We refer to our earthly weight in "pounds" or "kilograms". The Force I put on my scale is mass × acceleration = mass × 9.8 m/s^2.

My scale reads 98 kg, yet the units of Newton are kg m/s^2. Do I weigh 10 mass units? 98 Newtons? Or is it 960 Newtons?

The application is lifting force for a model rocket.

  • $\begingroup$ The scale is telling you your mass in kilograms. People who aren’t physicists call this your weight. $\endgroup$ – G. Smith Dec 16 '19 at 23:05
  • $\begingroup$ So, units of "mass" are standardized as "earth weight". Gravity pulls down at 98 kg × 9.8 m/s^2 resulting in a force of 960.4 Newtons? $\endgroup$ – Robert DiGiovanni Dec 16 '19 at 23:31
  • $\begingroup$ Yes, that’s right. $\endgroup$ – G. Smith Dec 16 '19 at 23:58
  • 1
    $\begingroup$ @RobertDiGiovanni You seem to have a pretty good grasp on it. A bathroom scale measures what we call as "mass" based on "Earth weight", so the two terms get changed around a lot. Interestingly, something like a triple beam balance should still measure actual mass in different gravity; whereas a bathroom scale would measure an incorrect "mass", because it is actually measuring "weight". $\endgroup$ – JMac Dec 17 '19 at 0:14

In everyday language, the terms "mass" and "weight" are used pretty much interchangably, but in physics, we distinguish them. Mass roughly speaking is a measure of the "amount of stuff", whereas when we say something like "the weight of the table is... ", what this means is "the gravitational force the Earth exerts on the table is..."

So, to directly address your question, here are the correct statements (and a few variations which say the same thing):

  • Your mass is $98$ kg.
  • Your mass on Earth is $98$ kg.
  • The gravitational force the Earth exerts on you is (approximately) $(98 \,\text{kg})(9.8 \, \text{ms}^{-2}) = 960.4 \, \text{kg m s}^{-2} = 960.4\, \text{N}$
  • You weigh $960.4\, \text{N}$ on Earth.
  • Your mass on the moon is $98 \, \text{kg}$
  • Your weight on the moon is $(98 \,\text{kg})(1.62 \, \text{ms}^{-2}) = 158.76 \, \text{kg m s}^{-2} = 158.76\, \text{N}$

So, as you can see, your mass is "a property of you", whereas your weight is "a property of you and where you are".

  • $\begingroup$ That's what I'm getting at. My mass should be 10. Our weight can vary depending on location, and also forces related to movement (merry go 'round, centrifuge, airplane). But, this will take a long time to change. $\endgroup$ – Robert DiGiovanni Dec 17 '19 at 14:14
  • $\begingroup$ @peek-a-boo, the weighing scale on earth showed his weight as 98 kg. You stated his mass was 98 kg and his weight on earth was 960.4 Newtons. All the weighing scales I know show a person's weight in kg (or lbs) units, whereas kg is a unit of mass. This is a disservice we as a society do, to budding physicists, or students attempting to take an interest in STEM. $\endgroup$ – RajuK Mar 11 '20 at 0:19
  • $\begingroup$ @RajuK indeed! language is a confusing beast, and certainly confused me immensely when i first learnt this stuff $\endgroup$ – peek-a-boo Mar 11 '20 at 7:15

To be more precise the weighing machine measures the $\frac {\text {normal reaction that you get}}{9.81}$ if you were on $45°$ latitude and not your weight. (You can easily verify this by considering the fact that you reweigh less if you move (at say $75 km \ h^{-1}$) in east direction and more in west direction.

  • $\begingroup$ Please add more info on the 45 degree latitude standard. We may "weigh" more at the north pole than at the equator too, correct? $\endgroup$ – Robert DiGiovanni Dec 17 '19 at 14:20
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    $\begingroup$ The value of $g$ changes with latitude. This is due to earths spin which applies a centrifugal force. This extra force varies as a $\cos{\theta}$ component of your latitude. $9.81$ happens to be the value of $g$ at $45$ degrees. $\endgroup$ – Sam Dec 17 '19 at 15:11
  • $\begingroup$ @RobertDiGiovanni Here is a related Vsauce video. (Skip to around 3:53 if you are in hurry). $\endgroup$ – user249451 Dec 17 '19 at 15:59
  • $\begingroup$ @RobertDiGiovanni Here are some relevant links : 45° latitude thing over here, - Wikipedia over here $\endgroup$ – user249451 Dec 17 '19 at 16:06

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