What Are the Key Differences Between Mass and Weight?

[TheWonderer1]

Hello,

Part 1: I've done some reading recently and found that Ibs is actually .435 kilograms equal to pound mass. This is the Pound mass definition but people seem to always argue that Ibs is measuring weight not mass... There is a difference between ibf and ibm. It's my understanding that the scales we use only measure force with a conversion to mass.

Part 2: I always imagined a scale measuring the force downward since the spring is brought downward or pressure plates. I recently learned that the scale is measuring normal force which I know is in the opposite direction. I've done some thoughts on this and I know that downward is negative and we don't write out our mass as a negative number. Also, you experience the normal force which the scales exerts on to you. You exert the force on the scale. Is this how I should think about it?

 

[scottdave]

It is good to know the difference between weight (force) and mass. There are times in daily life where these two terms are used interchangeably. It is my policy to not get worked up over it though, unless there is a good reason to. There was a video which discussed this, here:

Yes, scales which operate with springs, or some sort of strain gauge do actually measure force. If it is a balance (like a see-saw, or 2 pans hanging from a pivoted arm) then that actually will measure mass, as you are matching it up with known masses. If you took that device to the Moon or Mars, it would balance out with the same masses, because the same gravitational force is acting on both sides.

 

[jbriggs444]

Part 1: I've done some reading recently and found that Ibs is actually .435 kilograms equal to pound mass. This is the Pound mass definition but people seem to always argue that Ibs is measuring weight not mass... There is a difference between ibf and ibm. It's my understanding that the scales we use only measure force with a conversion to mass.

There is room for interpretation about what a scale "measures". If you look at it as a black box which sits on a table and displays a number when an object is placed upon it then one could very well say that it measures the force applied to its upper surface. If you look at it as a tool for determining an object's mass and if it is calibrated and used properly for that purpose then you could equally well say that it measures the mass of the object that it is weighing.

My preferred viewpoint is that a scale is a tool for measuring mass and that its inner workings are largely irrelevant. Yes, most scales use weight as a proxy for mass, using one to determine the other.

Part 2: I always imagined a scale measuring the force downward since the spring is brought downward or pressure plates. I recently learned that the scale is measuring normal force which I know is in the opposite direction.

Forces come in pairs. That's Newton's third law. Whether the scale measures the up-force of scale on object or the down-force of object on scale is not very relevant because those are both part and parcel of a single third-law force-pair.

I've done some thoughts on this and I know that downward is negative and we don't write out our mass as a negative number. Also, you experience the normal force which the scales exerts on to you. You exert the force on the scale. Is this how I should think about it?

It's just a sign convention. You seem to be over-thinking it. You put positive numbers on the dial so that larger strains from larger masses read out with larger numbers.

 

[TheWonderer1]

There is room for interpretation about what a scale "measures". If you look at it as a black box which sits on a table and displays a number when an object is placed upon it then one could very well say that it measures the force applied to its upper surface. If you look at it as a tool for determining an object's mass and if it is calibrated and used properly for that purpose then you could equally well say that it measures the mass of the object that it is weighing.

My preferred viewpoint is that a scale is a tool for measuring mass and that its inner workings are largely irrelevant. Yes, most scales use weight as a proxy for mass, using one to determine the other.

Forces come in pairs. That's Newton's third law. Whether the scale measures the up-force of scale on object or the down-force of object on scale is not very relevant because those are both part and parcel of a single third-law force-pair.

It's just a sign convention. You seem to be over-thinking it. You put positive numbers on the dial so that larger strains from larger masses read out with larger numbers.

This is actually what I thought. It seems silly to differentiate unless discussing g force or something.

I'm less concerned about the differences between mass and force since I have a fairly good idea. I just want to know if someone shows up, steps on my scale, sees that number is it pound mass or pound force?

 

[jbriggs444]

This is actually what I thought. It seems silly to differentiate unless discussing g force or something.

I'm less concerned about the differences between mass and force since I have a fairly good idea. I just want to know if someone shows up, steps on my scale, sees that number is it pound mass or pound force?

If he's stepping on your bathroom scale, the answer is simply "yes". Bathroom scales are not accurate enough for the distinction to matter.

If he's stepping on a scale in the doctor's office or if the grocer is weighing out a half pound of sliced ham then it's mass that is being measured. Those scales are designed and calibrated to report mass measurements.

Edit: If you intentionally misuse a spring scale (by using it in a centrifuge, for instance) then you could well say that it is then measuring force. If you misuse a balance scale the same way, it will still be accurately measuring mass.

 

[Dale]

if the grocer is weighing out a half pound of sliced ham then it's mass that is being measured. Those scales are designed and calibrated to report mass measurements.

This is important for legal and trade reasons. If you buy a half pound of ham from Singapore then it is the same quantity as a half pound of ham from Helsinki. This is despite the fact that g is different in the two cities. Therefore the lb that is measured is lb mass not lb force, even if the scale uses the deformation of a spring to do the measurement.

 

[Chestermiller]

Your interpretation in Part 1 is correct. There is a difference between 1 lbm and 1 lbf. 1 lbf is the force necessary to cause a mass of 1 lbm to accelerate with an acceleration of 32.2 ft/s^2.

 

[russ_watters]

There is room for interpretation about what a scale "measures". If you look at it as a black box which sits on a table and displays a number when an object is placed upon it then one could very well say that it measures the force applied to its upper surface. If you look at it as a tool for determining an object's mass and if it is calibrated and used properly for that purpose then you could equally well say that it measures the mass of the object that it is weighing.

My preferred viewpoint is that a scale is a tool for measuring mass and that its inner workings are largely irrelevant. Yes, most scales use weight as a proxy for mass, using one to determine the other.

The end view is fine for a bathroom scale (which doesn't get calibrated), but the "if calibrated and used properly" part (for science/engineering and maybe commerce) requires an understanding of the inner workings. Specifically, it is essential to understand that it uses weight as a proxy for mass and must be calibrated to the local gravity.

And I didn't realize just how important until googling: a decent scientific balance needs to be calibrated if moved upstairs:
http://www.labmanager.com/white-pap...ou-should-calibrate-your-balance#.WgMR01tSxEY

 

[russ_watters]

This is important for legal and trade reasons. If you buy a half pound of ham from Singapore then it is the same quantity as a half pound of ham from Helsinki. This is despite the fact that g is different in the two cities. Therefore the lb that is measured is lb mass not lb force, even if the scale uses the deformation of a spring to do the measurement.

Obviously the spring scale at your local butcher is not calibrated. I agree that assumption that it is mass is essential for legal reasons, but I suspect it only becomes a practical problem (meaning that people actually calibrate scales) on the wholesale level. Nobody cares if they don't tare the wax paper - thus selling you the wax paper at the price of ham - but one could get rich using the Office Space method to skim a tenth of a percent off the top of a million tons of grain going through a port.

 

[DrClaude]

Obviously the spring scale at your local butcher is not calibrated.

I thought that all legal-for-trade scales were calibrated and preiodically inspected.

 

[russ_watters]

I thought that all legal-for-trade scales were calibrated and preiodically inspected.

This was a conclusion on my part based on the difficulty in adjusting the span on a device that operates based on Hooke's law. A quick google tells me they must have a zero adjust and get inspected, but I don't see a calibration requirement. I'll look into it more...

 

[DrClaude]

See https://www.nist.gov/pml/weights-and-measures/handbook-44-2012-edition, section 2.20.

 

[Herman Trivilino]

I've done some reading recently and found that Ibs is actually .435 kilograms equal to pound mass. This is the Pound mass definition but people seem to always argue that Ibs is measuring weight not mass... There is a difference between ibf and ibm. It's my understanding that the scales we use only measure force with a conversion to mass.

There are various different kinds of pounds in use now and in the past. They always have been and still are units of mass. When merchants measure what they call weight, they are measuring what physicists call mass. The pound in use in the USA is defined as exactly 0.453 592 37 kg. Merchants are actually required by federal law to use this definition.

Thus when physicists say that the weight of something changes with location, they are not using the word in the same way that merchants use it. The thing that merchants use doesn't change with location, because it's the mass. But they call it weight. This is not a discrepancy in the physics, it's a discrepancy in the language. Any physicist who claims that the weight that merchants use changes with location is wrong!

None of this stops engineers from using pounds as units of force. To do so they simply adopt some agreed-upon standard value for the free fall acceleration, usually 9.806 65 m/s². But there is no officially-sanctioned definition of the pound force. (There used to be a kilogram-force, and its definition used that value for the free fall acceleration at that time. But note that there is no location on Earth where the value of the free fall acceleration remains at 9.806 65 m/s² over time. So the value is just a way to use units of force to measure mass.)

I recently learned that the scale is measuring normal force which I know is in the opposite direction.

It seems you misunderstood. The type of scale that you stand on to weigh yourself measures the normal force. In that case the normal force is upward. But the direction of the normal force is always perpendicular to a surface, which comes from the meaning of the word normal in mathematics, which is perpendicular to a surface.

Is this how I should think about it?

Just remember that if you're measuring it in Newtons it's a force and if you're measuring it in kilograms it's a mass. When something is measured in pounds you have to figure out from the context whether it's a force or a mass. Usually physicists use pounds to measure force.

 

[Herman Trivilino]

It is good to know the difference between weight (force) and mass.

It's essential to understand the difference between force and mass. (Choosing to insist that the word weight always refers to a force is just that, a choice. And it's just plain wrong because it contradicts the legal definition of the word weight.)

There was a video which discussed this, here:

This is an example of what's particularly bothersome. Physicists who insist that the word weight always refers to a force when they can't agree with each other about the definition of that force. The physicist in this video actually uses two different definitions for weight! First he says that a kilogram bag of sugar weighs 9.81 N, then he states that that's equal to the gravitational force exerted on the bag by Earth. But in fact the gravitational force is probably closer to 9.83 N, with the difference of 0.02 N being due to Earth's spin.

In other words, you can define weight $mg$ as the gravitational force, or you can define it as the force required to make an object accelerate at a rate equal to the local free fall acceleration. The latter definition is officially-sanctioned and corresponds to the force that you exert to keep an object from falling (in a vacuum).

I also note that when using the former $m$ is the gravitational mass and $g$ is the acceleration due to gravity. When using the latter $m$ is the inertial mass and $g$ is the free fall acceleration. You can easily measure the free fall acceleration, but I don't know how you'd measure the acceleration due to gravity at any latitude other than 90°.

Some textbook authors will take to calling the former the "true weight" and the latter the "apparent weight".

A search of the literature will reveal that these two are not the only force definitions of weight in use, but in my experience they are the most common ones.

Merchants, on the other hand, have only one definition of the word weight; it is universal, officially-sanctioned, and made with the highest precision possible.