Spencer Heath Archive

Item 2177

Random physics notes, Elkridge, Maryland, with penciling by Spencer MacCallum as dictated by Heath.

January 6, 1957

 

 

 

 

E = ½ mv²

 

A certain force acting for a second upon a mass of one gram and thereby imparting to that mass a velocity of one centimeter per second, is called a dyne. Since the average velocity is only half of the velocity at the end of one second, the distance moved can be only one-half centimeter. An erg is a dyne-centimeter; therefore, the energy imparted to the mass is only one-half dyne, as indicated by the formula, E = ½ mv².

 

     It is worthy of note that in this formula, v² repre­sents the product of two different things, namely, the velocity at the end of one second and the time elapsed. It is only because these are numerically the same that we can employ v² in the formula instead of v times t. Since velocity times time gives distance, v² in the formula really stands for twice the distance through which the

dyne actually moves. Therefore, mv² must be divided by two,

 

________

 

 

Radiation being spherical instead of linear, it is enormously diluted at considerable distances from its source. This may be why a whole train of waves is required to accumulate a necessary amount of energy which, when multiplied by the period, will give the constant quantity known as the quantum of action. For example, there may be a distant point between the earth and the sun at which a single wave would carry the necessary energy so that when this energy is multiplied by the period of the wave, a single quantum of action would result.

 

1 spherical wave = 1 quantum energy