When we talk about vertical motion, we introduce a concept of acceleration of gravity, which always acts to bring bodies closer to the surface.
Relating to Newton's 2nd Law, if a body of mass m, suffers the acceleration of gravity, when applied to it the fundamental principle of dynamics we can say that:
This force we call Strength Weight, and we can express it as:
or in module:
The weight of a body is the force with which the earth attracts it, and can be variable when gravity varies, ie when we are not close to the earth.
The mass of a body, in turn, is constant, ie it does not vary.
There is a unit widely used by industry, especially when it comes to weight force, which is the kilogram-force, which by definition is:
1kgf is the weight of a 1kg body mass subjected to acceleration of gravity of 9.8m / s².
Your relationship with newton is:
But this is a physically wrong term, because what we are actually measuring is our pasta.
In addition to the Weight Force, there is another that normally acts in the vertical direction, called Normal Force.
This is exerted by the surface on the body and can be interpreted as its resistance to deformation due to the weight of the body. This force always acts perpendicular to the surface, unlike the Weight Force that always acts vertically.
Analyzing a body that is under a flat surface we verify the action of the two forces.
In order for this body to be in equilibrium in the vertical direction, ie not to move or to change its velocity, it is necessary that the modules of the Normal and Weight forces are equal, thus acting in opposite directions they will cancel each other out.
What is the weight of a body mass of 10kg:
(a) On the Earth's surface (g = 9.8m / s²);
(b) On the surface of Mars (g = 3.724m / s²).