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Energy E has the units Joules, but is also equvalent to Work, which equals Force times Distance. In other words one Joule of Work is the energy transferred by one Newton of Force, to an object as it moves over one meter.

Wikipedia defines one newton of force as "the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared." In other words, Force = mass x acceleration (Newton's 2nd Law). The units of force are then

kilograms x meters/seconds-squared (or M *L *(1/T^2) in dimensional analysis).

From above Work in Joules = Force x Dist = kg*m/(s^)*m = kg*m^2/s^2. .. and is equivalent to Energy.

E = m*c^2 has the units kg*(m^2/s^2)*(m^2/s^2) which is identical to those for Work.

(sorry about the font .. it's much easier on paper)

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