How to calculate the "weight" of this piece of metal?

[scatterbrainz]

TL;DR Summary

Mass / Weight / Area / Density

Hello,

I would like to calculate the "weight" of a piece of metal. It seems a little confusing that weight is measured in Newtons or force. So I'm looking for a little help in understanding.

if I consider a piece of average aluminum.
Dimensions:
Length: 60.96 mm
Height: 60.96 mm
Thickness (Height): 3mm
I would have a Volume(v) of 1,114,836.48 cm³
If I then calculate Mass (m) from volume (v) 1,114,836.48 cm³ x density 2.710 g/cm³
m = 3021206.8608 g.
but mass is not weight.
W (weight) = mass * acceleration (gravity 9.81 m/s²)
W = 29638039.3044 g/m/s²)
Which makes no sense to me.

The end goal is to say this pieces of aluminum that is "x" long by "y" height and is "h" thick has a weight of ... "w".

 

[Ibix]

Your volume isn't correct - your piece of metal is about 6cm × 6cm × 0.3cm, so it should be about 10cm³. By the look of it you've correctly multiplied your mm values and then messed up the conversion from mm³ to cm³. If you do it correctly you should get a mass of about 30g, which is a lot more reasonable than the three metric tonnes you have.

If you want the weight in Newtons you need to convert the mass in grams to one in kilograms, then multiply by $g$. That should come out around 0.3N, since 1N=1kg m s^-2.

 

[DaveC426913]

I would have a Volume(v) of 1,114,836.48 cm³

This is where a sanity check would come in useful.
Never mind the numbers; just look at the orders of magnitude for a sec.
Off the top of your head, would a piece of metal no bigger than the palm of your hand have a volume of a million cubic centimetres?

 

[scatterbrainz]

You are correct, I screwed up the units. This is for a flat sheet of aluminum

I was actually using 24 inch Length x 24 inch width which is 0.6096 m or 0.6096 m
so really it should be:
V = 0.6096 m x 0.6096 m x 0.003 m
= 0.00111484 m³

The density of aluminium is about 2,710kg/m³. ( Ref Link: ThyssenKrupp )

Mass (m) = Volume (V) x Density (p)
Mass (m) = 0.00111484 m³ x = 2,710kg/m³]
3.02120686 kg
If I'm correct m³ and m³ cancel each other out.

Weight = m x a (in this case acceleration is gravity (g))
= 3.02120686 kg x 9.81 m/s²
= 29.638 kg*m/s²
= 29.638 N

This said weight is normally provided in pounds (lb) or kilograms (kg). So does weight have a different meaning?

Is 3.02 kg =( 6.66 lb ) my actual answer for weight?

 

[Ibix]

With your revised figures, the mass is 3.02kg, agreed.

Weight, in physics, is the force exerted by gravity on a body, which is its mass multiplied by the acceleration due to gravity. In every day use, though, people commonly use the word "weight" to refer to what a physicist would call "mass". That's why weighing scales largely report "weight" in kilograms.

Whether you want the weight in Newtons or the mass-but-we-call-it-weight in kilograms depends on why you want to know. For example, if you are wondering what the shipping costs will be, it's likely the mass in kilograms you want to quote.

 

[WWGD]

And Mass is constant, while Weight isn't. Ask an astronaut.

 

[Lnewqban]

This said weight is normally provided in pounds (lb) or kilograms (kg). So does weight have a different meaning?

Is 3.02 kg =( 6.66 lb ) my actual answer for weight?

Markings in balances (weighting machines), and common language, actually refer to kg-force and pound-force (lbf), only that nobody bothers to be precise about it.

Each of those, commonly and loosely used, units is a "non-standard gravitational metric unit of force. It is not accepted for use with the International System of Units (SI) and is deprecated for most uses."

Please, see:
https://en.wikipedia.org/wiki/Kilogram-force

https://en.wikipedia.org/wiki/Pound_(force)

 

[jbriggs444]

Markings in balances (weighting machines), and common language, actually refer to kg-force and pound-force (lbf), only that nobody bothers to be precise about it.

In commerce, I would argue that the measured quantity is mass, not force. The calibration and certification process is relevant. When certifying scales for compliance, the technician will use standardized masses, not standardized force generators.

A scale that reads "1 kg" when a 1 kilogram mass is placed upon it is a scale that is accurately measuring mass.

Even though the scale may employ electronic load cells to perform the measurement.

I do agree that on a bathroom scale, there is insufficient accuracy to decide whether mass or force is the measured quantity. Nobody cares.

 

[Dullard]

"A scale that reads "1 kg" when a 1 kilogram mass is placed upon it is a scale that is accurately measuring mass."

I won't argue, as long as the Calibration cert says: "For use on the surface of the Earth." All physical measurements (that I can think of) are inferential. Every scale that I've seen measures force first (deflection, stress...) and infers mass.

 

[jbriggs444]

A scale that reads "1 kg" when a 1 kilogram mass is placed upon it is a scale that is accurately measuring mass.

Quote repaired. Simple quotation marks are inelegant.

There are two ways to get an attributed quote like the one above. One is to mouse over the text that you wish to quote, highlighting it. e.g.

Then when preparing a response that you wish to make, there should be an Insert quotes push button below the editting window.

The other way is easier. Just click reply and edit out everything other than the passage that you wish to quote.

I won't argue,

Certainly there is room for disagreement about what it means to "measure" a quantity and what exact quantity a particular device is measuring. It would be a rather pointless discussion in my opinion, since there is no disagreement about the physics. Only about definitions and terminology.

I had considered crafting a few more paragraphs pontificating on the topic. But...

I won't argue.

 

[Lnewqban]

Every scale that I've seen measures force first (deflection, stress...) and infers mass.

In full agreement.
Also, an additional disclaimer could be: not to be used inside a functioning elevator.

I am not aware of another mundane way to measure mass.
I also believe that mass is not the main concern of people dealing with lifting or supporting mass above ground (examples: weight lifters, crane operators, planners of load distribution inside a cargo airplane, bridge designers, etc.).

Please see:
https://en.m.wikipedia.org/wiki/Displacement_(ship)

Engineers must consider loads induced onto an structure due to accelerating mass (dynamic loads like wind and sismic induced forces) besides static mass (people, construction materials, equipment, furniture).

Must nameplates of equipment shows “maximum capacity / allowed load”, which may imply force rather than mass (at least to this old fashion fool).

In the engineer world of the second half of the last century that I knew, kg-force and lb-force (and all related units) were of common use.

 

[pbuk]

Certainly there is room for disagreement about what it means to "measure" a quantity and what exact quantity a particular device is measuring. It would be a rather pointless discussion in my opinion...

This.

If we want to insist that a spring balance measures force and not mass then are we also going to insist that a laser rangefinder measures time, a pendulum clock measures local gravity, a torsion clock measures moment of inertia and an atomic clock measures radiation frequency? And what are we to say about a beam balance: does this measure force, torque or mass? Is there anything that we can actually measure?

Pointless.

 

[pbuk]

Must nameplates of equipment shows “maximum capacity / allowed load”, which may imply force rather than mass (at least to this old fashion fool).

No, the load rating of a lift system is a mass rating: a force rating would be useless because when you use a lift you do not know how fast it can accelerate (or, usually more critically, brake) any given mass so you would not know how much force you would be loading it with.

The designers of the system do know this, and they use it to convert the safe working load of the cable gear to a maximum load mass.