B What is the Correct Reading on the Scale in This Mass/Scale Puzzle?

[Herman Trivilino]

That's just a misunderstanding of how springs work.

There are ways to measure force that don't make use of springs. They all share this property, though, that if you apply forces of equal magnitude $F$ in opposite directions they report a value of $F$ for the force. That's by design.

So I would say that this is a misunderstanding of how forces are measured. And the misunderstanding is weird because it occurs in some scenarios and not in others.

It appears to be a stubborn refusal to form a consistent worldview.

 

[ergospherical]

Right, sure. It'll probably be some sort of strain-based sensor in any case. Whether it's the extension of a spring, the refractive index of the material, resistance, etc., due to the strain that gives rise to the reading internally is not important for this question.

I don't think "tension" is very clearly explained, at least not when I was in school. In the sense that it's a "thing" (read: tensor, hence why it's not explained in school) that exists everywhere in the body. Every part of the elastic body is applying an internal tensile force on every other bit. So until you get to that stage, you just have to accept that elastic materials apply a force equal to their internal tension on anything attached to them. (Again, at least in a linear 1d geometry.)

 

[tech99]

Aftyer all that, as we measure weight in Newtons, the question is meaningless.

 

[PAllen]

I should point out that most laypeople, including myself, don't usually think of weights and scales in terms of Newtons.

I see a diagram with two 10kg weights being pulled down by gravity on a single scale, I intuit the scale is going to read 20kg. It is very hard to break that conclusion without resorting to an alteration of the scenario.

Well if you look at the crude diagram I posted some poste ago, you will see what balances the 20 kg.

 

[DaveC426913]

Well if you look at the crude diagram I posted some poste ago, you will see what balances the 20 kg.

I did look at it and tried to follow it. I'll have to spend more time on it.

 

[Herman Trivilino]

Aftyer all that, as we measure weight in Newtons, the question is meaningless.

The $\mathrm{SI}$ unit of force is the newton. Weight is defined in physics and engineering differently than in international treaty and law. In the latter case the $\mathrm{SI}$ unit of weight is the kilogram.

 

[OmCheeto]

Ok. I'm out. I thought about it in terms of a tug of war, couldn't figure out the answer, found the following video, and the replacement of the one group of tuggers with the tree answered the question.

 

[kuruman]

So I would say that this is a misunderstanding of how forces are measured. And the misunderstanding is weird because it occurs in some scenarios and not in others.

I think it is also due to partial understanding of Newton's Third law. Here is a diagnostic question related to @OmCheeto's video that probes one's understanding of the 3rd law and what a spring scale displays.

The figure shows a team of four men engaged in a tug o wall. Nothing is moving. Which of the forces on the list has a magnitude that matches the reading on the scale? Circle all that apply.

(A) The force exerted by the left side of the scale on the rope.
(B) The force exerted by the right side of the rope on the scale.
(C) The force exerted by the rope on the wall.
(D) The total horizontal force exerted by the men's hands on the rope.
(E) The total static friction force exerted by the men's feet on the ground.

Spoiler: Answer

All five choices (A)-(E) must be circled.

 

[A.T.]

I should point out that most laypeople, including myself, don't usually think of weights and scales in terms of Newtons.

I see a diagram with two 10kg weights being pulled down by gravity on a single scale, I intuit the scale is going to read 20kg. It is very hard to break that conclusion without resorting to an alteration of the scenario.

You talk about masses not forces. Thus you ignore the force that is always needed at the other side of the scale, even in the simple vertical setup, because you see no bannanas there.

 

[sophiecentaur]

I should point out that most laypeople, including myself, don't usually think of weights and scales in terms of Newtons.

Weights are appropriate when talking to the handyman or the DIY store but you can't use weight in any context except when the Earth's gravity is producing it. A member of PF, even if he/she is a 'layperson', should make the effort and be an honorary Physicist / Engineer / Mathematician. Mass v weight is a standing joke with many comedians and can be funny as the context is usually a cranky Science teacher; fair do's. But you can't join a club if you don't use the right terms. That's even down to the direction the referee points after an infringement in rugby and 'soccer'.

 

[Herman Trivilino]

I see a diagram with two 10kg weights being pulled down by gravity on a single scale, I intuit the scale is going to read 20kg. It is very hard to break that conclusion without resorting to an alteration of the scscenario.

But that is the process of altering an intuition. It won't change by itself, and leaving it unchanged means a discord in your own worldview. So if you're not happy with either choice, for no other reason than it prevents you from advancing your knowledge, and resorting to alternate scenarios helps you change your intuition, then why not do that?

 

[Herman Trivilino]

Weights are appropriate when talking to the handyman or the DIY store but you can't use weight in any context except when the Earth's gravity is producing it.

True in the world of physics and engineering, which is indeed where we are right now as we participate in this forum.

But by international treaty and its concomitant laws, the definition of weight is identical to the physicist's definition of mass. That is of course the reason you see it being used that way in the DIY store or by the handyman or in countless other contexts.

It's a definition, so contrary to what appears in nearly every physics textbook, it can't be wrong. It's a definition!

 

[sophiecentaur]

That is of course the reason

No it's not. The reason people use weight for mass is because all the others in their everyday lives use it. In the same way they confuse kW with kWh and use the verbs for current and volts the wrong way round? Everyday language just doesn't cut it for discussing any serious activity.

You seem to be holding a torch for this sort of error. Why?

 

[jbriggs444]

You seem to be holding a torch for this sort of error. Why?

I share the same sentiment as @Mister T. Because it is not always an error. We (as scientists and physics students) need to avoid the self righteous attitude that makes us look down at the merchants and regulatory bodies who use the term "weight" in a way that goes counter to our textbooks.

The merchants have thousands of years of experience and good reason to use the term "weight" to refer to mass. For them, "weight" is what a balance scale measures. Using the word to refer to a force would be erroneous in that context. (Force is used as a proxy for mass under the reasonable assumption that the local gravitational acceleration does not vary greatly over the diameter of the apparatus)

"Weight" is also what a spring scale measures. A spring scale that is properly calibrated for use in commerce will measure mass (using force as a proxy to compare the unknown mass with the known reference weights used in the calibration under the reasonable assumption that neither the spring constant nor the local gravitational acceleration vary greatly over time).

 

[A.T.]

The reason people use weight for mass is because all the others in their everyday lives use it.

Wasn't the word 'weight' around long before physists started using it as a technical term, and telling everyone how to use it properly? Just like power, force, work, current? If you want to avoid this confusion, then you have to make up completely new words for new physical concepts.

 

[Herman Trivilino]

You seem to be holding a torch for this sort of error. Why?

Because it's an error made in virtually every introductory physics textbook and classroom. The so-called Treaty of the Meter was signed in Paris in 1875 by, among other nations, the United States. It established the International Bureau of Weights and Measures (BIPM) as the governing body over what is now called the SI. It requires a meeting every 4 years IIRC of the General Conference on Weights and Measures (GCPM) to keep the system updated.

It established the meter as the unit of length and the kilogram as the unit of weight. Member nations are free to use other units, but they must be defined in terms of SI units. Thus the foot is exactly 0.3048 m and the pound Avoirdupois is exactly 0.453 592 37 kg.

The newton was later added as the unit of force.

Weight is a term with a definition. It's defined by law one way and in physics another way. Neither can possibly be wrong because they are definitions.

The error made in physics books and classrooms is the insistence that the only correct definition of weight is one where it's a force.

 

[AlexB23]

TL;DR Summary: What does the scale read in this diagram?

My learning is a bit rusty. I can intuit the answer but I can't formalize it.


What does the scale read?
View attachment 363598


I say the scale reads 10kg.

My logic is this:

1. Fix the left cable and pulley in place with a giant glob of glue.
2. Cut the cable holding the left weight.
3. The scale is holding up a 10kg weight. Nothing has changed as far as the scale is concerned.

But what is a more elegant way of getting the answer?

Is this like the same type of thing where you have a car crash into a stationary car at 10 m/s, then have both cars travel at 10 m/s towards each other, and the damage is the same as in what Mythbusters did many years ago?

Source:
https://www.wired.com/2010/05/mythbusters-energy-explanation/

 

[tech99]

Is this like the same type of thing where you have a car crash into a stationary car at 10 m/s, then have both cars travel at 10 m/s towards each other, and the damage is the same as in what Mythbusters did many years ago?

Source:
https://www.wired.com/2010/05/mythbusters-energy-explanation/

Or the supposed impossibility of moving an object because every applied force has an equal and opposing reaction.

 

[AlexB23]

Or the supposed impossibility of moving an object because every applied force has an equal and opposing reaction.

Yep, Newton's third law. So this scale problem is the same exact thing.

 

[hutchphd]

That's just a misunderstanding of how springs work.

Perhaps but who cares. For the purposes of this problem a scale is a black box with a hook and a calibrated readout of the static force on that hook. It could be filled with microprocessors and elves and it wouyld not be relevant to the question. Have humams here (and everywhere!) lost all ability to concentrate.???.......this approaches the absurd

 

[PAllen]

Is this like the same type of thing where you have a car crash into a stationary car at 10 m/s, then have both cars travel at 10 m/s towards each other, and the damage is the same as in what Mythbusters did many years ago?

Source:
https://www.wired.com/2010/05/mythbusters-energy-explanation/

Wait a minute - depends on whether the stationary car is able to roll, or how slippery the surface is. Extreme case: stationary car on ice starting at collision point. To whatever extent both cars move after collision, there is less damage in the stationary car case.

 

[ergospherical]

Perhaps but who cares. For the purposes of this problem a scale is a black box with a hook and a calibrated readout of the static force on that hook. It could be filled with microprocessors and elves and it wouyld not be relevant to the question. Have humams here (and everywhere!) lost all ability to concentrate.???.......this approaches the absurd

Right. But I gathered the whole confusion of the OP was why the scale reads T if you pull on both sides with a force of size T. It’s somewhat helpful to know how a spring works (!).

 

[kuruman]

It established the meter as the unit of length and the kilogram as the unit of weight.

I don't know what "it" established in 1875, but the NIST site today says that the kilogram is the unit of mass. I go by that.

 

[AlexB23]

Wait a minute - depends on whether the stationary car is able to roll, or how slippery the surface is. Extreme case: stationary car on ice starting at collision point. To whatever extent both cars move after collision, there is less damage in the stationary car case.

Assuming it does not roll.

 

[Herman Trivilino]

I don't know what "it" established in 1875, but the NIST site today says that the kilogram is the unit of mass. I go by that.

Me, too. But "it" established the BIPM, and as part of the treaty agreement each member nation must establish its own organization to insure compliance. In the US that organization is the NIST.

What you're saying is not incompatible with what I said.

 

[hutchphd]

Right. But I gathered the whole confusion of the OP was why the scale reads T if you pull on both sides with a force of size T. It’s somewhat helpful to know how a spring works (!).

You need to pull equally on any "scale" to keep it in place while in use. and in general it is very useful to understand how a spring works. I don't think the two are equally necessary here. This post headed for the weeds faster than I would have deemed possible. I was just saying K. I .S.S. I guess.

 

[DaveC426913]

Right. But I gathered the whole confusion of the OP was why the scale reads T if you pull on both sides with a force of size T. It’s somewhat helpful to know how a spring works (!).

That is an illuminating way of phrasing it...

Even though it's been alluded to many times by many people in this thread, you've phrased it in a way that is so simple, it is immediately intuitive.

The scale does not know it is suspended from the ceiling. All it knows is that there is a force pulling on each end (equally - as they must - or the scale would shoot off screen.)

 

[DaveC426913]

I'm starting to understand how to intuit the 10kg reading in the scale without resorting to altering the scenario.

We only need to look at one tiny section of the diagram:

A 10kg mass is supported on a string. It is static, meaning something is holding it up else it would fall.

We (i.e. a layperson) can immediately see that any scale above this would read 10kg. The string is under 10kg of tension (100 Newtons, if you wish.)


We expand our scope:

Nothin has changed. Everything is static. String is still under 10kg tension.

We expand again:

Literally nothing has changed. All I've done is show more of the setup.

It must still be under 10kg of tension. And indeed, our spring scale says so.

Again, nothing has changed.



Finally, we reveal what has ensured the string and mass stays static:

Even the layperson will have to acknowledge that merely revealing what is hidden cannot suddenly change the reading on the scale from 10kg to 20kg.


That wasn't quite what I had been appealing for; I'd been appealing for it a single diagram, labeled in such away as to show why it works. But at least the above doesn't require altering the scenario.

 

[DaveC426913]

Weights are appropriate when talking to the handyman or the DIY store

Yes. I am trying to intuit the diagram from a handyman's (layperson's) point of view.

They don't know from Newtons; forces are hard to see. What they know is that a 10kg weight will read 10kg on a spring scale.

but you can't use weight in any context except when the Earth's gravity is producing it

I'd hoped it went without saying that the diagram was in the context of Earth.

If you were in the presence of laypeople, and started insisting "this only works here on Earth" and "you need to be an honorary physicist/engineer/mathematicin" you would get a lot of eyerolling - including from me.

i.e. it is an unnecessary complication to a very simple scenario.

. A member of PF, even if he/she is a 'layperson', should make the effort and be an honorary Physicist / Engineer / Mathematician.

But the diagram in post 1 is not aimed at PF members. Everyone here got it right away, of course.

Laypeople do not. But could, if the diagram were labeled in such a way as to make it obvious and inescapable.

 

[Herman Trivilino]

We only need to look at one tiny section of the diagram:

A 10kg mass is supported on a string. It is static, meaning something is holding it up else it would fall.

We (i.e. a layperson) can immediately see that any scale above this would read 10kg. The string is under 10kg of tension (100 Newtons, if you wish.)

That's what I was trying to explain to you in Post #7.