Question

Heya Mates ,

Derive:

E = mc²
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#No Copy paste
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Answer 1

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$\sf{\underline{\boxed{\green{\large{\bold{ DERIVATION OF E=MC^2}}}}}}$⠀⠀⠀⠀⠀⠀

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Consider a body that moves at very close to the speed of light. A uniform force acts on it and, as a result, the force pumps energy and momentum into the body. That force cannot appreciably change the speed of the body because it is going just about as fast as it can.

# So all the increase of momentum = mass x velocity of the body is increase of mass.

#We want to show that in unit time the energy E gained by the body due to the action of the force is equal to mc2, where m is the mass gained by the body.

#We have two relations between energy, force and momentum from earlier discussion. Applying them to the case at hand and combining the two outcomes returns E=mc2.

The first equation is:

Energy gained

Energy gained  = Force

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  

${\boxed{E=mc ^2}}$

   

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