainguage,
> the substrate strain in a piezoresistive element.......
Yes, that thought did cross my mind and I should have pointed out that
there would necessarily be some deflection when a load is placed on a
non-rigid object and rigid objects only exist in physics and statics and
other engineering textbooks.
Gene Nygaard
Weight does not vary on different planets, as the term weight is used
in medicine and physiology and in sports.
Therefore, the Hayden's "Earth" scale should be sent to the moon, and
it will give the accurate and correct weight, the "Honest Weight, No
Springs" that we are looking for. It will, of course, be essentially
the same as the weight would be on earth, maybe just a slight bit more
because of no atmosphere to buoy up the person being weighed more than
it buoys up the counterweights.
Having a "Honest Weight, No Springs" scale that measures something
other than kilograms, or pounds in their normal, legal meaning as units
of mass, is nonsense. A Toledo Scale should read essentially the same
on the moon as it does on the earth.
Of course, physics textbooks and science museum exhibits have often
used a different definition of the ambiguous word "weight" in this
context, ignoring the well-founded conventions of medicine.
This medical definition is, of course, quite legitimately and properly
called "weight." This isn't a question of physics, but rather of
history and linguistics, and of the law.
The word "weight" entered the English language over 1000 years ago to
mean exactly that, the quantity measured with a balance. This "honest
weight" is of course a measure of mass, not of force. The force
definitions of weight now common in the jargon of physics are much,
much newer--first appearing less than 300 years ago, probably in the
1720s.
Consider the many ways in which we use that meaning of weight today, in
addition to human body weight in medicine and sports: "net weight" in
the grocery store (pounds and ounces appearing on U.S. labels are every
bit as much units of mass as the grams that appear alongside them here
and standing alone most everywhere else); the "troy system of weights"
still used for platinum, gold, and the like (there is no troy ounce
force, and never has been); the phrase "weights and measures" as in the
International Bureau of Weights and Measures (in the introduction of
their SI brochure, they explain that for many years they were only
concerned with standards of length and mass); "carat weight" of
gems; "atomic weight" of elements; "weight classes" in wrestling,
boxing, and judo; etc.
Consider also the NASA doctors who study the "weight loss" of
astronauts in space flight--a search of the NASA pages will confirm
that they indeed to call it exactly that.
See NIST Special Publication 811 (1995 ed.), _Guide for the Use of the
International System of Units (SI)_ by Barry N. Taylor (NIST is the
National Institute of Standards and Technology, the successor agency to
the National Bureau of Standards as the U.S. national standards
laboratory):
In commercial and everyday use, and especially in common
parlance, weight is usually used as a synonym for mass.
Thus the SI unit of the quantity weight used in this
sense is the kilogram (kg) and the verb "to weigh" means
"to determine the mass of" or "to have a mass of".
Examples: the child's weight is 23 kg
the briefcase weighs 6 kg
Net wt. 227 g
*****
Note that there is no confusion here. This is a quite honest and
legitimate meaning of the word "weight" and when weight is given in
kilograms or in pounds mass (the primary, legal definition of pounds,
much older than pounds force) those are usually the proper units for
that weight.
--
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
Sent via Deja.com
http://www.deja.com/
David A Karr
>> One [scale]
>> was a standard scale which showed your weight on Earth. Others were
>>
>> [...]
>> NASA will publicly weigh an astronaut on the No Springs--Honest Weight
>> Moon scale at the Hayden, then _ship an actual Toledo Scale to the
>> Moon._ On arrival at the Moon the astronaut will be weighed there, and
>> all the schoolchildren watching on television can see that the "Moon"
>> scale at the Hayden had been telling the truth.
>>
>> Quick, now: in order to get the "right" answer, what scale should NASA
>> send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth" scale,
>> or a scale calibrated in some different way altogether?
>
>in medicine and physiology and in sports.
In other words, you think the entire "Weight on Other Worlds" exhibit
at the Hayden Planetarium was a complete and utter fraud.
In that case, merely sending the correct scale to the Moon isn't
enough. In order to get the "teaching experience" right, you first
have to correct the "Moon" scale at the planetarium so that it shows
the correct "weight" --i.e. (according to your definition) the same as
the "Earth" scale shows, since "weight does not vary on different
planets." At that point it is then correct to send the "Earth" scale
to the Moon to do the weighing there. Of course in that case, your
answer is also equivalent to sending the "Moon" scale to the Moon as
Daniel's solution prescribed.
So in fact you're not disagreeing with the solution, you're
disagreeing with the problem setup (i.e., with the initial calibration
of the scales when they were being prepared for display at the
Planetarium, not with the choice of which of those scales to send).
OTOH, all your reasons why the "weight" measured by the scales should
actually have been "mass" are predicated on Earth-bound thinking which
is common even among scientific and technical people--but which
doesn't say anything about the fact that you could jump higher on the
Moon than on Earth. (OTOH, the fact that your hang time would be
greater on the Moon is not due to the reduction in your "weight" in
the sense of "force," but to the fact that your mass meanwhile remains
the same.)
--
David A. Karr "Groups of guitars are on the way out, Mr. Epstein."
ka...@shore.net --Decca executive Dick Rowe, 1962
Lee
"David A Karr" <ka...@shore.net> wrote in message
news:TNv%5.1209$JG.1...@news.shore.net...
: Gene Nygaard <gnyg...@nccray.com> wrote:
: > "Daniel P. B. Smith" <dpbs...@bellatlantic.net> wrote:
: >> But the best exhibit was "Your Weight on Other Worlds." [...]
: >> One [scale]
: >> was a standard scale which showed your weight on Earth. Others were
: >> calibrated to show your weight on the Moon, Jupiter, etc. [...]
: >>
: >> [...]
: >> NASA will publicly weigh an astronaut on the No Springs--Honest Weight
: >> Moon scale at the Hayden, then _ship an actual Toledo Scale to the
: >> Moon._ On arrival at the Moon the astronaut will be weighed there, and
: >> all the schoolchildren watching on television can see that the "Moon"
: >> scale at the Hayden had been telling the truth.
: >>
: >> Quick, now: in order to get the "right" answer, what scale should NASA
: >> send to the Moon? The Hayden's "Moon" scale, the Hayden's "Earth"
scale,
: >> or a scale calibrated in some different way altogether?
Send the "Earth" scale, the standard Toledo model.
: >Weight does not vary on different planets, as the term weight is used
: >in medicine and physiology and in sports.
Weight is directly proportional to gravity and mass
(the PROPER scientific term).
Daniel P. B. Smith
discussed the meaning[s] the words "weight" and "mass" and generally
argued that the distinction between "mass" and "weight" is a technical
one applicable only to physics, and invalid in medicine, law, etc. In
part:
> Weight does not vary on different planets, as the term weight is used
> in medicine and physiology and in sports.
...
> Of course, physics textbooks and science museum exhibits have often
> used a different definition of the ambiguous word "weight" in this
> context, ignoring the well-founded conventions of medicine.
>
> This medical definition is, of course, quite legitimately and properly
> called "weight." This isn't a question of physics, but rather of
> history and linguistics, and of the law.
H. G. Wells plays on this distinction amusingly in his short story, "The
Truth about Pyecraft," from _Twelve Stories and a Dream_. Pyecraft
persuades the narrator to give him a secret, occult, old family recipe
for weight loss, and summons the narrator to his house a few days later:
...abruptly I realised that he was not holding on at all, that
he was floating up there--just as a gas-filled bladder might have
floated in the same position. He began a struggle to thrust himself
away from the ceiling and to clamber down the wall to me. "It's that
prescription," he panted, as he did so. "Your great-gran--"....
It was really a most extraordinary spectacle, that great, fat,
apoplectic-looking man upside down and trying to get from the
ceiling to the floor. "That prescription," he said. "Too
successful."
"How?"
"Loss of weight--almost complete."
And then, of course, I understood.
"By Jove, Pyecraft," said I, "what you wanted was a cure for
fatness! But you always called it weight. You would call it weight."
On the other hand, in the context of interplanetary travel, the use of
"weight" to refer to the force exerted on an object by the local
gravitational acceleration is as old as science-fiction:
"But the heat developed by the rapidity of the projectile in
crossing the strata of air?"
"Oh! the walls are thick, and I shall soon have crossed the
atmosphere."
"But victuals and water?"
"I have calculated for a twelvemonth's supply, and I shall be only
four days on the journey."
"But for air to breathe on the road?"
"I shall make it by a chemical process."
"But your fall on the moon, supposing you ever reach it?"
"It will be six times less dangerous than a sudden fall upon the
earth, because the weight will be only one-sixth as great on the
surface of the moon."
"Still it will be enough to smash you like glass!"
"What is to prevent my retarding the shock by means of rockets
conveniently placed, and lighted at the right moment?"
--Jules Verne, _From the Earth to the Moon_
On the earth we should have smashed one another a dozen times, but
on the moon, luckily for us, our weight was only one-sixth of what
it is terrestrially, and we fell very mercifully.
--H. G. Wells, _The First Men in the Moon_
Of course, both passages are probably wrong... They are referring to
the forces exerted on the occupants of a spacecraft when it crashes onto
the surface of the moon. This depends much more on the deceleration
during impact, which in turn depends on the design of the spacecraft and
final speed just before impact. Even an equal speed of impact, the
danger of the collision would be about the same... wouldn't it?
--
Daniel P. B. Smith
Leon Garde
> Here is sort of a follow-up question concerning scales and balances.
> Of course, we are all aware of the digital electronic SCALES available
> today that have no moving parts
How do you think that they do this ?
Can you tell us, or is the answer the subject of non-disclosure
agreements made with the the makers of electronic scales with moving parts
(or stretching parts) ; as the makers of these prefer them as they do wear out.
ie have you had your invention bought out and made to dispapper due to the
requirement to maximise profits ?
>. My question: Is there such a thing
> as a digital electronic BALANCE with no moving parts?
no.
All scaled must have moving parts too.
At least one end of the elastic material must move a small amount.
leon
Leon Garde
You've missed the point of specifying the measuring device
did not use a spring. (hint , the only other way (when you consider
strain/pressure detectors to be just a very tight spring )
is to use a balance;
They work differently, and this should get you thinking about how
they might indicate different things on the moon.
leon