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I understand that weight is a measure of force acting on an object due to gravity and mass is a measurement of the quantity of matter than an object contains. With mass having units of kilograms or slugs and weight having units of newtons or pounds.

  1. Based on my research online I see that scales on earth are calibrated for earth (via a spring constant, piezoelectric material, etc. means of measurement depending on the type of scale). But it is not clear to me if it gives a mass of say 70kg on earth would that mean that I would also be 70kg on the moon? Using that particular scale it probably would not read right, correct? But a scale with a calibrated measuring device should give me 70kg on the moon as well since that is a unit of mass?

  2. Are weighing scales we typically use at home measuring mass or weight? The output tends to be in kg OR lbs which is baffling to me because they are giving a measure of mass OR weight? It seems we can convert a kilogram to pound by multiplying 1kg by 2.2046, how is it that we can directly convert from a unit of mass to a unit of weight like this?

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Strictly speaking a scale measures weight and a balance measures mass, but it is common, especially in non-technical English, to refer to a "scale" in either case.

Most probably your home device is actually a scale and is somehow measuring the force imparted by whatever you put on the platform due to your local gravity. The function to display the result in either kilograms (mass) or pounds (force) is typically just a software conversion that assumes that your local gravity is a standard value for Earth, which is to say $g$ given approximately as $9.8\ \mathrm{m/s^2}$ or $32\ \mathrm{ft/s^2}$, depending on which system of units you are using.

Since this is typically not just a conversion from mass to force but also between metric and Imperial units, you can think of having two steps. Starting in pounds first "convert" to mass (slugs) staying within Imperial using the value of $g$ and then convert from Imperial to metric.

If you take that scale to the Moon, you will still get the correct weight, but that weight will now be less than what you would have measured for the same object on Earth because the Moon's gravity is less. So far so good, because that is the correct answer. If you ask the scale to give you a reading in kilograms though, you're probably in trouble. Unless it has a function that lets you recalibrate or reprogram it, it will not know that you are on the Moon and will happily do the conversion assuming the Earth's gravity rather than the Moon's. Of course this depends on your scale and how sophisticated it is. But if you're just talking a standard, household bathroom scale that was never meant to go to the Moon, this is probably what you'll get.

Now if you really did have a proper balance - something measuring mass - the situation is the same on Earth but reversed on the Moon. On Earth you get consistent results as shown in kilograms or in pounds under the same assumption about the strength of gravity, just now converted the other direction. On the Moon, you now get the correct mass, but if you ask for the result in pounds it will be wrong. (Again unless you've got some unusual device that let's you reprogram it for being on the Moon or otherwise recalibrate the internal conversion function.)

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  • $\begingroup$ If we use a balance with kg weights on it on one side and I stand on it on the other it would give my mass in kg of course. I also believe that if I took this setup to the moon it would still give me my mass in kg and it would be the same value. But what if I used lb weights on the balance? I think this would be a violation of using a balance because it only measures mass by definition? If you took a balance and weights labelled in lb to the moon it would read incorrectly because the weights are calibrated for earth's gravity? Isn't it weird that gyms have weights labeled in lbs and kg? $\endgroup$
    – Xcalibur328
    Feb 16, 2021 at 5:29
  • $\begingroup$ I tried to address this in my answer, and I'm not sure that I can do better here. No matter what label you put on your masses/weights their mass is what it is. The only way to make an equivalence between mass and weight is to assume the strength of the gravitational field. Because for most everyday purposes the Earth's field is close enough to constant, this works ok on Earth. If you need high precision and repeatability in different strength fields (including an extreme case like Earth and Moon), then you cannot generally make the equivalence, as you seem to have understood from the start. $\endgroup$
    – Brick
    Feb 16, 2021 at 18:41

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