## Description

Newton’s Second Law (F=ma), where force is a function of mass and acceleration is relatively simple to derive, but harder to prove. The force equation is based on Coulomb’s Law which is used for the force of particles, except that it is the force on the sum of particles measured in mass (m) as opposed to particle charge (q). Unlike gravity, there is no change in amplitude that needs to be considered.

Like all forces, particle motion is a result of constructive or destructive wave interference that causes a change in amplitude. Particles move to minimize amplitude. This movement becomes the force. A greater difference in amplitude causes a greater force.

Given the nature of electrons, it can be difficult to measure acceleration and distances, required for the proof for this equation. However, acceleration due to gravitation is well known and thus the proof for Newton’s Second Law comes from the derivation of the gravitational force (Section 2.5). The acceleration due to surface gravity was calculated using Eq. 2.6.3 for the planets in the solar system in the* Forces* paper.

## Derivation

Similar to Coulomb’s Law, the derivation begins with the Force Equation, which is derived from the Longitudinal Energy Equation. This was originally proven to have its roots in the Energy Wave Equation.

Force is energy multiplied by the particle radius (K^{2 }λ), where energy is based on longitudinal, standing waves (hence the Longitudinal Energy Equation). The first derivation is the Force Equation. In the Force Equation, acceleration (a) is found. The calculations for acceleration match known experiments and can be found in the Forces section as proof. Similarly, mass was solved in the Particles section, and match the calculation of the electron’s mass. Thus, with proof of both acceleration and mass, their values can be substituted into the Force Equation. The result is Newton’s second law of motion, **F=ma**.

**References to Eqs. 1.10 and 1.5.2** come from the *Key Physics Equations and Experiments* paper.** **.

**Proof**

Acceleration (a) values were calculated in the Forces section for various planet surface gravity/acceleration values, including Earth which was found to be 9.81 m / s^{2}. The calculations require an explanation for obtaining particle count (Q) based on estimated nucleons for planets, not covered here. Acceleration units are correct in Eq. 2.6.3 as m / s^{2}.

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