Why is e=mc^2 when kinetic energy is e=1/2*mv^2. why is it twice compared to kinetic energy?

Answer 1

E = mc^2 is not a kinetic energy, that is why it is not the same as
KE = 1/2 mv^2.

The famous Einstein equation is for rest mass and it omits the term for a moving object. The reason why this equation is famous is that it basically says than any object, even if not moving will have lots of energy.

The total energy equation is:
E^2 = p^2c^2 + m^2c^4

This is also relativistic. So the kinetic equation that you are used to is non-relativistic and not for the rest mass. That is why there are all the discrepancies.

Look at the source link for some background.

Answer 2

To expand on taurianyoj's answer, mc^2 is a term that sort of dropped out of Einstein's work when he was mucking about with total energy after taking special relativity into account.

The total energy of something is its kinetic energy plus its potential energy (to vastly simplify, of course). However, as you approach the speed of light, you get alteration of mass, distance and time in order to make sure that everyone always measures the speed of light as being the same. Einstein plugged these factors in and then did some algebra to separate everything back out. Once he'd done so, he found that he had a term left over, mc^2 (strictly speaking, m is m-sub-zero, the "rest mass"). After making sure he hadn't erred somewhere, he realized that this was the energy that represented just existing.

Thus, total energy is based on kinetic (how fast you're moving), potential (where you are in relation to other stuff) and rest energy (how much of you there is in the first place). E=mc^2 isn't a statement of the theory of relativity, it's a very interesting consequence of that theory.

As for why the 1/2 in kinetic energy, that's because of calculus. :) The rate of change in kinetic energy is power, which is force times velocity (among other things). dE/dt = d/dv(1/2 mv^2)*dv/dt = mv * dv/dt = mva = mav = Fv.

Answer 3

E=mc^2 is the energy equivalent of mass. E is proportional to m. it shows a loss in m will release energy and a gain in m will absorb energy

E=1/2mv^2 is the expression for kinetic energy of a body. they are 2 different types of energy so u cant compare