Pressure formula and infinitesimal

[Aleoa]

I'm studing classical physics and I'm stuck with the simple pressure formula defined as:

$$P=\frac{dF_{\perp }}{dS}$$

Now, i know some calculus and the concept of infinitesimal in physics; however what i don't understand is :

1) according with the fact that in Calculus $$dF_{\perp }$$ represent an infinitesimal change, it's an infinitesimal change from which quantity ?

2) If we obtain a constant value for the pressure, this means that the $$dF_{\perp }$$ decreases as i take smaller dS (according with the definition of limit ) . Why the force decreases as the surface decreases ?

 

[Orodruin]

1) according with the fact that in Calculus $$dF_{\perp }$$ represent an infinitesimal change, it's an infinitesimal change from which quantity ?

It is the change in the force if you change the area.

2) If we obtain a constant value for the pressure, this means that the $$dF_{\perp }$$ decreases as i take smaller dS (according with the definition of limit ) . Why the force decreases as the surface decreases ?

Because you have assumed constant pressure. Pressure is force per area. If you have the same pressure but double the area, the force will be twice as large.

 

[Aleoa]

But the force is defined point to point ?

 

[Orodruin]

No, it is the total force. You integrate the pressure over the surface to obtain the total force.