Mass .v. Weight and vice versa

Max Q

The conflation of the terms 'mass' and 'weight' in everyday parlance is something I'm trying to get my head around.

The unit of mass is the Kilogram (kg), the unit of weight (W=mg) is the Newton (N). Yet we say things weigh 'x' Kilograms or Pounds in everyday parlance. I understand that taking the acceleration due to gravity to be constant at the earth's surface (I know it's not, it varies slightly from pole to equator) it is permissible to ignore the effect of gravity on mass since it's a directly proportional relationship and is the same everywhere. Thus, ignoring gravity still allows us to compare weight on earth in a meaningful way by just talking about it's mass.

Am I correct so far?

If I take the example of weighing myself on a typical digital weighing scales;

So I stand up on the scales and it reads 75.0kg on the screen.

Is it telling me that my mass is 75.0kg? Is it sensing the reaction force due to me standing on the scales by load cell or some such, getting a force in Newtons and dividing this by 9.8m/s2 to get my mass and this is what it displays on the screen?

So what's my mass and what's my weight?

Thanks for reading.

Lbeard

BadTeacher wrote: »

The conflation of the terms 'mass' and 'weight' in everyday parlance is something I'm trying to get my head around.

The unit of mass is the Kilogram (kg), the unit of weight (W=mg) is the Newton (N).

Your mass is your mass. Newton's equation for force is F = (Mass)(Acceleration)

When you standing still you're still accelerating due to gravity - so the force is your Mass multiplied by the Acceleration due to gravity.

Yet we say things weigh 'x' Kilograms or Pounds in everyday parlance. I understand that taking the acceleration due to gravity to be constant at the earth's surface (I know it's not, it varies slightly from pole to equator) it is permissible to ignore the effect of gravity on mass since it's a directly proportional relationship and is the same everywhere. Thus, ignoring gravity still allows us to compare weight on earth in a meaningful way by just talking about it's mass.

Gravity is the same everywhere on earth. That is if you try to lift a kilo, the force you'll feel pressing against your lift will be the same everywhere.

Am I correct so far?

No.

If I take the example of weighing myself on a typical digital weighing scales;

So I stand up on the scales and it reads 75.0kg on the screen.

Is it telling me that my mass is 75.0kg? Is it sensing the reaction force due to me standing on the scales by load cell or some such, getting a force in Newtons and dividing this by 9.8m/s2 to get my mass and this is what it displays on the screen?

So what's my mass and what's my weight?

Your mass would be 75 Kg. If you went to the moon your mass would still be 75 kg.

The difference on the moon would be since the gravity is weaker, the Force would be weaker - you would feel lighter, you could jump very high into the air (okay there's no air on the moon).

If you were deep in outer space, in zero gravity, you would be weightless, but your mass would still be 75kg

What a weighing scales does on earth is measure the force of you pressing down on it due to gravity. Since gravity is a constant on earth, it just gives you your correct mass. If you took the weighing scale to the moon, it would give you an incorrect mass, (you would appear to have less mass) unless you adjusted the weighing scale to account for the weaker gravity on the moon. Then it would give you your correct mass.

Force = MassXGravity.....The gravity is a constant..... Your Mass equals = Force/Gravity but gravity is just some constant, so You Mass = Force by some constant. That constant can be accounted for in the spring of the weighing scale.

On different planets you will weigh more or less, depending on the strength of gravity - in zero gravity you weigh nothing - but your mass is the same regardless of where you are in the universe.

Max Q

Thanks for the reply.

Lbeard wrote: »

What a weighing scales does on earth is measure the force of you pressing down on it due to gravity. Since gravity is a constant on earth, it just gives you your correct mass. If you took the weighing scale to the moon, it would give you an incorrect mass, (you would appear to have less mass) unless you adjusted the weighing scale to account for the weaker gravity on the moon. Then it would give you your correct mass.

Force = MassXGravity.....The gravity is a constant..... Your Mass equals = Force/Gravity but gravity is just some constant, so You Mass = Force by some constant. That constant can be accounted for in the spring of the weighing scale.

Ok, this is a little clearer now. So my digital weighing scales is measuring a force and to tell me what my mass is it needs to divide by g which is presumably done in the circuitry of the scales? In the same way that a spring in a conventional weighing scales is calibrated to eliminate g from the reading to display mass?

Lbeard

BadTeacher wrote: »

Ok, this is a little clearer now. So my digital weighing scales is measuring a force and to tell me what my mass is it needs to divide by g which is presumably done in the circuitry of the scales? In the same way that a spring in a conventional weighing scales is calibrated to eliminate g from the reading to display mass?

Yes, it's one of these things that's really simple, but there's a confusing twist in it. The circuit of the digital weighing scales doesn't even have to do a calculate. It just measures the force of whatever is standing on the scale. There's no gravity calculation. The weighing scales are calibrated - you do this by placing one kilo on the scale and then setting whatever the device is to displaying 1 kilo for that weight (which is the force caused by its' mass and gravity)

A weighing scale is essentially a dumb device - you can make one from virtually anything. Calibrate it with agreed measures, and you have a weighing scale.

I'll explain the confusing twist. Weights (as in measures) pounds, ounces, etc, have been around for a very long time. Before Isaac Newton no one really knew why things weighed anything or why things fell - but they did weigh, pounds, ounces, etc. The weight is just the force and the force is caused by the gravitational effect on the mass. So Newton separated the mass from gravity. The mass of an object is the same anywhere in the universe - but the gravity is different (so the weight will be different)

The confusing twist. Why do we say something weighs a kilo, but we also say something has a mass of a kilo?............Because we're on earth. .....If we were on the moon, we couldn't say that. But confusingly if we were on the moon, we could say an object of mass 1 kg, weighs 0.17 kg.....We could say that but we really shouldn't as the mass hasn't changed, but the gravity of the moon is different. If 1 kg was floating in deep space, we could say that it weighs 0 kg. Again we shouldn't. It's fine on earth to say something with a mass of 1 kg weighs 1 kg. But weight and mass are not the same thing. And we confuse people by using the units for mass kg, to describe things like weight on the moon. Weight doesn't have unique units - so we improperly use the units for mass.

It's a conceptual thing. Think about how things fall on earth or how you don't drift off up into outer space, how astronauts can jump around the moon - and how astronauts in the space station float around as if they were lighter than a feather.

Max Q

Lbeard wrote: »

The confusing twist. Why do we say something weighs a kilo, but we also say something has a mass of a kilo?............Because we're on earth. .....If we were on the moon, we couldn't say that. But confusingly if we were on the moon, we could say an object of mass 1 kg, weighs 0.17 kg.....We could say that but we really shouldn't as the mass hasn't changed, but the gravity of the moon is different. If 1 kg was floating in deep space, we could say that it weighs 0 kg. Again we shouldn't. It's fine on earth to say something with a mass of 1 kg weighs 1 kg. But weight and mass are not the same thing. And we confuse people by using the units for mass kg, to describe things like weight on the moon. Weight doesn't have unique units - so we improperly use the units for mass.

I think this is the real crux of the matter for me. It's unfortunate how we intermix the terms 'mass' and 'weight' with no regard to their scientific meaning.

Being pedantic - is it incorrect to say my 'weight' is 75kg? To be scientific about it, I should instead say I have a 'mass' of 75kg? If weight is defined as a force and has units N, then we should only ever speak about weight in terms of a force in N (or any other unit of force). To talk about 'weight' in kilograms is scientifically incoherent as it refers to a force in units of mass.

Lbeard

BadTeacher wrote: »

Being pedantic - is it incorrect to say my 'weight' is 75kg? To be scientific about it, I should instead say I have a 'mass' of 75kg?

If you want to be pedantic, be pedantic, though it's never really considered such an attractive feature. On earth you weigh 75kg, you only really have to get precise if you plan on leaving the planet. If you want the physical experience of feeling your weight changing, go on a roller coaster. At different points in the ride you feel heavier or lighter depending on how the different forces are acting on you.

If weight is defined as a force and has units N, then we should only ever speak about weight in terms of a force in N (or any other unit of force).

That isn't really good either. Because we have to think of force as independent from weight. Because, the deeper you go into these things, the more confusing it will become - the phenomenon of the experience of things having weight, or weighing, is due to a force, the nature of the force is something else.

To talk about 'weight' in kilograms is scientifically incoherent as it refers to a force in units of mass.

To talk of sugar in terms of cups in certain sense is also incoherent. In scientific terms weight is abandoned. Mass and Acceleration are not. Giving weight its' own units would just confuse things (I know it can be confusing as it is).

It's only incoherent if people can't agree on what they mean. In roller coaster design, and in the design of rockets and jets, the forces experienced by people are often given units in G (pronounced Gees). The G encapsulates weight, force and mass. Earth's gravity is 9.78 m/s^2 (let's just say 10 m/s^s so I don't have to reach for the calculator).....If you're in a car that can travel very fast. If you hit the accelerator, and accelerate at a rate of 20 metres per second, per second, you'll feel a force pushing you back into your seat of 2 G.....Accelerate at 30 metres/s^2, you'll feel 3 G. etc.

At 1 G you feel as you do normally, at 2 G you feel twice as heavy, 3 G three times as heavy. A second ago, I wrote that you'll feel a force of 2 G. But Gs are not units of force. To be scientifically coherent, everyone has to know what is and what is not meant by the use of a unit. A roller coaster engineer will not get confused, or if they do, they will lose some holiday makers on their ride's maiden voyage.

Or bridge makers. I saw a photo of a sign at a foot bridge somewhere in South America. In English it says, only two people at a time. In Spanish it says, up to six Latinos, but only two Americans at a time.

Max Q

Lbeard wrote: »

If you want to be pedantic, be pedantic, though it's never really considered such an attractive feature.

I wasn't asking for life advice but thanks anyway. You'll be glad to know I'm not pedantic in daily life. I posted my question here in the hope that someone could clarify my understanding. You have somewhat, so thank you for that. A lot of what you have posted in reply is not what I asked. I have a good understanding of basic Newtonian mechanics. I was specifically interested in the interchanging of the terms 'mass' and 'weight' in modern parlance and particularly the common use of a unit of mass to describe weight (a force). I know this is pedantic, but that's the nature of this discussion.

Lbeard

BadTeacher wrote: »

I was specifically interested in the interchanging of the terms 'mass' and 'weight' in modern parlance and particularly the common use of a unit of mass to describe weight (a force). I know this is pedantic, but that's the nature of this discussion.

My school physics teacher, among a few things, didn't understand the concepts of weight and mass.

Weight is used in cooking, mass is a far more complex subject. There's a lot more to mass than weight. You can use weight in scientific terms, but you have to be explicit in what you're doing, not necessarily pedantic - so you can use the units kg, but they come with a caveat. Wherever you go in the universe mass is important. But because of gravity, on earth we have an easy way of determining mass - measure the force of something being pulled by earth's gravity. In zero gravity, everything more or less weighs the same, (but that too is a misleading statement, as all masses exert a gravitational force on each other)

But go further down the rabbit hole of theoretical physics, and mass becomes as iffy as weight. If you want to be really pedantic, you could say something neither has weight nor mass, but energy. E = mc^2

But I have people, who really should know better use the term weight, when they really mean mass. If someone throws you out of an airplane, your weight will increase as you fall, but not your mass. The effect when you hit the ground, would be just the same as if your weight somehow magically increased to the same level as falling from an airplane has made it. You'd spontaneously squish like a pancake. (Like if you traveled to Jupiter and stood on its' surface - Jupiters gravity would squish you instantaneously - because the gravity is far greater than earth.

Morbert

BadTeacher wrote: »

I think this is the real crux of the matter for me. It's unfortunate how we intermix the terms 'mass' and 'weight' with no regard to their scientific meaning.

Being pedantic - is it incorrect to say my 'weight' is 75kg? To be scientific about it, I should instead say I have a 'mass' of 75kg? If weight is defined as a force and has units N, then we should only ever speak about weight in terms of a force in N (or any other unit of force). To talk about 'weight' in kilograms is scientifically incoherent as it refers to a force in units of mass.

In most cases, saying you weigh 75 kg is fine, as it will be tacitly assumed you are talking about the force of a 75kg mass under Earth's gravity.

Strictly speaking, however, weight would indeed be measured in newtons.

Some definitions.

Delphi91

Lbeard wrote: »

...Gravity is the same everywhere on earth. That is if you try to lift a kilo, the force you'll feel pressing against your lift will be the same everywhere...

This is not strictly true.

There is a variation in the value of g over the globe.

There are two factors at play - (1) centrifugal force at the equator produces an outward force which reduces the net inward gravitational force slightly. (2) Because the earth is an obloid, the radius at the equator is slightly higher than the radius at the poles and since gravity is a 1/r^2 force, that means g at the equator is lower than g at the poles. The value of g ranges from 9.78ms^-2 at the equator to approx 9.83ms^-2 at the poles. This would result in a difference in weight of an object of approx 0.5% if it was measured at the equator and the pole.

FISMA

BadTeacher,

I always say that if you want to lose mass, diet. If you want to lose weight, go to the moon!

Mass is a primitive concept, that is, it cannot be broken down in to more simple terms.

Force is not primitive, it can be broken down in to mass and acceleration.

Force and mass are different measurements and hence, have different units. However, the two are so closely related, they are often used interchangeably, with caveats not always stated.

Example. If you take a 1.0kg mass and put it on a scale located on Earth's surface, the scale will read 2.2lbs. However, if you took the same mass and measured its weight on the moon, the scale would read only 0.37lbs. Same mass, different Forces on the body.

Likewise, a mass of 75.0kg weighs 165lbs on Earth.

Some fundamental differences: mass is a property of matter, Force is not. Force has to have a [single] direction, mass does not.