Question

A particle has rest mass 10-30 kg and travels at 0.5 c with respect to the Laboratory. Find its inertial mass, its momentum, its kinetic energy and its total energy

Answer 1

Explanation:

It is given that,

The rest mass of the particle, $m_o=10^{-30}\ kg$

Speed of the particle, v = 0.5c

Firstly calculating the relativistic factor. The formula is as follows :

$\gamma=\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$

$\gamma=\dfrac{1}{\sqrt{1-\dfrac{(0.5c)^2}{c^2}}}$

$\gamma=1.032$

1. Inertial mass is given by :

$m=\gamma \times m_o$

$m=1.032 \times 10^{-30}$

2. The momentum is given by :

$p=\gamma\times mv$

$p=1.032\times 1.032 \times 10^{-30}\times 0.5c$

$p=1.59\times 10^{-22}\ kg-m/s$

3. Kinetic energy of the particle is given by :

$E_k=(\gamma-1)mc^2$      

$E_k=(1.032-1)\times 1.032 \times 10^{-30}\times (3\times 10^8)^2$  

$E_k=2.97\times 10^{-15}\ J$

4. The total energy of the particle is :

$E=\gamma mc^2$

$E=1.032\times 1.032 \times 10^{-30}\times (3\times 10^8)^2$

$E=9.58\times 10^{-14}\ J$

Hence, this is the required solution.