exchemist
Valued Senior Member
How do you account for electrostatic potential energy? This is not a function of mass but of charge, of course.Obviously you have not read our work, due to the fact that we use Calculus throughout The Yaldon Particle Theory.
When a mass (m) is under a net force that is equal to zero, then the energy will be potential energy.
For example: When a mass is elevated and kept at a height of y meter(s), it will have potential energy $$(E_p=mgy)$$. In the same way, when a mass travels in empty space with a constant velocity, it will have a net force that is equal to zero (Newton's First Law). Then this mass will have potential energy that is equal to $$E_p=mv^2_c$$; where $$v_c$$ is the constant velocity. When this mass (m) has a variable velocity, then it will have kinetic energy.
We will translate the above statement to Math using Newton's Laws:
For Kinetic Energy:
$$F(v)=\frac{m}{t}v$$
$$[F(v)=\frac{m}{t}v]\cdot dv$$
$$\int\limits_0^{v_{max}}F(v)\cdot dv=\frac{m}{t}\int\limits_0^{v_{max}}v\cdot dv$$
$$Fv_{max}=\frac{1}{2}\frac{m}{t}v^2_{max}$$
$$F[v_{max}\cdot t]=\frac{1}{2}mv^2_{max}$$
Where $$F\cdot s_{max}=E_k$$
$$E_k=\frac{1}{2}mv^2_{max}$$
For Potential Energy:
$$F(s)=m\frac{v}{t}$$
Where $$m\frac{v}{t}$$ is a constant value; then the velocity will also be a constant $$(v_c)$$.
After multiplying both sides of the above equation by ds and taking the limit from zero to $$s_{max}$$:
$$F(s)\int\limits_0^{s_{max}}ds=m\frac{v_c}{t}\int\limits_0^{s_{max}}ds$$
$$F\cdot s_{max}=m\frac{v_c}{t}\cdot s_{max}$$
Where $$F\cdot s_{max}=E_p$$
$$E_p=mv_c\frac{s_{max}}{t}$$
Where $$\frac{s_{max}}{t}=v_c$$, since both are properties of the same mass (m)
$$E_p=mv^2_c$$
When $$E_k=E_p$$ for the same mass (m)
$$\frac{1}{2}mv^2_{max}=mv^2_c$$
Then:
$$\frac{1}{2}v^2_{max}=v^2_c$$Or:
$$v^2_{max}=2v^2_c$$
The above mathematical proof is not needed to explain The Yaldon Particle Theory, we just want to show the relation between the Laws of Newton and energy. Since the formulas $$E_k=\frac{1}{2}mv^2_{max}$$ and $$E_p=mgy$$ are accepted, then one must accept the Laws of Newton; due to the fact that these formulas have been derived from Newton's Laws. As one can see, we don't need a "rest mass" versus "relative mass" philosophy.
As one can see, when a mass moves with a constant velocity; it will have potential energy. The Yaldon Particle Theory has arrived at this conclusion; due to the correct interpretation of Newton's Laws.