|In science we learned that mass is the amount of
matter in a body no matter where we are, and
weight has to do with gravity. But if I am only
thinking about living on Earth, is mass and
weight here not the same? Do I "weigh" 49 kg or
do I "mass" 49 kg? What is my bathroom scale
telling me, my weight or my mass?
|Question Date: 2003-10-09|
Actually, this is a tough question... but in fact,
even on the earth mass and weight are not the
same. The earth spins, so if you are at the
equator, you are traveling at over a thousand
miles an hour to the east. At the equator, your
mass is essentially the same, while your weight is
a few pounds (or kg) less than at either pole.
For low velocities and accelerations, mass is
the constant of proportionality between an applied
force and the resulting acceleration. Mass is
related to weight (gravitational acceleration)
because gravity creates an acceleration for which,
for you to remain at rest on the earth's surface,
you need to apply an opposing force through your
feet. Since the acceleration from the force of
your feet exactly balances that due to gravity,
(or you wouldn't stay motionless) the force you
measure on a balance or bathroom scale (the
weight) is also proportional to your mass.
F(total)= m * a -F(on your feet) ,
from gravity and the F(feet) is what you
weight. (Since the earth is a spinning platform
you are actually accelerating when you think you
are at rest -- and this causes the deviation from
equator to pole).
The notion of mass
independent of material is due to Galileo, the
laws of inertia (F = m a) was worked out
and the notion of mass causing a true acceleration
(not a force) is from Einstein.
Mass is an absolute quantity (I will
that means) but weight (on earth) is really the
force with which you are pulled towards the center
of the earth. Weight is what the bathroom scale
measures. There is a spring in the scale. When you
stand on it, the spring is pushed down because of
the force with which the earth pulls you. How much
the spring is pushed is what is
Mass on the other hand is what
would be measured using a comparative balance, by
hanging two objects on the ends of a beam, and
then seeing by how much one side is pulled down.
Masses are measured by comparing an unknown mass
against a known one.
While on most parts of
the earth, the weight and mass turn out to be the
same, there can be small changes in the weight, if
for example, you take your scales to the top of a
very high mountain and weigh yourself. If you
compared yourself with a standard mass, this would
not change, whether you are on the earth or the
That's a good question. It can get confusing
because some words that have very specific
meanings in science have much more general
meanings outside of science. When you learned in
science that mass is a measure of the amount of
matter in a body and that weight has to do with
gravity it was right, but outside of science the
terms are often treated like they both have the
If your mass is 49 kg, that
means your weight is
480 kilogram-meters-per-second-squared or 480
Newtons. Both of those terms are a bit awkward to
say, and most people outside of science don't have
a clear concept of what they mean physically. As
you pointed out, most people only plan on hanging
out on earth, so they only care about what weight
results from their mass due to the gravity on
earth. Instead of telling people that they weigh
480 Newtons, then, and instead of saying "I have a
mass of 49 kg", people started treating the words
"weight" and "mass" as the same in daily speech
despite the fact that the meanings are still very
different in science.
Whether your bathroom
scale is measuring your weight or your mass
actually depends on the type of scale you have.
Old-fashioned scales involving small metal masses
that you slide across a bar (like the kind you
would usually see at a doctor's office) measures
your MASS by balancing the mass on the pad you're
standing on with the masses you move on the bar.
Newer scales, though, like digital and spring
scales, measure the FORCE your body exerts on the
pad you're standing on, which is your WEIGHT.
scale then divides your weight by gravity to give
you your mass.
So if you have a digital
scale at home, your scale measures your weight(480
Newtons), then divides it by gravity to show you
your mass (49 kg),and then everyone goes ahead and
calls that "mass" your "weight". It's a little
bit crazy, but it's the way the world works...
That is a very good question! For practical
purposes of your daily life,you are correct. You
understand that mass is the amount of matter
contained in your body, and that if you were to go
up in the international space station, you would
be in a state of free fall, and feel weightless,
but you would still have the same mass. However
on earth, we use the gravitational field of the
earth to measure our mass by how much the earth
and our bodies attract each
Technically, we say that one
kilogram weighs 9.8 NEWTONS on earth, because w =
mg, and g = 9.8 meters/second2
. On the moon,
for example, where g is only 1.6
one kilogram of mass would weigh 1.6 Newtons,
not 9.8 Newtons, and you could not use the kilogram
to stand for the same unit of mass and weight -
you'd have to either invent a new unit of weight,
or simply use the common unit of Newtons, which is
a unit of force, that we use on earth.
you understand that weight is really a
force and mass are related to each other by a
Force/mass = acceleration.
I'll show you why we use the convention that our
mass = our weight on earth.
On earth, the
acceleration of gravity we call "1 g", and its
average value is 9.8 meters/second2.
here's how we get 1 kilogram of mass = 1 kilogram
of weight on earth:
Since Force/mass =
acceleration, we DEFINE the unit of gravitational
acceleration ONLY FOR REGIONS CLOSE TO THE SURFACE
OF THE EARTH to be 1 g.
So, in these
units, Force/mass = 1, therefor force = mass.
Since weight is the force that the earth exerts on
you when the acceleration IS 1 g, then we can say
your weight on earth = your mass.
are quite right, that if you only want to restrict
yourself to the earth, then you can say your mass
= your weight. But now you know that this
definition is ONLY true if you are on or very
close to the surface of the earth, and it is not
true anywhere else in the universe.
I think what your teacher was trying to get across
is that mass is a fundamental property. If you had
a loaf of Wonder bread and you sat on it or
otherwise squished it into a ball, it will be
smaller but it will have the same mass. If you
took the loaf of bread to the moon, it will
weightless but will have the same mass. An
object's size, density and weight are all ways to
describe it, but they can change. An object's mass
cannot change. If you ate a couple slices of the
bread, the bread loaf is now smaller and weighs
less because it is missing a few slices, but the
slices you ate have the same mass inside your body
that they would have had when they were part of
the loaf of bread. The slices are just in a
different form: they get mushed up in your mouth
and liquefied in your stomach and are then
absorbed by your body and converted into tissue or
are removed as waste. Mass can not be created or
destroyed. If you left the loaf of bread on the
counter for years and years and years, it would
slowly change form but would still have the same
mass, if you could track the molecules. (This
would be pretty hard to do since some will be
carried away by ants and other bugs, some will be
converted to mold spores and waft away in the air,
etc.) The universe has the same mass(the same
number of atoms) now as it did when dinosaurs
walked the earth. It's just that the mass -
the atoms - keep shifting into different molecules
and take different forms. If you consider the life
of your loaf of bread only on earth, then yes,
mass and weight are sort of the same thing. That
is, the relationship between the loaf of bread's
mass and its weight will not change. Assuming you
could track all the molecules of bread in your
body as you ate the slices, and could retrieve
those molecules a few days later and weight them,
the weight would not have changed. But just beware
that weight is a descriptive term for mass
that the relationship between mass and weight is
not constant if the force of gravity
By the way, you weigh 49
kilograms. Your bathroom scale is telling you your
weight. Your mass would be the number of atoms in
your body. As the number of atoms in your body
changes, you weight will change. So here's a
question: when loose weight, where you think those
atoms go, if they are not destroyed?
Let me answer your middle question first: a very
careful scientist would say that you "mass" 49 kg
because the kg is a unit of mass. Of course, most
folks would just say that you "weigh" 49 kg. This
is ok because most folks are talking about how
much you weigh on Earth and since the conversion
factor between weight and mass on Earth is always
the same for everybody (well, *almost* the same),
you can always convert one to the other. Your
bathroom scale is probably giving your weight in
pounds, however, and pounds is actually a unit of
force - so it is measuring your weight. It may
also give you your "weight" in kg, but this number
assumes you are on the Earth.
If you lived on
Mars, you would have to get a new scale. On Mars
gravity is different, and the scale would read a
smaller number of pounds when you stepped on it.
This number of pounds *correctly* measures the
force you are exerting on the scale. On the other
hand, your mass has not changed - so the same
scale on Mars would tell you your mass was smaller
than it was.
that is sort of the point. If we tried to keep
track of weight in science, it would become very
confusing very quickly because, to different
people, it would mean different things. That is
the beauty of mass - everybody has the same mass
no matter where they are or what they are doing.
This is especially important because the
mathematical laws of physics don't care where you
are or what you are doing either - the laws of
physics are always the same for everyone. I guess
this is an assumption scientists make and there is
no proof, but it has never, ever failed before.
So if the laws of physics are the same everywhere,
they should depend only on things that are also
the same everywhere. This is why the
important number in science is the mass, not the
When you study collisions in a physics
class, for example, the weight of an object is
completely unimportant. It is the mass (and a few
other things), that tell you what happens after
they collide. That is the real reason why you
have to learn about mass - it comes up again and
again in all sorts of places in science.
course, if you know the weight and you know you
are on Earth, you can always work out the mass.
So in most situations, you can safely interchange
Your mass is 49 kg. Your weight on
Earth is: 2.2
lb/kg x 49 kg = 108 lb.
kg is a metric
measure of mass. When you stand on a scale on
Earth, gravity is pulling on you, so you exert a
force on the scale, which is measured in Newtons
(or in dynes, being a dyne a derived unit of force
specified in the centimetre–gram–second (CGS)
system of units). But you will always use the scale
on earth (probably !) so it can give you mass
readings that are accurate on Earth.
pound is an English measure of weight, which is a
force, so it gives you the force you exert on the
scale when you stand on it.
will say you are lighter on the moon, because
they're both actually measuring force; but they're
only designed to use in earth's
You and your friend could sit on
a see-saw and be exactly balanced, if whoever was
heavier would sit a little farther from the end of
the see saw. You could sit in those same places
on the see-saw if it was on the moon or anywhere,
and it would still be balanced. That happens
because your mass is the same
The same thing happens if you
put 2 identical weights (= 2 identical masses) in
the 2 pans of a pan balance. The 2 pans will be
balanced on earth or the moon, because the masses
are the same everywhere.
As long as you're on Earth, and as long as you're
not talking to a physicist, you can basically
think of your weight as a measurement of your
mass. (I say basically, because, believe it or
not, you really do weigh lightly different
amounts at sea level or on the top of mount
To be totally accurate, though,
here's the difference: Mass is a measurement of
how much matter is in an object, and weight is a
measurement of the force applied to that object by
The connection between mass and weight is
that the amount of force that gravity applies to
an object is directly related to how much mass
that object has. More mass = more force applied by
gravity = greater weight. What you heard about
weight being related to gravity is thus
The reason why most people confuse
the two, and why the difference doesn't matter to
most of us, is that most of us never leave Earth.
If you went to the Moon (which you may someday!),
your mass would be the same, but you would weigh a
lot less because the Moon exerts less
gravitational pull on objects. (Incidentally, the
reason why it exerts less gravitational force than
the earth does is that it's smaller than the
earth--it has less mass!)So, stay on Earth and
your mass and weight will be essentially the same.
You will "weigh" 49 kg, which is the same as
saying you "have a mass of" 49 kg.
that helps. Keep asking such great questions!
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