Difference between Mass and volume

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Mass refers to the amount of matter in an object, while volume is the space that matter occupies. Volume remains constant regardless of the material, as demonstrated by objects of different densities having the same volume. The relationship between mass and volume is expressed in the equation m=p*V, where mass equals density multiplied by volume. Inertial mass relates to how an object responds to forces, while gravitational mass is linked to the attraction between masses; both types of mass are considered equivalent based on current scientific understanding. Understanding these concepts is essential for foundational physics knowledge.
kwmwtaj
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OK, I've googled it, I've tried to make sense of it, but I still have this one thing in my head that doesn't go away. Mass vs volume.

What is the difference between the two. If mass is the amount of matter,matter contains and volume is the space enclosed by matter; then it's basically saying how much space there is in an object or shape? Also I keep stumbling upon that there are different types of mass like inertial mass or gravitational mass, are they classified by a formula of such?

Reason why I'm asking is because I'm starting to learn physics in a book to get ready for college since I've lost a lot of memory since high school.
 
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Volume does not depend on matter, simply put it is the amount of 3D space in a certain place or object.

For example, if i have an iron ball that is same size as a ping pong ball they will both have the same volume, because the matter inside the space of either ball does not determine the Volume. You could have a piece space with nothing in it but it would still have Volume.

Both mass and volume are linked in the equation:
m=p*V (Mass = Density * Volume)

This basically means that the mass of an object is equal to the density of its material multipled by the space it takes up.
 
kwmwtaj said:
Also I keep stumbling upon that there are different types of mass like inertial mass or gravitational mass, are they classified by a formula of such?
Inertial and gravitational mass are equivalent as far as we know. Newton's 2nd law gives an inertial mass relationship between net force and acceleration. The force gravitational 'attraction' of masses per F=mMG/r^2 relates to gravitational mass. But they are one and the same until proven otherwise.
 
The notion of gravitational and inertial mass arises because there are two different ways to look at mass. First and foremost, mass decides how readily or reluctantly a body will respond to forces that other bodies exert on it. This mass is known as the inertial mass. For example, you can easily topple a vase because its mass is small. However, you can't topple a filing cabinet even if you apply the same force to it because its mass is considerably bigger.

Mass is also the source of gravitational interaction between bodies. A body will attract all other bodies which have mass through its gravitational field. In other words, just because an object has mass, it gives rise to gravitational potential which in turn gives rise to gravitational field. That;s why this type of mass is known as the gravitational mass.

If I remember correctly there has been an experiment which proved that the inertial and gravitational masses are equivalent, i.e. they are essentially one and the same. The same mass acts both as a source of gravity and as a means to respond to gravitational interaction from other bodies.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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