In LAMENS terms, why is velocity always squared in E=mc^2 and E(k)=1/2mv^2?

Question

I've already seen some badly organized math and pictures on it, which didn't help, so does anybody have a simple explanation/example of why its always squared? it seems intuitively to me that it would just be E=mc, why the squared?!

Answer 1

It has to do with the mathematical relationship between the momentum of an object what happens when that momentum undergoes a transformation into energy. Essentially, the speed or velocity is a one dimensional quantity, like a line, and energy is the area of a two dimensional quantity, in this case the energy with respect to a reference frame.

Energy is a model of work, which is force times distance, which are two dimensions multiplied together. The kinetic energy is the "potential for doing work of a mass in motion with repect to a reference frame". The work gets done when momentum, m*v, gets converted to work, energy. The kinetic energy is a model of the magnitude of the work that can be done.

Even potential energy has the square relationship. It is m*a*h. Note that m*a=Force and h is a distance.

E=m*C^2, was a revelation since it unified an electromagnetic constant, the speed of light, or electromagnetic waves in a vacuum, to mass and energy. This explained the loss in mass during a chemical or nuclear reaction where there was a net loss of mass and a net release of energy. There are derivations of the Law that all involve calculus, so I won't get into it here.

I hope that helped.

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