This is quite an interesting question. In the most simplistic terms, you need to consider torques. Where does you body pivot? Where does your weight act? Where does the 'push up force' act? (Both in relation to the pivot. If you wish to go any further in depth you are delving into the field of kinesthiology.
As for your equation;
This is
not a valid equation. mg is your weight (
force) and 1/2 mv^2 is kinetic
energy. You cannot equate energy and force.
As for a pratical set-up, you need to ask yourself what you need to measure and what equipment will allow you to measure this.
-Hoot