Spencer Heath Archive

Item 318

Pencil notes by Heath on lined notepad paper. See also Item 493.

Transcribed July 12, 1958

 

 

    

     The formula, E = ½ mv² contemplates a mass or particle as having been accelerated from zero velocity to a velocity V — the velocity increasing by one centimeter per second during each second elapsed — the velocity at the end of any number of seconds being numerically the same as the number of seconds elapsed. Since mean velocity multiplied by time represents distance or length, and since the mean velocity is V/2, then V/2 times T is the same as V /2 which represents the length or distance through which, during its acceleration, the mass or particle has moved.

     Now since M represents the number of grams of mass and since the force engaged in the given acceleration is, by definition, one dyne for each gram of mass D, then MV²/2 is numerically the same as DVT/2, a given force acting through a certain distance, the divisor 2 being employed to reduce the attained velocity V to the mean velocity V/2. E Therefore represents the work in dyne-centimeters or ergs requisite to be performed upon the given mass to accelerate it to the given velocity without any reference to time, some period of which is of necessity required.

     Now in the formula E = MC², to be consistent with E = MV²/2,

 

E must represent a quantity of work in ergs,

M must represent a number of mass or force units, dynes, and

V must represent ½