# Help With Mass and Weight Units

• Engineering
tomtomtom1
Homework Statement:
Help With Mass and Weight Units
Relevant Equations:
Help With Mass and Weight Units
Hello all

I was hoping someone could clear up the units & difference between Mass and Weight.

I live in the UK.

I weighed myself today on the scale and the scale told me that I weighed 95kg.

What bothers me is that if:-

Mass - Is the amount of "stuff" I am made from which is measured in kg
Weight - Is how strongly gravity pulls on that Mass, where gravity is taken as 9.81m/S^2

Then shouldn't my weight be given in units of:-
kg * m/s^2
These units are Newtons

If that is correct then why does my scale only say 95kg??

OR

Is the scale measuring my Mass which is 95kg and it is just normal practise to say my weight is the same as my Mass even though that is incorrect?

From my perspective the scale should read 95kg * m/s^2 which is my weight or 95 Newtons.

Thank you.

mfig
The scale is likely reporting your mass with the assumption that you live where the gravitational acceleration is equal to the standard value. In other words, the scale detects a force of 931.95 N and tells you that your mass is ##\frac{931.95 N}{9.81 \frac{m}{s^2}} = 95 kg##. If you took that scale to the moon, it would measure ##95kg \cdot 1.625 \frac{m}{s^2} = 154.375 N## and tell you that your mass is ##\frac{154.375 N}{ 9.81 \frac{m}{s^2}} = 15.74 kg##.

Yes, your weight is not the same as your mass, though they are proportional by the value of ##g##. It is a convenience to assume that the calculated value would be the same everywhere on Earth even though it wouldn't in reality.

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Homework Helper
Then shouldn't my weight be given in units of:-
kg * m/s^2
These units are Newtons

In a physics setting, yes. Weight is the gravitational force between you and the earth. It is measured in Newtons.

If that is correct then why does my scale only say 95kg??

Because in the English language, "weight" is the term commonly used for what physicists would call "mass". We are interested in our mass more than our weight. That's what we're used to comparing.

Also, mass is invariant. It doesn't matter what planet you're on, or where on Earth you are. But weight does change at different places on Earth as there are slight variations in the gravitational field, around 1%.

Is the scale measuring my Mass which is 95kg and it is just normal practise to say my weight is the same as my Mass even though that is incorrect?

Most scales measure how much force you are exerting, so they are responding directly to your weight. But the readout has been calibrated to give the mass equivalent of that force, by dividing by g.

However, since as I said g varies from place to place by about 1%, the scale is calibrated for only one particular place and isn't necessarily going to be giving your correct mass.

Note that balance-type scales that compare you to a standard mass are measuring mass directly, not weight. So they won't suffer the same problem of differing from place to place.

It is correct in non-technical English to report your mass when people want to know your weight. That is the common meaning of the word. It is incorrect in a physics class to do that. If you are asked for a weight, multiply m by g and give the answer in force units.

This isn't the only word that differs between common and in physics usage. Velocity and acceleration are two others that I can think of.

Staff Emeritus
I weighed myself today on the scale and the scale told me that I weighed 95kg.
If you are reading your weight off the scale, the display is saying your weight is 95 kg wt
or 95 kg f ("kilograms force")

If you are reading your mass off the scale, it is saying your mass is 95 kg

Homework Helper
Gold Member
If you are reading your weight off the scale, the display is saying your weight is 95 kg wt
or 95 kg f ("kilograms force")
Is "kilograms force" a suitable unit to use on Physics Forums? In any case, the purpose of a weighing scale is to measure mass not weight. Just because a spring balance approximates mass by measuring weight and assuming local g (which may introduce an error of c.1% which can be eliminated by calibration in situ) does not mean that its readout should be interpreted in anything other than mass units.

Edit - just noticed this
I live in the UK.
In the UK we do not suffer the confusion that results from (or results in, I am not sure which way round it is) the concept of "kilograms force". Since the adoption of the metric system for all science/engineering/education purposes decades ago, force has only been measured in Newtons. We do still have a problem with torque, but that is another story.

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Dr.D
In the UK we do not suffer the confusion that results from (or results in, I am not sure which way round it is) the concept of "kilograms force". Since the adoption of the metric system for all science/engineering/education purposes decades ago, force has only been measured in Newtons.
And this is why scales in the UK read in Kg?

Staff Emeritus
Is "kilograms force" a suitable unit to use on Physics Forums?
It's a unit of force that is perfect to use in any learned company.

In any case, the purpose of a weighing scale is to measure mass not weight.
Whatever gave you that erroneous idea?

Just because a spring balance approximates mass by measuring weight an
A spring balance measures force. Don't let anyone try and tell you otherwise.

Dr.D
While units like "kg-f" and "lb-m" are still in use in some places, and particularly they are common in the older literature, a knowledgeable person should know how to deal with them, even if their further use is discouraged.

Many years ago, I worked for a watch manufacture in the USA. There I encountered in the work of others some really strange units, such as torque in gram-inches. I certainly would not recommend that to anyone today, but if I were to dig out old work from there, I would have to know how to read such bastardized units.

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