
I am an 8th grade science teacher and I have the
following question: How do we measure true mass
on Earth? I teach that a balance measures mass,
but I find that a spring scale gives the same
answer. If, on Earth, a 100 g object weights
approximately 1 N, it's mass should be 100 g on a
balance, but not a spring scale. Yet I get 100 g
on the spring scale as well. I have not found an
answer to my quandary so perhaps I am not asking
the correct question. Thanks for your help.

Question Date: 20040423   Answer 1:
A balance measures mass by comparing the
unknown to a standard mass...like a 1 kg gold
standard... a spring scale, on the other hand,
DEPENDS on the local value of G.
So a spring scale on EARTH IS CALIBRATED to
give the same as the balance on EARTH...i.e. when
the spring is stretched so far, the mass is 1 kg.
But if you now take this spring scale to the MOON
and use it, you will see that the 1 kg mass shows
up at a weight which is UNLIKE (less) than the
value on Earth. But if you took your balance with
you, you would still get the same value for the
mass.
So a balance is independent of the planet
because you compare an unknown to a STANDARD mass.
But a spring scale depends on the local
gravitational field. I hope this helps.
  Answer 2:
You are asking a fine question. The weighing
devices are all either calibrated to read mass on
earth or to measure force. I have a couple of
spring scales that read in Newtons. Yours is
obviously calibrated to read mass, so it would
give you the wrong answer in a place where the
force of gravity was different. You are a good
observer  I used to be amused and a bit annoyed
when I sorted the science materials at IV School.
There were a bunch of boxes labeled 'spring
balances,' and it seemed to me they should be
labeled 'spring scales,' since they were clearly
not balances.
  Answer 3:
Mass is a fundamental quality of an
object that does not change, and is measured in
grams and kilograms (or ounces and pounds if you
are in the US). Weight is mass times gravitational
acceleration, which actually makes weight a
measure of force. If you wanted to be technical,
something with a mass of 100 grams should have a
weight (or force) of 100 grams times 9.80665
meters per square second (gravitational
acceleration), giving you 980.665 grammeters per
square second.
Here's the tricky part: we don't measure weight
this way. Instead we define the Earth's
gravitational acceleration as 1 "Gee"
(creating a new unit) and measure weight in
kilograms of force or pounds of force, which is a
kilogram or pound multiplied by 1 "Gee". This
operational definition makes mass and weight equal
in number, though not in units. People don't
get the units right, so they tend to confuse mass
and weight, saying "I weight 130 pounds" and not
"I weigh 130 pounds of force". Chances are, your
spring scale doesn't say 100 grams of force just
100 grams.
If you were to take your 100 gram
object to a planet where gravitational
acceleration was only half that of the Earth's
(onehalf Gee), the mass would still be 100 grams
measured on the balance, but the weight would no
longer be 100 grams of force on the scale.
What would it be now?
  Answer 4:
Hello, It depends on how the spring scale is
calibrated. I have seen spring scales calibrated
in grams, Newtons, or even old ones in ounces. If
you want a spring scale that is calibrated in
Newtons, you can probably order one through any of
the science product catalogs. Now, I'm not sure
if you are asking about calibrating spring scales,
or if you are really asking about the fundamental
difference between mass and weight. On Earth,
any device that uses the gravitational field of
the earth in making the measurement is really
measuring WEIGHT, so both your measuring devices
are actually measuring weight, even though they
are calibrated in grams. But, if your scales are
calibrated correctly, you are also measuring their
true mass; you are just using the gravitational
field of the earth to do so. Mass we define
loosely as the quantity of matter in a given
object, which is really saying how many atoms are
in a given chunk of "stuff", and what are the
atomic masses of these atoms. Weight is a measure
of how that mass behaves in a gravitational field.
We define weight as "mass x g" where "g" is the
acceleration of a freely falling object near the
surface of the earth, for which the air resistance
is so small as to be negligible. The value of
g is approximately 9.8 meters/second/second, using
the metric system. So, 1 kg of mass has a weight
of 9.8 Newtons, or approximately 10 Newtons. 100
gr = 0.1 kg, so it has a weight of 0.98 Newtons,
or approximately 1 Newton. Conversely, we
define a Newton as the force that you would have
to apply to a 1 kilogram mass to give it an
acceleration of 1 meter/second/second. If you
apply 9.8 Newtons of force to a 1 kilogram object,
it will have an acceleration of 9.8 m/sec^2, and
if you drop a 1kg object on earth, it will also
have an acceleration of 9.8 m/sec^2. We call this
an acceleration of "1g". That's pretty fast. Just
to make sense out of this, if you have ever been
on the "Scrambler" at Magic Mountain  it has a
horizontal acceleration of about 1g. I once tried
to measure it with a mass and a spring
scale! You have hit, actually, upon one of
Einstein's fundamental questions! Why should two
objects have the same mass when measured in two
different ways, by accelerating them horizontally
(independently of gravity) and vertically, using
gravity? So he defined gravitational mass and
inertial mass, and one of his fundamental
postulates is that gravitational and inertial mass
are equivalent. Give a student two different
objects and ask her to tell you which one is
heavier, and then observe what she does. She'll
move them up and down in each hand. The mass that
offers greater resistance to beingmoved up and
down or side to side has more "inertial mass". The
one with more mass will weigh more on a scale,
too. We call this way of measuring mass
"gravitational mass", that is, the resistance to
being pulled "down" by the mass of the
earth. Ok, so "everyone" knows that if you go
to the Moon you weigh less, and if you go to
Jupiter you weigh more. But, what if you go into
orbit? You appear to be weightless, but you have
not lost any mass! So how can you measure mass in
free fall, as you are in orbit? (You are not
really weightless, as "g" is about 70% of g on
earth, so you don't actually weigh that much less.
You only feel weightless because the shuttle is
also in orbit, and everything is in orbit, and so
the floor is falling as fast as you are, so you
can't stand on it!) What do you do? You would
use the same principle you used to compare the
inertial masses of two objects on earth: you would
shake it! Really, that's what they do. They use an
"inertial balance". They put an object in a pan
balance, but instead of moving up and down in a
gravitational field, the balance moves side to
side, and has springs, and they TIME it. The
smaller the mass, the faster it oscillates, and
vice versa. The instrument iscalibrated to read
mass in kilograms. You can see roughly how this
works if you have a spring and a few masses. Hook
each mass on the end of the spring, and hold the
other end in your hand, and give the mass a slight
tug, and watch it bounce up and down. The heavier
masses will take longer to bounce up and down,
because it has more inertia. (It will also stretch
the spring more, because it has more weight on
earth! What would you do with it in a 0g
environment?) So, you ARE measuring "true mass"
on earth, you are just using the gravity of the
earth to help you. I think you wanted to know how
you could measure true mass without using gravity
at all. I hope I have answered your question.
  Answer 5:
A spring scale measures force F. If the mass of
the object (measured by a comparative balance) is
m. Then the Force measured by the spring balance
(by Newtons Laws) is F = mg, where g is the
acceleration due to gravity. F = 9.8 N for a 1 kg
mass. The spring scale is set up for an
acceleration due to gravition of g = 9.8 ms^2, so
that when the spring scale says 1 g, it has
actually calculated the force in N and divided by
the g to obtain m. So the spring scale is
calibrated for the surface of the earth (sea
level) where g is 9.8 ms^2. If g were
different, the spring scale would not work. This
can be demonstrated by trying to use a spring
scale in a moving elevator, or (better) by taking
it to the moon. A mass of 1 g would be the same
anywhere, but on the moon, it would have a weight
(measured using a spring scale) that is
approximately 1/6 g. So in a nutshell, weight is
defined on the surface of the earth (sealevel) so
that it is numerically equal to the mass.
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