Question

what is the application of the formula $E=mc^{2}$

Answer 1

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The first equation is:

Energy gained
  = Force
     x Distance through which force acts

The energy gained is labeled E. Since the body moves very close to c, the distance it moves in unit time is c or near enough.

The first equation is now

E = Force x c

The second equation is:

Momentum gained
  = Force
     x Time during which force acts

The unit time during which the force acts, the mass increases by an amount labeled m and the velocity stays constant at very close to c. Since momentum = mass x velocity, the momentum gained is m x c.

The second equation is now:

Force = m x c

Combining the two equations, we now have for energy gained E and mass gained m:

E = Force x c = (m x c) x c

Simplified, we have      E = mc2

We now see where the two c's in c2=cxc come from. One comes from the equation relating energy to distance; the second comes from the equation relating momentum to time.

This derivation is for the special case at hand and further argumentation is needed to show that in all cases a mass m and energy E are related by Einstein's equation.

Back to main text E = mc2