# Mass/Weight on Scales

Gold Member
Hello;

Let's say I put an object on the scale. The scale reads: 10 kg. Is this the mass of the object? I know mass is measured in kg but I just wanted to know if it is actually doing the conversions.

Thanks.

## Answers and Replies

Yeah I think it's the mass...
It's a Newton meter that measures the weight.

Gold Member
But how does it convert it? Does it take your weight in Newtons and divide it by 9.8 or 10? Or some other value?

How does what convert it?...
I thought the scales measure mass and didn't do any calculations of converison...

Balance scales give the mass or weight beacuse gravity acts equally on both arms, spring scales like the one you use to measure your weight give the weight

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Then what are bathroom scales?

D H
Staff Emeritus
Balance scales measure mass but obviously don't work in a free-fall environment. Most bathroom scales are spring scales that measure apparent weight (everything but gravitational force) but display this as mass by a built-in assumption regarding the relation between weight and mass. This assumption obviously fails in a reduced (or increased) gravity environment. Nothing measures actual weight (mass times gravitational acceleration) because actual weight is actually unmeasurable.

Nothing measures actual weight (mass times gravitational acceleration) because actual weight is actually unmeasurable.

Spring scales measure actual weight, distance is calibrated in terms of force needed to stretch the spring to there.
http://home.howstuffworks.com/inside-scale1.htm"

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D H
Staff Emeritus
Nothing measures actual weight. Think equivalence principle. The actual weight of an astronaut in the space station is about 90% of the astronaut's actual weight on the surface of the Earth. A spring scale in the space station would measure zero because the astronaut's apparent weight is zero.

A spring scale on the Earth similarly measures apparent weight, not actual weight. The two differ in direction and magnitude. Actual weight is a vector pointing downward, apparent weight, upward. Moreover, because the Earth is rotating the two vectors are not quite 180 degrees apart and do not have the same magnitude (except at the poles, of course).

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DrGreg
Gold Member
I think different authors disagree over the meaning of the word "weight". Some make the distinction between "actual weight" and "apparent weight", as DH has in this thread. Others just describe "apparent weight" as "weight" and don't have a name for "actual weight".

D H
Staff Emeritus
... and yet others describe "actual weight" as "weight" and don't have a name for "apparent weight". Since there are multiple names, and different uses for these names, I'll define them here (these are fairly standard definitions).

"Actual weight", sometimes just called "weight", is the product of mass with gravitational acceleration. In other words, actual weight is a synonym for gravitational force. Actual weight cannot be measured but it obviously can be calculated.

"Apparent weight", sometimes called "scale weight" and sometimes just called "weight" is the sum of all real (i.e., non-fictitious) forces acting on an object except for the gravitational force. (In GR, apparent weight is the sum of all real forces acting on an object, period; gravitation is a fictitious force in GR.) Apparent weight can be measured. This is exactly what spring scales measure -- and that is why another name for apparent weight is "scale weight".

SpectraCat
"Actual weight", sometimes just called "weight", is the product of mass with gravitational acceleration. In other words, actual weight is a synonym for gravitational force. Actual weight cannot be measured but it obviously can be calculated.

Ok, I am confused now ... how does "the product of mass with gravitational acceleration" yield an arrow pointing up, as you said was correct for actual weight in an earlier post?

"Apparent weight", sometimes called "scale weight" and sometimes just called "weight" is the sum of all real (i.e., non-fictitious) forces acting on an object except for the gravitational force. (In GR, apparent weight is the sum of all real forces acting on an object, period; gravitation is a fictitious force in GR.) Apparent weight can be measured. This is exactly what spring scales measure -- and that is why another name for apparent weight is "scale weight".

Again, confusion ... if a scale measures "all of the real forces except gravitation", and you are not moving when the weight is measured, how can this not be seen as a measurement of the actual weight? If you measure all the forces save one on a stationary object, the remaining force must exactly balance the others, or else the measured object would be in motion. So it seems that the distinction you are making is purely a semantic one ... or am I missing something?

jtbell
Mentor
It's all a matter of convention:

Convention #1, which is followed by most physics textbooks:

"Weight" or "actual weight" is the gravitational force on you, which is always downwards on the surface of the earth, and is constant.

"Apparent weight" or "scale weight" = what a bathroom scale or similar device measures, which is actually the magnitude of the action/reaction pair of contact forces between you and the scale (downwards on the scale, upwards on you). It varies with your upward/downward acceleration.

Convention #2, which is followed by Hewitt's Conceptual Physics and maybe some other textbooks:

"Weight" = what a bathroom scale or similar device measures, identical to "apparent weight" or "scale weight" in convention #1.

In this convention, the gravitational force on an object is called the "gravitational force."

I personally prefer convention #2, because it agrees with everyday usage of "weight" and "weightless" in examples like the elevator and a freely-falling astronaut. Nevertheless, I conform with convention #1 when I'm teaching an introductory course out of a textbook that uses it (which is most of the time).

SpectraCat
It's all a matter of convention:

Convention #1, which is followed by most physics textbooks:

"Weight" or "actual weight" is the gravitational force on you, which is always downwards on the surface of the earth, and is constant.

"Apparent weight" or "scale weight" = what a bathroom scale or similar device measures, which is actually the magnitude of the action/reaction pair of contact forces between you and the scale (downwards on the scale, upwards on you). It varies with your upward/downward acceleration.

Convention #2, which is followed by Hewitt's Conceptual Physics and maybe some other textbooks:

"Weight" = what a bathroom scale or similar device measures, identical to "apparent weight" or "scale weight" in convention #1.

In this convention, the gravitational force on an object is called the "gravitational force."

I personally prefer convention #2, because it agrees with everyday usage of "weight" and "weightless" in examples like the elevator and a freely-falling astronaut. Nevertheless, I conform with convention #1 when I'm teaching an introductory course out of a textbook that uses it (which is most of the time).

@jtbell ... thanks, I've got all that (I think). What I am having trouble with is DH's assertion that actual weight can't be measured, which is a new idea for me. I think I'd have had an easier time with it if he'd said that mass can't be measured absolutely. I would have thought that the measurement of force by a spring scale would be an accurate measure of actual weight (barring calibration errors). Unless this distinction is all about the fact that we (and the scale) are never at rest, but are whizzing around on the surface of a rotating sphere flying through space at some ridiculously unsafe speed. Is that what the statement "we can't measure actual weight" really means?

D H
Staff Emeritus
Ok, I am confused now ... how does "the product of mass with gravitational acceleration" yield an arrow pointing up, as you said was correct for actual weight in an earlier post?
Oh jeez. Sorry for the confusion. I had a bad night sleep's last night. Actual weight (gravitational force) points downward, apparent weight upward. Also corrected in post #9. Thanks.

Again, confusion ... if a scale measures "all of the real forces except gravitation", and you are not moving when the weight is measured, how can this not be seen as a measurement of the actual weight?
But you are moving when you stand on a scale. You are rotating about the Earth's axis at one revolution per day.

The forces acting on you are the downward force of gravity, the upward normal force exerted by the surface of the Earth, and the upward buoyant exerted by the Earth's atmosphere. The first is your actual weight while the two upward forces are your apparent weight. The sum of these three forces is zero only at the Earth's poles. Anywhere else the net force is exactly that needed to keep you in uniform circular motion. The difference is small but real. The force required to keep a 70 kg person in uniform circular motion at one revolution per sidereal day and 6378 km from the origin (i.e., standing on the equator) is 2.37 newtons. That person's apparent weight at the equator is 684.62 newtons, the actual weight, 687 newtons.

D H
Staff Emeritus
What I am having trouble with is DH's assertion that actual weight can't be measured, which is a new idea for me.
The equivalence principle says that no local experiment can be conducted that distinguishes between being in free-fall subject to gravity from massive object and being in uniform motion while far removed from all massive objects. In other words, you can't directly measure actual weight.

You can infer "actual weight" from non-local experimental data. For example, suppose you are in orbit about some planet. You can measure the size and period of your orbit, and from this calculate your actual weight. However, these orbital measurements are non-local experiments.

I don't see how taking a measurement of the size and period of your orbit will give your actual weight. Seems to me that making a measurement of weight is for the most part dependant on something outside of whats being measured. Am I understanding what is ment by actual weight right? Seems to me something called actual weight should be what is the "actual" weight of an object that just happens to be unknowable possibly?

D H
Staff Emeritus
Actual weight, once again, is a pseudonym for gravitational force. If you know your orbit you can compute gravitational acceleration. That coupled with knowledge of your mass gives you gravitational force, i.e. actual weight.

Actual weight, once again, is a pseudonym for gravitational force. If you know your orbit you can compute gravitational acceleration. That coupled with knowledge of your mass gives you gravitational force, i.e. actual weight.
Don't you have to have the knowledge of your weight(which cannot be measured) to be able to compute your mass.

D H
Staff Emeritus