Relativistic mechanics - class-XI

According to the theory of special relativity, length contraction occurs only in the direction of the relative motion between the observer and the object.

Rest mass $(m _o)$ is defined as the mass of the object at rest (or in rest frame) which remains constant.

Kinetic energy in relativistic mechanics is the difference between total energy (Mc^2) and rest energy (mc^2), which simplifies to (M - m)c^2.

Mass of the moving object as seen by the person in rest frame,  $m = \dfrac{m _o}{\sqrt{1-v^2/c^2}}$  $\implies m>m _o$

Mass of the moving man as seen by the woman in rest frame           $m = \dfrac{m _o}{\sqrt{1-v^2/c^2}}$      $\implies m>m _o$

Mass of moving object    $m  = \dfrac{m _o}{\sqrt{1 - \dfrac{v^2}{c^2}}}   = m _o \gamma$      where $m _o$ is the rest mass and  $\gamma  = \dfrac{1}{\sqrt{1- v^2/c^2}}$

Given :   $v = 12$ km/h $ = 12\times \dfrac{5}{18}  =3.33$  m/s

Mass of the moving electron is,

$m = \dfrac{{{m _0}}}{{\sqrt {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)} }}$

$ = \dfrac{{{m _0}}}{{\sqrt {\left( {1 - \frac{{{{\left( {0.8c} \right)}^2}}}{{{c^2}}}} \right)} }}$

$ = \dfrac{{{m _0}}}{{\sqrt {\left( {0.36} \right)} }}$

$ = \dfrac{{{m _0}}}{{0.6}}$

$ = \dfrac{{5{m _0}}}{3}$

Thus mass of the moving electron is $\dfrac{{5{m _0}}}{3}$.

Rest mass of an object is the inertial mass of that object when it is at rest. The relation between object's mass and rest mass is given by: