# What does a bathroom scale measure?

Hi I'm in grade 11 physics and my teacher assigned a question where he asked "What does a bathroom scale measure? Explain you're reasoning"

Ok for this I would say it measures normal force, according to newton's 3rd law you apply a force on the scale it exerts a force back on you and that is what it's measuring.

The next part of the question is "Explain how you know it is not measuring mass and/or weight"

It's not measuring mass because mass remains constant even in outer space but the scale reading changes even if you move your arms around while standing on it (air friction I guess?) and if you redirect your force that you're putting on it, like step on the scale and hold something at the same time.

Also because of the same reasoning it's not weight because weight is just the force of gravity.......(?)

Thats all, am I on the right track? What is exactly is weight? And mass? We never had a definition for mass in class, it was just, the amount of "stuff" and there is no real way to measure mass.....

Any help would be appreciated.

## Answers and Replies

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arildno
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Welcome to PF!
1. You are correct in assuming that it (basically) measures the normal force; however, look at your precise wording here:
"Ok for this I would say it measures normal force, according to newton's 3rd law you apply a force on the scale it exerts a force back on you and that is what it's measuring."
Doesn't it make more sense that the force actually measured by the scale is the force exerted by YOU on the scale, rather than the other way around?
(Do you know, BTW, HOW the scale measures this?)

Agreed so far?

arildno
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1. The reason why it doesn't measure MASS is that it measures a FORCE, and mass is no force.
2. Why can we say that the bathroom scale doesn't measure your weight?
Remember:
The reason that you don't fall into the earth due to the force of gravity (that is, weight) is THAT OTHER FORCES hinder you from doing so.
Suppose you take a firm grip on a cupboard or something, so that you basically can hang from it (the force from the cupboard keeps you from falling).
Furthmore, let someone slide the bathroom scale underneath your feet, so that the just touch the scale.
What do you think the reading will be then?
Your weight hasn't changed..

Hi Arildno, thanks for replying..Im sorry I couldnt reply quicker...

Ok yeah the reason I worded normal force weird because I thought it's the force opposite of gravity basically, for example if gravity is exerting a force or on us we are exerting an equal an opposite force back on it which is normal force (right?) ...

Ok I agree with you on mass is not a force, that is a better answer :) , but does my answer also make sense?

Weight..... You are right that it is weight if do the hanging from a cupboard and stuff but...isn't it also NOT weight sometimes? lol... Like weight is the force of gravity on you right? Well shouldnt that be constant? In your example yeah it will remain constant but only in those type of cases....Basically when ISNT it weight that it's measuring? (when it's normal force?).

Thanks a lot, Im really finding this usefull btw.

arildno
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First:
The bathroom scale is an instrument which (basically) measures FORCE.
This means that you shouldn't regard it as an instrument which measures other quantities than force; for example, mass.
Even though the bathroom scale spits out a number which is meant to represent your MASS (for example, 80kg), you should still regard the bathroom scale as primarily a measurement of force .
It is calibrated to calculate from the force measured the apparent weight of the object on it, and converting that "weight measurement" (actually, normal force measurement) into a "mass measurement".

Second:
You have rightly noted that if you wave your arms up and down, the needle will start to wiggle.
You made an assumption that this might be explained from air resistance; I'll put that into a proper perspective:

Think for a moment of your arm and the rest of your body as two separate objects:
Why?
Because your arm, all by itself has a weight, clearly this means that the rest of your body keeps it from falling down!
(Agreed?)
Hence, when your arm hangs still, the rest of your body EXERTS AN UPWARDS FORCE ON YOUR ARM, equal in magnitude to your arms WEIGHT (which tries to drag your arm down).
By NEWTON'S 3.LAW, your arm EXERTS A DOWNWARDS FORCE ON THE REST OF YOUR BODY, equal in magnitude to your arm's weight.

HENCE, the total downwards force on the rest of your body is it's own weight+a force equal to your arm's weight.
That is, in order for the ground to keep you from falling into the earth, it must exert on the rest of your body an UPWARDS FORCE EQUAL TO YOUR TOTAL WEIGHT!

By Newton's 3.law then, your body exerts a downwards force on the ground equal to your own weight.

Now, what happens if you fling your arm upwards in the air?
Clearly, your arm experiences an UPWARDS ACCELERATION, and so, by Newton's 2.law, must be subject to a net, upwards force!
What is the agent of this force?
Clearly, the rest of your body! (through a complicated machinery of muscular contractions).
That is, in the case where you fling your arm upwards, the rest of your body exerts A GREATER UPWARDS FORCE ON YOUR ARM COMPARED TO WHEN YOUR ARM IS AT REST!!!!.

Hence, by Newton's 3.law, your arm exerts A GREATER DOWNWARDS FORCE ON THE REST OF YOUR BODY COMPARED TO WHEN YOUR ARM IS AT REST!.

Hence, in order for the rest of your body not to fall through the ground, the ground must in this case exert a force on the rest of your body EXCEEDING YOUR OWN WEIGHT!!
That is, the normal force from the ground is greater than your weight.
Hence, by Newton's 3.law, the force exerted by you on the ground is greater than your own actual weight, and the bathroom scale will notice this.
Clear so far?

Last edited:
Yes, so far clear....

arildno
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All right, then!
As I'm sure you've realized, if you fling your arm downwards, this will reduce the normal force which the spring scale must exert upon you.

Now, to your idea of air resistance:
First, the pro:
Your idea is not bad at all!
Reason:
If I fling my arm upwards, I will push air upwards, and hence, the air resists that, and imparts a downwards force on my body. Similarly the other way.
So, your proposed mechanism satisfy what we will see:
If we fling our arm upwards, the needle on the scale will go up, whereas if we pull our arm down, the needle on the scale will go down.

The con's.
1) Note that in order to take into account the effect of air resistance, we are basically comparing what would happen if we compared the effects between motions done in vacuum (where my explanation is valid, but your not) and doing the same motions in a room filled with air (where my explanation is equally valid, but where yours might add something new).
The trouble is, that when we add up the actual numbers, the contributions from air resistance are MUCH less than the contributions from my effects.
That is, basically, the effects from air resistance are insignificant.
2) It might be argued that although the effects from air resistance are small, they are still detectable, and in taking account of them, we'll predict better what the bathroom scale spits out.
Unfortunately, this is untrue.
Every instrument is uncertain to some extent in its measurements, and the effects of air resistance are so tiny as to be within the uncertainty limit of the ordinary bathroom scale.
Hence, we might as well forget about it, since we can't measure the effect properly..

I would like to say, however, that it is by far more important that you came up on your own with a mechanism which qualitativily gives the correct behaviour; that the numbers don't add up quite, is a relatively minor issue.
Your example with air resistance shows that you have a good UNDERSTANDING of physics, even if you, naturally enough, haven't yet gained expert knowledge in physics..

Thank you :)