# How does a scale work?

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1. May 29, 2015

### christian0710

Hi and welcome to my curious posts :)
If a scale measures force then i assume it's measuring mass*acceleration, so does that mean that the scale is actually measuring my mass (like a balance does ), and then multiplying it by a 9.8m/s^2? Or how exactly is it built/programmed to work?

2. May 29, 2015

### HallsofIvy

On the contrary, the scale cannot directly measure mass. What it measures is the force of gravity, the weight of the object- the force with which the object pushes on the scale. In order that the object not just drop through the scale, the scale pushes back on the object with the same force. That force is caused by the compression of the spring inside the scale. If the scale reads "mass" rather than "weight" (some do) then it divides by 9.8. That "division" is actually done at the factory by putting the appropriate distance between "1 pound", "2 pounds", etc.

3. May 29, 2015

### DEvens

There are different kinds of force. Only in the case of unbalanced force is F=ma.

Consider tension in a cable. This is clearly a kind of force also. But, if the cable is attached at both ends and so nothing is moving, then it is balanced force.

Different scales work in different fashions. For example, an actual balance scale works by comparing the weight of the test object to the weight of standard objects. Such a scale would give the same answer on the Moon as it does on the Earth.

Other scales work by some such method as measuring compression of a spring, or of a crystal in a strain gauge, or some such method. This depends on the gravity when the measurement is taken, and will give different readings on the Moon to what it gives on the Earth.

Yet another kind of scale is available for use in free-fall. In this case, you attach the too-be-measured weight to the end of a spring-equipped rod. Then you pull it back and let it go. Then the device measures the oscillation period. And from that the mass is estimated. Its accuracy does tend to suffer from "slosh." If it was you being weighed, then if your arms flailed around it would affect the reading. But in this case it really is F=ma that is being considered. At least indirectly.

4. May 29, 2015

### Svein

The oldest form of a scale actually measures mass - by placing the unknown mass on one pan and a combination of known masses on the other.

5. May 29, 2015

### christian0710

So actually a scale works like a newton meter? a newton meter , as far as i understand cannot measure mass directly. but if you were to build a newton meter (like the guy in the video below) you would have to calibrate it first. You would set a mark for the position of the spring at mass = zero, then you would apply a known mass and set a new mark, and each mark represents units of force, so actuallt a newton meter is like a cartesian X,Y cordinate system, plug in a X(mas) and output a corresponding Y(Force) and which can be found by multiplying the mass with 9.8m/s^2 which is the proportionality constant.

6. May 29, 2015

### christian0710

Thank you for bringing that up- I'm very interesting in how that works: Before we even defined mass, how would people attempt to actually define it? If i had a balance like the one in your picture and i wanted to be the first to define what mass is and what values/magnitudes of size to give different objects. How would i start?
Is this the correct approach: I'd find 2 objects- Object A and Object B of same mass and made of the same material (so they have the same density and vulume) and place them on each side of the balance, so now the balance is balanced. Then from that same material i'd cut out small cubes of that same material (with same density) equal in size, and put them on one side of the balance. For each cube i'd read the a corresponding measurement, and then i'd just make up a rule and say "I'm going to say one cube has a mass of 1kg" and then I'll remove object B and see how many cubes go there to balance object A, and then I know the mass of object A? So i'm guessing back in the days when mass was being defined, someone just decided to give an object a definite Magnitude/value/number (fx 1kg for this cube) and then use the measurement reading on the balance indirectly to derive masses of bigger objects indirectly from that cube?

Or actually i might be mistaken, because if there were no gravity the scale would not move, and so different mass values could not accurately be assigned in that way. So how was it then done?

Last edited: May 29, 2015
7. May 29, 2015

### SteamKing

Staff Emeritus