Inertial Forces while analysing forces on a Piston in a Slider - Crank Mechanism?

Question

I get that we are analysing the Piston in a non-inertial frame of reference, but the point of my question is that according to D'Alembert's Principle, whenever an inertial force comes in the line of motion of the object the net Force on the body becomes zero and the body is in a state of Dynamic Equilibrium. But even then, we write:

$$F_{net} = F_p -F_f - F_i$$

where

• $F_p =$ Force due to combustion/pressure
• $F_f =$ Frictional Force
• $F_i =$ Inertial Force

Due to the occurrence of inertial forces, shouldn't $F_{net} = 0$?

Answer 1

Yes, the inclusion of D'Alembert forces makes a dynamics problem into a static one. The equations of motion change from

$$ F_{\rm gas} - F_{\rm friction} - F_{\rm conrod} = m_{\rm piston} a_{\rm piston} $$

to

$$ \sum F = F_{\rm gas} - F_{\rm friction} - F_{\rm conrod} - m_{\rm piston} a_{\rm piston} = 0 $$

In your example, you have forgotten the contribution of the connecting rod via the wrist-pin and thus you won't get net forces equals zero.