Relativity Calculator - Mass as a Variable Quantity

mass as a variable.png

The Problem:

At velocities approaching a fractional but noticeable amount of the speed of light, c, it's incumbent to maintain both the law of conservation of mass as well as the law of conservation of momentum under conditions utilizing the additions of relativistic velocities.

§ Assume frames of reference for systems S, S', and S'' with the following stipulations:

S is stationary relative to S'

S' is moving away from S with relative velocity mass as a variable

mass as a variable quantity , and that each is flying towards the other with a combined total relative velocity in S'' which is wholly contained in S'

§ Assume further that immediately after the collision both mass as a variable coalesce into one larger mass-particle, Pasted Graphic 4.pict - i.e., an inelastic collision.

Analysis:

Solution:

Einstein devised a relativity mathematics such that mass is a variable quantity and is dependent on velocity ( and hence ultimately on its energy content ) as follows:

Here we can observe that the conserved mass, Pasted Graphic 3_1.pict , is certainly not equal to the sum of rest masses Pasted Graphic 4_1.pict . That is,

mass as a variable

Therefore from before,

End equation.png

Maclaurin Series.png .

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