Some of the most basic concepts of modern physics include the following relationships.
A force, “F”, is how hard we push on something. And the effect of a force is to change the momentum of an object which is its mass, “m”, multiplied by its velocity, “v”. This is Newton’s Second Law of Motion expressed mathematically as
where we have assumed that the mass does not change and “a” is the acceleration. We quantify our measurement of forces by using the units of Newtons which is (kg m/s2).
Energy is the ability of something to influence or cause a change in something else. Objects with more energy cause, or can cause, greater changes. In more concrete terms, we say that energy, “E”, is related to an applied force, “F” and a distance, “s” over which that force is applied. This is expressed as
where the integral follows the path of the force. Or we can differentiate and write this same equation as
and the units of energy are in Joules which is (Newton-meters or kg m2/s2)
For the specific case of an object which is initially at rest but which at time, t=0, has a constant applied force, F, we can write
And we can now calculate the resultant energy
An electrically charged particle creates an electric field around itself. This field exerts forces on other nearby electrically charged particles in proportion to the amount of charge. Electrons have a negative charge which repels other electrons but which attracts positively charged protons. Basically unlike charges attract and like charges repel.
A voltage is the potential energy of an electrical charge which has been forced to move some distance against an electrical field. At some point we stop pushing and the restrain the electron. When the restraints are released this potential energy will be converted back into kinetic energy as if the original force was applied in the opposite direction. The units of voltage are thus energy/coulomb or Newton-meters/coulomb or kg m2 / (s2 coulomb)