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If a person stepped on a home bathroom scale, and weighed 170 lbs, he would weigh a different weight on this same scale when on other planets due to the force of gravity.
If, however, a person stepped on a professional medical scale — the kind with weights attached that you slide (as opposed to a bathroom scale) and weighed 170 pounds on Earth, would the weight of the person be the same on the other planets as it is on Earth (170 lbs)? This has become a bone of contention in an otherwise ideal marriage.
-Asked by David Fuchs and Sheila Moreland from Los Angeles
Hello, Sheila and David!
You've opened up a small can of worms with this one. Let me explain what I mean. Generally speaking, an introductory physics textbook will go into the first part of this question in relative detail. It will discuss how a person's weight would change on other planets (where the acceleration due to gravity is different) or in cases where the person was accelerating (where the additional acceleration changes the effective gravitational acceleration).
Image Credit: NASA
But in all of these cases, the textbook will never tell you what type of scale is being used to measure the person's weight. It is implicitly assumed, but not expressed, that the scale in question actually measures force.
Now, a weight is a force — it's the force exerted by the Earth (or other planet) on the mass of your body — so this assumption on the part of the textbook is not an invalid one. All bathroom scales measure force: underneath your feet is a spring with a known compressibility (or "spring constant"), which will compress by a distance that is linearly proportional to the force applied to it.
Thus it wouldn't matter where you took that bathroom scale, because it would always (within the limits of its engineering) correctly tell you the force being applied to it. So if our 170 pound person were to take the bathroom scale to the Moon, it would rightly show that the person's weight there was roughly 28 pounds (about 16% of what it is on Earth), due to the weaker gravity.
So what about a fancy, doctor's office style scale? If our 170 pound person took the fancy scale to the Moon and took a measurement, the scale would read: 170 pounds.
However, of course, there's a catch! It isn't that the person's weight is actually 170 pounds. It is, in reality, 28 pounds, like what the bathroom scale would have measured. But the way the doctor's scale measures weight is essentially by balancing masses, not with a direct measurement of force.
Each of the little metal weights on the doctor's scale corresponds to a certain force here on Earth, because it balances that force. So the slider labeled "40 pounds" balances a 40 pound weight on the scale, but only because both the 40 pound weight and the "40 pound" metal slider are subject to the same gravitational pull (acceleration).
So long as the acceleration that the slider and the thing being weighed experience is the same, the ratio (or balance) will always be the same, too. A 170 pound person weighs 28 pounds on the Moon, but correspondingly, the little metal sliders only "feel" a fraction of their own weight, so the sliders showing 170 pounds only balance 28 pounds in the Moon's gravitational field.
A 170 pound person will always read 170 pounds from the doctor's scale, so long as the person and the scale experience the same gravity. But the "170 pound" reading from the scale will cease to actually mean 170 pounds.
If, somehow, you could isolate the scale and the 170-pound person in different gravity (or if somehow they experienced a differing acceleration) during the weight measurement, then the doctor's scale would no longer read 170 pounds.
I hope this brings some balance back to your married life!
How bathroom scales work: http://home.howstuffworks.com/inside-scale.htm
How balance scales work: http://en.wikipedia.org/wiki/Weighing_scale#Balance
Kelly Chipps (AKA nuclear.kelly)
Department of Physics
Colorado School of Mines