# Force equation: use mass or weight?

• escape_velocity
In summary: Formally, a spring balance measures the extension (or compression) of a spring, not the weight. But the extension of the spring is simply related to the weight and the weight is simply related to the mass. So generally you just stick a 1kg mass on it and mark...In summary, a spring balance measures the extension (or compression) of a spring, not the weight.

#### escape_velocity

I require to calculate acceleration of an object caused by a force of 100N acting upon it.
The weight of the object is 0.5kg
I'm using the equation

F = m * a

Is it correct to use weight of the object instead of mass in the equation.
Will it yield correct results?

Or would I need to calculate "mass" of the object first using the equation

m = W / g
where W is weight of the object and g is acceleration due to gravity.

What does m stand for in your first equation?

vanhees71
escape_velocity said:
The weight of the object is 0.5kg
That is the mass.

What does m stand for in your first equation?
m stands for mass

A.T. said:
That is the mass.
In earthly terms wouldn't we call that he "weight" since I measured the weight on a weighing scale.
Isn't weight the effect of gravity acting on the mass of a object?

The first thing you have to learn when doing science is that you need a way more precise language (implying a much more precise thinking as well!) than in everyday language.

Mass is an intrinsic property of a piece of matter (for the purpose of Newtonian classical mechanics), while weight is a force due to the gravitational interaction between this piece of matter and the Earth. Even the qualitative nature of the two quantities is different. While mass is a scalar quantity, weight is a vector quantity. Mass has only "a magnitude" but no direction, weight has.

Close to Earth the weight can be approximated (locally, i.e., for a region small compared to the distance scale given by the radius of the Earth) by
$$\vec{F}_{\text{grav}}=m \vec{g},$$
where ##\vec{g}## is approximated as a constant gravitational acceleration in this "small region".

If you measure the mass with a beam balance, what you in fact to is to compare the weight of the measured object due to the gravitational interaction with the Earth and that of some other object with a known mass, using the basic laws of Newtonian mechanics, here particularly the lever rules.

escape_velocity
escape_velocity said:
In earthly terms wouldn't we call that he "weight" since I measured the weight on a weighing scale.
Isn't weight the effect of gravity acting on the mass of a object?
The one thing that is drilled into our heads in first year physics is the distinction between "weight" and "mass". Those of us who live in the U.S. are especially challenged in this regard because we use an identically named unit for both quantities -- the pound.

The mass of an object is how much stuff there is. In SI units, it is measured in kilograms.

The weight of an object is how much force it takes to support the object, keeping it motionless against gravity. In SI units, it is measured in Newtons.

A balance scale or a properly calibrated spring scale will determine the mass of an object. Even though the scale is sensitive to the gravitational down-force on the object, the resulting numeric reading reflects the object's mass.

The equation: ##F=ma## is only valid in certain systems of units. The unit of force has to be the amount of force it takes to accelerate a one unit mass (e.g. a kilogram) at one unit of acceleration (e.g. one meter per second squared).

In other systems of units, one has to include a constant of proportionality. ##F=kma## where k is a constant that depends on the chosen units. For instance, in the U.S. common system of units, ##F=\frac{1}{32.17}ma## for force in pounds-force, mass in pounds-mass and acceleration in feet per second squared.

vanhees71 and escape_velocity
escape_velocity said:
In earthly terms wouldn't we call that he "weight" since I measured the weight on a weighing scale.

You're overthinking it. If the equation asks for a particular quantity, that's what you should give it.

jbriggs444
escape_velocity said:
In earthly terms wouldn't we call that he "weight" ...
It's in kg so it's the mass.

A.T. said:
It's in kg so it's the mass.
I agree its in "Kg". I'm just a confused since all I have here is the capability to measure what we call "weight" of the object and that showed 0.5 Kg. Now my question is since I didn't ever measure the mass of object. How would I be sure that the number I'm putting in is actually the mass of the object.

escape_velocity said:
I'm just a confused since all I have here is the capability to measure what we call "weight"...
A scale measures neither weight nor mass directly, but something like deformation or resistance change, and then converts it to mass given in kg.

Ibix
escape_velocity said:
I'm just a confused since all I have here is the capability to measure what we call "weight" of the object and that showed 0.5 Kg.
Formally, a spring balance measures the extension (or compression) of a spring, not the weight. But the extension of the spring is simply related to the weight and the weight is simply related to the mass. So generally you just stick a 1kg mass on it and mark where the spring stretches to "1kg". Repeat for 2kg, 3kg, etc.

So if you want to read the scale on your balance as "a 0.5kg mass in Earth's gravitational field at sea level makes the needle deflect to here", rather than a direct measurement of mass, knock yourself out.

If you want to be really accurate, you can not practically be sure that the weight you measure will give you the mass unless you know the exact gravitational force where you are making the measurement. You should also account for the centrifugal force due to the rotation of the Earth and for your altitude. For an equation, see How gravitational force varies at different locations on Earth

FactChecker said:
If you want to be really accurate, you can not practically be sure that the weight you measure will give you the mass unless you know the exact gravitational force where you are making the measurement. You should also account for the centrifugal force due to the rotation of the Earth and for your altitude. For an equation, see How gravitational force varies at different locations on Earth
Certification (e.g. for scales used in commerce) is often performed on-site against reference standards whose mass is known. One need not know the local acceleration of gravity to know that a scale that reads 1 kg has accurately measured 1 kg.

escape_velocity and FactChecker
jbriggs444 said:
Certification (e.g. for scales used in commerce) is often performed on-site against reference standards whose mass is known. One need not know the local acceleration of gravity to know that a scale that reads 1 kg has accurately measured 1 kg.
Interesting. So certified scales are calibrated at each location to measure mass, rather than weight.

In the metric system, there is no such thing as a kg of force (or a weight of 0.5 kg). When we say that something weighs 0.5 kg, what we mean that its mass is 0.5 kg, and its weight in Newtons is 0.5 x 9.81. I know it doesn't make a whole lot of sense, but get used to it.

escape_velocity
escape_velocity said:
I agree its in "Kg". I'm just a confused since all I have here is the capability to measure what we call "weight" of the object and that showed 0.5 Kg. Now my question is since I didn't ever measure the mass of object. How would I be sure that the number I'm putting in is actually the mass of the object.
No! It's in kg!

lewando
FactChecker said:
Interesting. So certified scales are calibrated at each location to measure mass, rather than weight.
There is some useful information here and here. which calls for annual inspection/re-certification.

This scale service company said:
Scale Calibration

Scales can become out of calibration for a variety of reasons including wear and tear on components, environmental changes, buildup under the scale and more. The problem with a scale out of calibration is someone always loses. In commercial transactions, either the seller is giving away free product or the buyer is paying for product he or she did not receive. Scale calibration is one of the core services provided by Quality Scales Unlimited. Our technicians can calibrate any manufacturer or capacity of electronic or mechanical scale. Our technicians use certified known weights, traceable to NIST to calibrate. After weight testing and calibration, we create Certificates of Calibration. We can customize calibration certificates to meet your business needs. Contact our service department for more information or a sample of our Certificates of Calibration.

jbriggs444 said:
Those of us who live in the U.S. are especially challenged in this regard because we use an identically named unit for both quantities -- the pound.

The mass of an object is how much stuff there is. In SI units, it is measured in kilograms.
To be fair to the US, Europeans don't use SI units when they buy meat at the store. There is no US versus non-US divide here, the divide is between scientific units and everyday units.

Well, in Germany we use SI units when we buy meat. I had no problem in the US with pounds. It took just a while to get used to it. It's also interesting to measure lengths in different units like distances on the road in miles and heights of bridges in feet. This always reminded me on the fact that something similar is the case in the SI, where one measures time and distances, and (even less intuitive) electric and magnetic field components (which after all belong to the one and only electromagnetic field) in different units too.

At the end it doesn't matter much in which units we express quantities since the physical laws are independent on which system of units we use. Only some are much more convenient than others, and which ones also depends on the specific physics you are considering.

anorlunda said:
Europeans don't use SI units when they buy meat at the store.
They mostly do, except maybe the British.

nasu
A.T. said:
They mostly do, except maybe the British.
Yeah, in an earlier thread, they said they buy meat by the kg in UK. When I lived in Sweden in the 80s it was also by the kg.

Edit: I never heard of buying one Newton of beef.

jbriggs444 said:
The equation: F=ma is only valid in certain systems of units.
The equation only relates physical quantities. If constants of proportionality need to be inserted, they're between units of measure.

anorlunda said:
Yeah, in an earlier thread, they said they buy meat by the kg in UK. When I lived in Sweden in the 80s it was also by the kg.
So which Europeans don't use SI units when they buy meat at the store?

nasu
A.T. said:
So which Europeans don't use SI units when they buy meat at the store?
When you weight meat at the store on a spring scale, it measures force. But the scale indicates kg. Therefore, you are using ##kg_f## and ##kg_m## analogous to ##lb_f## and ##lb_m## in English units. In my book, that is not SI. SI would force the spring scale to indicate Newtons.

Hair splitting I know, but the point is that the mass/weight confusion is somewhat deliberate and the same on both sides of the pond.

anorlunda said:
When you weight meat at the store on a spring scale, it measures force. But the scale indicates kg. Therefore, you are using ##kg_f## and ##kg_m## analogous to ##lb_f## and ##lb_m## in English units. In my book, that is not SI. SI would force the spring scale to indicate Newtons.
Essentially all measurements are indirect. In my book the quantity that is "measured" is the numeric value that a device is designed to accurately determine. A properly calibrated spring scale measures mass, not force.

jbriggs444 said:
Essentially all measurements are indirect.
OK, bear with me. I intend to be stubborn and pedantic in this case.

We are all familiar with the number 2.2 lb/kg. That can't be lb force and kg mass.

The SI system does not recognize the kg force. The English system does not recognize the pound mass. The public has been told that in school, but they don't give a damn. The public can and will continue using pound mass and kg force because they like it. Science and engineering don't yet rule this world.

russ_watters
anorlunda said:
SI would force the spring scale to indicate Newtons.
Why not millimeters of spring elongation? You seem to conflate two separate issues:
- How direct is the measurement of mass?
- What system of units do we use to quantify mass?

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anorlunda said:
OK, bear with me. I intend to be stubborn and pedantic in this case.

We are all familiar with the number 2.2 lb/kg. That can't be lb force and kg mass.
I agree that a scale with modes that enable output in kg or lb is presenting a contradiction to the user and at the very least it means we should be a lot more sympathetic to the OP than was the initial response in this thread.

A spring-scale measures elongation. It then converts the elongation to force by way of the spring constant. And then, perhaps, to mass by way of an assumed g. We should not be making posters feel like they are missing something obvious when the different modes of a scale are in fact telling them very different things.

anorlunda said:
Science and engineering don't yet rule this world.
That's the reason for a lot of problems, but now it really gets off-topic...

weirdoguy
anorlunda said:
The English system does not recognize the pound mass
Yes, it does. The pound mass is the standard for commercial purposes.

Back when I went to school, my physics teachers and textbooks took great pains to say that the U.S. pound is always and exclusively a unit of force. Those teachers and textbooks were simply wrong. If you see packaged goods with a label such as "net weight 1 lb 2 oz", those are mass units and that net weight refers to a mass quantity.

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escape_velocity said:
I require to calculate acceleration of an object caused by a force of 100N acting upon it.
The weight of the object is 0.5kg
I'm using the equation

F = m * a

Is it correct to use weight of the object instead of mass in the equation.
Will it yield correct results?

Or would I need to calculate "mass" of the object first using the equation

m = W / g
where W is weight of the object and g is acceleration due to gravity.
F is the weight.
m is the mass.
a is the acceleration due to gravity.

In light of this, it will be less confusing for you if, when discussing weights and gravity, you use:

W = m * g

Your confusion arises because we have distinct concepts using the same terminology. People use kg for weight in everyday usage, when N is the more correct term for weight. Saying that I weigh 87kg is incorrect. I consist of 87kg of matter.

I weigh 950N on the Earth because gravity accelerates my mass of 87kg at 9.81 m/s^2 against the Earth.

I weigh 160N on the Moon because gravity accelerates my mass of 87kg (which stays the same) at 1.62 m/s^2 against the Moon.

anorlunda said:
When you weight meat at the store on a spring scale, it measures force.
Those scales are calibrated, by law, to read what a physicist defines as mass. They do call it weight, as that is also required by law.

nasu and jbriggs444