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

Question

asked Jun 2, 2020 198k views

1 Answer

Akhil S · Answer 1 · 2020-06-07T22:42:58+0000

Step-by-step 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 :

$\gamma=\frac{1}{\sqrt{1-(v^2)/(c^2)}}$

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

$\gamma=1.032$

1. Inertial mass is given by :

$m=\gamma * m_o$

m=1.032 * 10^(-30)

2. The momentum is given by :

$p=\gamma* mv$

p=1.032* 1.032 * 10^(-30)* 0.5c

$p=1.59* 10^(-22)\ kg-m/s$

3. Kinetic energy of the particle is given by :

$E_k=(\gamma-1)mc^2$

E_k=(1.032-1)* 1.032 * 10^(-30)* (3* 10^8)^2

$E_k=2.97* 10^(-15)\ J$

4. The total energy of the particle is :

$E=\gamma mc^2$

E=1.032* 1.032 * 10^(-30)* (3* 10^8)^2

$E=9.58* 10^(-14)\ J$

Hence, this is the required solution.