# Density mass and volume

Brajesh kedia
The question seems to be of quite low level yet many of teachers i found are unable to explain me the exact concept that what is mass density and volume.Yeah i know the formula d=m/v also v=a^3...
Please explain what practically & exactly they are and how both formula has came exactly.
Please explain each with a practical demonstration showing them or giving exact concept and there relation..

When we kidding, we ask young students: what have more weight, 1(kg) of iron or 1(kg) of cotton?
Definition of mass density can answer this (stupid) question. Because to take 1(kg) of iron you need about 135(cm3) of material but to take 1(kg) of cotton you need many litres.
This definition have this form because we like. We make easier calculation. We can ignore this but thus we need to give explanations every time about m and V on a problem.
Another example is the mass density of printing paper measured on (gr/m2). Because thus is useful.

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Simon Bridge
Homework Helper
I don't know what you mean by "exact concept" for mass and density or what sort of explanation would satisfy you.
You will need to tell me what was wrong with the explanations you have had so far in order for me to answer the question properly.

Mean-time:

Simply put: "mass" is how much stuff an object has, and it's "volume" is how much space it occupies.
"mass density" (usually just "density") therefore, is the amount of stuff that occupies a unit volume.

theodoros.mihos provides reasonable examples.

technical note: "weight", in physics, is the magnitude of the gravitational force acting on an object.

Brajesh kedia
Can any one explain how the formula came and exactly if i ask for how 3 sides multiplication can bring the volume of container....the question arises how stuff can be measured in terms of no.?? And last but not the least how d=m/v and whats the concept that i can easily accept this formulas as othera

Are you asking why the volume of a cube is calculated as V = a^3?
I could go into a deeper analysis of orthogonal dimensions and such, but I don't think that would help you actually. I think you should just accept the fact that the volume of a "box" (i.e. a rectangular prism) is V=height*width*depth. Since those are all the same in a cube, the volume becomes a^3.
In short, that's just how volume is defined.

Density is a definition. Like speed, height, radius and colour. You accept that the sky is blue don't you? This is no different from accepting that density is mass / volume. There are more subtle reasons such as wavelength and atomic structure but non the less, they are just definitions which are useful.

The question seems to be of quite low level yet many of teachers i found are unable to explain me the exact concept that what is mass density and volume.Yeah i know the formula d=m/v also v=a^3...
Please explain what practically & exactly they are and how both formula has came exactly.
Please explain each with a practical demonstration showing them or giving exact concept and there relation..

Volume is a measure of how a given frame of reference predicts an amount of space within a confined area.

Density is the amount of matter within a volume, which also depends on frame of reference.

Isn't it that simple?

Other than volumes moving at relativistic speeds, I fail to see how the frame of reference has any bearing on the definition of volume.
Also, it doesn't predict anything. It's a measurement.

Other than volumes moving at relativistic speeds, I fail to see how the frame of reference has any bearing on the definition of volume.
Also, it doesn't predict anything. It's a measurement.

If you have a box that travels at a relativistic velocity, it will be measured as thinner. A measurement is also a prediction since nothing which is objective can be proven.

It would be wrong to say that volume is the measure of amount of space, since we cannot be informed about space. Thus it is how we predict space that relates to any definition of volume. We are just informed about relative velocities and predictions of relativistic effects due to different frames of references and thus not informed about true space. At least not according to my own philosophical stance consisting of only one true frame of reference, which I cannot discuss further on this forum.

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The OP clearly has some very basic questions regarding the definition of volume. Bringing in relativistic effects is utterly counter-productive.

billy_joule, Chestermiller and Merlin3189
The OP clearly has some very basic questions regarding the definition of volume. Bringing in relativistic effects is utterly counter-productive.

He was curious to why teachers had trouble explaining these concepts. Perhaps relativity is exactly why.

Chestermiller
Mentor
He was curious to why teachers had trouble explaining these concepts. Perhaps relativity is exactly why.
What could possibly make you think this? Please stop confusing the OP by bringing relativity into the picture, or you will be receiving some infraction points.

Chet

Simon Bridge
Homework Helper
Can any one explain how the formula came and exactly if i ask for how 3 sides multiplication can bring the volume of container....the question arises how stuff can be measured in terms of no.?? And last but not the least how d=m/v and whats the concept that i can easily accept this formulas as othera
Volume is just a special word for the size of a room - it is how much space there is inside a boundary.
This is a concept you can hold in your head quite easily - some spaces you can fit lots into and some not so much. You should have an idea of what a volume is without having a mathematical formula for it. If you are having trouble with the idea of "the size of an empty space", then you have bigger issues than we can handle in these forums.

You may, personally, have a feel for how big a particular space is, but what if you need to tell someone else how big it is? You could just show them, but the volume may be difficult to move about. You need a way to tell them how big your room is without them having to see it.

You could make a small model of the room, show them the model, and say "the room is just like this but 1000x bigger" or whatever. Then they would have an idea. But then you need to make a different model for every space you need to talk about - which can be cumbersome to carry around. Instead, it is more useful to make one small object and compare all spaces to that one ... you can say "the room is just like this cube only 5x wider, 3x taller, and 6x longer".

This object, then, becomes the "unit of volume" and the volume of the room becomes how many of those units you can fit inside the room.
By convention we use a cube as our unit of volume. We don't have to, but it is handy because simple rooms are rectangular.

To find the volume of a rectangular room, then, you fill it with unit cubes so there are no gaps and then just count them all.
That's the volume. Everyone will understand wat we mean when we say the vlume is 235 unit cubes, provided we also show them the particular size cube we used.
By definition, the unit cube is 1 unit of volume.

But there is a shortcut - you can just count how many cubes fit along each edge of the room and multiply them together. When you do that, the product is the same as the total number of cubes - only you didn't have to count them all one at a time. So if the room was a cubes long, b cubes deep, and c cubes tall, then the volume is V=abc.
If b=a and c=a then V=a3

With different shaped volumes we have to use other tricks to work out how many unit cubes fit inside it.

This is how all measures are done - to find a distance, we work out how many unit lengths fit inside that distance and we call that "the distance". The area uses a unit area - which is usually a square made of two unit distances, for angle we use a unit circle, and so on. All "sizes" are actually comparisons to some standard "unit" size. The various equations are all about finding a shortcut to counting up the number of units one at a time.

Brajesh kedia, Entanglement, Vagn and 3 others
Nice description, Simon.

Simon Bridge
Homework Helper
But I left out mass and density - which was also in the question.

When I was in High School, 1kg was the mass of a lump of metal (lead I think) kept in a vault in France.
When we said that someone massed, say, 55kg, what we mean is that if that person stood on one side of a balance you would need 55 of those lumps of metal to make the balance, well, balance.. That lump of metal was the "unit mass" for the SI system.

I want you to notice that one unit mass occupies some volume ... and two unit weights occupies twice that volume... and so on.

Also, some things that have 1 unit mass have more volume than other things with one unit mass.
For example: 1kg of feathers occupies much more space than 1kg of lead ... and 1litre of lead weight a lot more than 1litre of feathers.

So it becomes useful to find out how much unit mass fits into one unit volume.
This quantity is named "density".

You can find the density of something by assembling 1 unit volume of it and finding out how many unit masses that comes to.
This is seldom convenient - i.e. the King may object to us bashing his crown into a cube (see Archimedes) and people usually object to having bits cut off (see Merchant of Venice).
Fortunately there is a shortcut that involves exploiting the relationship between mass and volume implied by the definition: If 1 unit volume has mass ##\rho## unit masses, then ##V## unit volumes must have mass: #m=\rho V## unit masses (that's just normal arithmetic). Rearranging: ##\rho=m/V##

... and that's how you get the formula.

All the various formulas are like that ... you start with a common concept, define it more carefully, then work out how it is related to other things.
The maths is a description of that relationship which is just a fancy way of counting.

You should find a description of how things get measured at the start of a junior undergraduate or secondary-level physics text book.
But they don't usually go into this much detail.

In science it is not good enough to measure things, it is also important to know how the different measures are related to each other.

nasu
Gold Member
He was curious to why teachers had trouble explaining these concepts. Perhaps relativity is exactly why.
No, he was curious why teachers have trouble explaining them to him. Which may be a completely different problem.

It seems that it may be just another example of the general question "what does it really mean". The person asking knows the definition(s) but is looking for some deeper meaning or simply cannot accept the simple answer. Probably is part of the process of getting familiar with new concepts.

Brajesh kedia
So it becomes useful to find out how much unit mass fits into one unit volume.
This quantity is named "density".

You can find the density of something by assembling 1 unit volume of it and finding out how many unit masses that comes to.
This is seldom convenient - i.e. the King may object to us bashing his crown into a cube (see Archimedes) and people usually object to having bits cut off (see Merchant of Venice).
Fortunately there is a shortcut that involves exploiting the relationship between mass and volume implied by the definition: If 1 unit volume has mass ##\rho## unit masses, then ##V## unit volumes must have mass: #m=\rho V## unit masses (that's just normal arithmetic). Rearranging: ##\rho=m/V##

... and that's how you get the formula.

Quite difficulty in understanding this

Brajesh kedia
Thank u nasu ji for understanding me...Often i found teachers dont clear the origin of many concepts neither the concepts which is quite troublesome and their demotivation that our questions are rubbish had never allowed us to grew...Thank a lot

Simon Bridge
Homework Helper
Quite difficulty in understanding this
Please explain what you find difficult. Don't make me guess.

Which country/jurisdiction are you studying an and at what level?
I know that many countries have a standard "by rote" approach to teaching up to senior undergrad level - the student is expected to accept the definitions, do the coursework as a kind-of abstract mathematics, and make the connections to the real world on their own. It's part of the test - students who are unable to make the connections ultimate fail the final exam.

However, the concepts you are talking about above should have been pretty clear intuitively - i.e. you live with and within volumes all your life: how can you not know what it is?
Is it really surprising that people don't know how to answer your question when nobody has much reason to think about it? Consider: how many of your fellow students struggle with the same or similar issues?

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Brajesh kedia
I am from howrah sir and i completely agree wid ur point of view and as u said about teaching approach.
Right now i am in class 12 and all the teachers(qualified level ass well) failed to clear the doubts and my friends dont care or even dare to ask and just use formulas and i cant accept the formulas and definations like that so i get demotivated when they find solutions easily.But the magical thing about me is that if they have solved lots of question and a tricky question is given they dont dare to attempt and as i think nothing in world can be hard and when concepts are clear i solve it in seconds...
Planning to work for a great revolution with some leaders(great personalities) as I found when i teach(where obviously i am cleared with concept) my students 99% doubts are cleared.
On the mission towards a great change..your small helps which is bigger for me would mean a lot...thank u..

Brajesh kedia
Sir can u please clear me wid this first how can mass be equal to volume.
I guess when the solid is full compact the mass and volume must be same but units should also be same ..am confused..?? And density is compactness so what is the value of density when a body is totally compact

Brajesh kedia
Also clear that as we know kg is just a name given to a prototype and if i say mass of my room is equal to some no. Of that prototype then i can also say that volume is equal to that no of protype why not??

Simon Bridge
Homework Helper
OK... but I cannot help you with that if you cannot tell me what you found difficult to understand about my description.

 Excuse - our posts crossed each other. I see you have tried to do that.

Aside: English language note - in "qualified level ass well" the "ass" should be "as" (only one "s".)
An "ass" is a donkey, the part of your body that you sit on, or a stupid person, so it is important not to mix it up ;)
Your English is generally good though. Howrah is the place I know as "Haora" - West Bengal, India. I've had teachers from there so I think I know what you mean.
You may want to have a look at the teaching resources from other countries that you will find online.

Simon Bridge
Homework Helper
Sir can you please clear me wi[th] this first how can mass be equal to volume[?]
Mass cannot be equal to volume in the same way that an elephant cannot be equal to a snake. As you have realized, they are completely different things.

Also clear that as we know kg is just a name given to a prototype and if i say mass of my room is equal to some no. Of that prototype then i can also say that volume is equal to that no of protype why not??
You are free to choose any prototype you like for units - though "prototype" is not quite the right word.
You can choose to make 1 unit volume to be "the volume occupied by 1kg of lead" if you want to, then different properties of the same object can be used to show people the units for volume and mass.

Brajesh kedia
Thank u sir ..but yet i found it difficult to differentiate mass and velocity.
I know that mass and volume are if a container is totally packed and filled wwith matter and if not than mass is less...mass can never be greater than volune