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Units we use daily- pounds, kilograms

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hopefully I am posting in the right area. I apologize if not.

I am studying the physics iBook "Physics - fundamentals and problem solving" , which is an absolutely amazing book by the way.. i had no idea one could teach through a book with a few videos and get the same results as a full on physics classroom. But anyway, there is a concept I am having trouble grasping. I understand that the force of the gravitational pull is mass times acceleration of gravity but what I'm having trouble with is what we are measuring when we stand on a scale.

I was browsing the net and I got onto the Wikipedia site, http://en.wikipedia.org/wiki/Pound_(mass) , where it says that pounds are units of mass in the imperial system we use here in the US. It also goes on to talk about pound-force and pound-mass and that is where It gets me confused. When I step on a scale, is that scale measuring my mass? or my weight here on earth? Pound force would be weight (mass times gravity) and pound mass would just be mass I suspect?it might be a silly question to most, but I've never heard of this.

and coincidentally, if one pound is .45359 kilograms, does that mean 1 pound-mass or pound-force equals .45359 kg? When they step on a scale with kilograms, is it measuring their weight or mass? In weight lifting, or on truck scales in kilograms, is that the mass or the weight? Thanks!

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Ok I did a little more reading on it. I'm starting to understand it now. Apparently you would need to understand the construction of the scale. So if the scale has a spring in it that compresses with more FORCE applied, it is measuring your weight ( mass x acceleration of gravity) but if the reading is showing kilograms..which are a measurement of mass, NOT weight..then the scale is automatically converting the weight that is is reading into mass by dividing the newtons of force it reads from you stepping on it by the acceleration of gravity. So if I step on a scale and it tells me I am 80kg..that means the scale is reading that 784 newtons of force are being applied to the spring and, it is assuming that we are on earth so it divides 784 by earths gravitational acceleration 9.8m/s2 and displays the result of that equation to me.

now the question I have is, does an American scale which displays pounds, display pounds-force or pounds-mass? If it displays force, then theoretically we could take that scale to the moon and weigh ourselves and still get the correct reading in pounds. But if we take a scale which displays kilograms, and "mass" ourselves..because kg is a measurement of mass, not weight.. It would give us the incorrect reading of mass because it is assuming that we are on earth where gravity has a different acceleration

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Great exploration Tony, and I'm thrilled you're enjoying my book!

The readings on a scale are actually pretty tricky, and you've gotten a great start on understanding it. Let's start with metric scales. Typically metric scales have readings in kilograms, which is an inaccuracy. Scales read the normal force on an object (your weight, or the force of gravity pulls you down toward the center of the earth (mg). The normal force, aka the force of the scale, pushes back on you with the exact same force). So a scale reads force. Technically, it should be giving you a reading in Newtons. However, since most scales are used only on Earth, manufacturers have long since started putting the readings on the scale in kilograms (which, as you say, is the force in newtons divided by 9.8 m/s^2.) If you were to take the scale to the moon, it would be inaccurate, as it would show only 1/6th of your mass on the Earth, and mass doesn't change when you go to the moon. If it read in newtons, however, and showed 1/6th of your weight (in newtons), that would be correct.

An American scale, on the other hand, typically gets it right in that it reads in pounds, which is a unit of force. On the downside, however, in the United States we do a miserable job of measuring mass correctly. We treat pounds (a force) as synonymous with mass, which it is not. In the English system, the correct unit of mass is the slug... and you hardly EVER hear anybody talking about a mass in slugs.

Things get even trickier when you get to scales which accelerate (for example, put a scale in an elevator and watch its readings as it accelerates up and down). I had some students who put together a cool little video about it a few years ago...

Thanks for the great feedback, and the great questions. You're definitely on the right track!!!

Best Wishes,

Dan Fullerton

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