How Do Lever Rules and Newton's Laws Explain Forces in Physics?

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The discussion centers on the fundamental principles of levers and the relationships between forces and distances, highlighting the equation F1 * D1 = F2 * D2. It explores transformations of this equation, including the implications of Newton's third law when distances are equal and how forces can be expressed in terms of mass and charge. The conversation also delves into the combined effects of gravitational and electrostatic forces, presenting equations that describe these interactions under various conditions. The final point raises the question of whether the derived equations represent a charge-mass interaction at equilibrium. Overall, the thread emphasizes the complex interplay between force, mass, and charge in physical systems.
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One of the basic rules of lever are:
1) F1 * D1 = F2 * D2
F = force; D=distance; 1 and 2 are for states 1 and 2 or objects 1 and 2;
The 3rd Newton's law is a special case when D1 = -D2.
1) can be transformed into:
2) F1 / D2 = F2 / D1 = (F1 + F2) / (D1 + D2)
2.1) F1 * F2 = sqr(F1 + F2) * D1 * D2 / sqr(D1 + D2)
If F is caused by mass it's
3) F1 = L * M1 and F2 = L * M2
as masses attract.
If F is caused by charge it's
4) F1 = K * Q1 and F2 = - K * Q2
as charges repel.
- K and L are constants;
If both
5) F1 = L * M1 + K * Q1 and F2 = L * M2 - K * Q2

6) (L * M1 + K * Q1) * (L * M2 - K * Q2) = F1 * F2 = sqr(F1 + F2) * D1 * D2 / sqr(D1 + D2)

7) sqrt{L * L * (M1 / D1) * (M2 / D2) - K * K * (Q1 / D1) * (Q2 / D2) + L * K * (Q1 * M2 - M1 * Q2) / (D1 * D2)} * (D1 + D2) = (F1 + F2)

If Q1 = Q2 = 0 then sqrt{L * L * (M1 / D1) * (M2 / D2)} * (D1 + D2)= Gravity force = Total force in the system

If M1 = M2 = 0 then sqrt{- K * K * (Q1 / D1) * (Q2 / D2)} * (D1 + D2)= Coulombian force = Total force in the system

So what represents sqrt{L * K * (Q1 * M2 - M1 * Q2) / (D1 * D2)} * (D1 + D2)?
 
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addition

All the above magnitudes are with respect to the equilibrium point.
 
Could it be charge - mass interaction?
 
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