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In our everyday life the concept of mass is pretty straightforward and seems so deceivingly simple. We don't make any distinction between
**weight** and **mass**, they both mean the same thing to us. But in Physics things look a'bit different, we need to be more precise if we are going to
discover better approximation of reality. What are those differences ?
To show you the distinction I will start with two approaches we can use to measure the "massivity" of objects. Using a **scale** (image on the left) or with a
**spring** (image on the right).

Why would I trouble you with those examples ? The reason is a subtle difference of the resulting measurement when we use those two methods. Here is it ... the

So to summarize the scale measures the

With the invention of the theory of special relativity this effect could now be explained i.e. the electrons have

Finally we can sleep easy, we got to the bottom of it ....

There is this curious fact that even after we do the mentioned corrections we still do not get the same "proper mass" for the same object. If the object receives energy (i.e. becomes "hotter") there is slight increace of mass and vice versa.

This is very appearent in one of the basic reaction happening inside the core of the Sun i.e. the combining of the 4 hydrogen into a one helium atom. The resulting helium atom is little bitty less massive than the combined hydrogen atoms !!! Where did the mass go ? As any fifth grade kid will tell you, it became energy : `E = m*c^2`, need I say more.

We still have to go one step further though, if we are to take General relativity into account ... where the things become even more blury.. ... ultimately our goal was to find a definition of mass that do not change under different curcumstances i.e is invariant, that is general trust in every natural phenomena exploaration, right. ... todo

**Intertial mass**- this is the measure of intertia of an object i.e. the amount of**resistance**of an object to accelerate when force is applied. f.e. push,pull ). This definition comes from Newton second law of motion : `m = F/a`**Gravitational weight**- this is defined by law of Gravitation i.e. the measure with which object responds to a gravitational force (falls), `F = G*(m_1*m_2)/r^2`

All experiments point that*graviataional weight*and*intertial mass*are the same. That is why the acceleration due to gravity is independednt of the mass of the object itself. The bigger the mass of object the higher the gravitational attraction, but also the higher the resistence to acceleration.

General relativity equivalence principle states that "inertial" and "gravitational" force are the same i.e. acceleration and gravity are the same thing ( `m*a = m*g => a = g` ).**Relativistic mass**- Is the intertial mass as defined by and observer with respect to whom the object is at**motion**.**Proper mass (rest mass, invariant mass)**- Is the intertial mass as defined by and observer with respect to whom the object is at**rest**.

The last two definitions come from special realitivity and their relation is as follows :

`m_r = m_p / sqrt(1-(v^2/c^2)` or `m_r ~~ m_p + (m_p*v^2)/(2*c^2)`

where `m_r` is relativistic mass and `m_p` the proper mass, `v` is the velocity of the object and `c` the speed of light.

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