# Aren't 'sliding weight' scales actually measuring mass, not weight?

This has bugged me for a long time. It seems that since these ‘scales’ are actually comparing your weight to a counterbalanced set of weights, that they are actually comparing (measuring) your mass.
What I’m getting at is, I think if you took one of these scales to the moon, you’d show the same weight as you did on Earth, even though it should be much less.

Any thoughts?

-Aero

They are measuring weight (The force with which a body is attracted to Earth or another celestial body) by comparison. You can infer mass only because the gravity is the same when the measurements were taken.

Scales of this type are not influenced by size of the object being measured (provided that what you’re measuring will fit on the scale).
Hence, a two pound brick will weight two pounds, as will two pounds of feathers.

The “sliding weight” setup is a balance, not a scale, and it does indeed measure mass, not weight. Results will be independent of gravitational force, as long as the force is locally consistent (which is pretty much “anywhere humans can live”).

No, they’re measuring mass. The OP is referring to a triple- or double-beam balance, similar to what you find in many doctor’s offices. These measure mass, because the reading will be the same regardless of gravitation. That’s because gravity pulls equally on the object to be measured, and the counterweights.

This topic is more complicated than I first thought. o:

I stand corrected.

You are absolutely right, as others have already pointed out.

Your typical home bathroom scale is measuring weight, and you’d get a different result if you used it to wiegh yourself on the moon (for example).

The OP’s suspicions are correct. It is measuring comparative masses, not weight.

However, until we are in a position of commonly weighing things in orbit, on the moon, or Mars, it’s not really going to be a problem.

There is further confusion because when we say “weight” we often mean “mass.” When I say my weight is 75 kg, that’s actually a measurement of mass. Pound is even more confusing because it can be used as a unit of both mass and weight.

But hang on… the same is true of ordinary balance scales, because the force acting on the object being weighed (in one cup) and the assortment of standard weights (in the other cup) will be the same, so 1.5kg of sugar is going to balance brass weights of 1 +0.5 kg, regardless of whether the local g is 9.81 or some other non-zero value.

Spring balances, on the other hand, will give different readings under different gravitational conditions.

Well, the thing you stand on is a scale, but why quibble.

If properly calibrated, the balance will measure both weight and mass.

Q.E.D. is correct. A beam balance is a torque-null system, and it directly compares two or more masses. Gravity is not a factor as long as all the masses are “seeing” the same acceleration.

But beam balances aren’t used much anymore; they’re difficult to use, have quite a few moving parts, and difficult to instrument & automate. Today, most balances measure mass by measuring the force (in N or lbf) of an object using a load cell. Mass is then computed using the familiar F = ma formula. Of course, the drawback here is that you have to know the acceleration due to gravity, which is a function of longitude, latitude, and altitude. Instead of trying to precisely nail down the acceleration value, most owners of such balances simply use known masses to calibrate and adjust the balance in situ.

By “properly calibrated,” you mean calibrated for the gravitational field it is used in, right? So what it’s really doing is measuring mass and displaing weight using the given gravitational field.

If the gravity were to suddenly change, your weight will change but not your mass. A balance will not detect this change. So in this sense it’s not measuring weight.

Huh? 'Splain this, Lucy.

Weight changes, depending on the local gravitation. A balance, however, will always read the same, no matter where you are.

<bold is mine>

See, that is what I said. The scales are measuring weight, but we can infer mass.

Example:
Suppose for instance that we can generate different strengths of gravity (supercool technology for this example). We make one side of the balance experience Earth gravity, and the other side experience Moon gravity. If the balance is level, the mass of the weights on either side are not going to be equal. The scale is giving you back the information that their weight is the same, but says nothing about the mass.

The reason the balance can give us the mass of an object is because we know that objects of equal mass will weigh the same amount if subjected to the same strength of gravity. A balance is almost certainly experiencing the same amount of gravity on either side, in which case it is ok to call the masses equal if the balance is level. However, the balance is still only measuring the pull of gravity on either side of the arm(s). Assumptions about the gravic conditions are left up to us.

Phage: I think we’re all in agreement here. Yes, when it comes right down to it, the moment arm is acted upon by a force. And since F = ma, the force is directly proportional to the acceleration. But a beam balance also assumes the acceleration is identical for the all the masses hanging off the beam. When this assumption is made, the acceleration is no longer a factor. Not only that, but the forces don’t even have to be identical (and they’re often not identical). In a torque-null system, only the torques have to be equal and opposite…