Question

Find the speed at which the mass of a particle will be double?

Answer 1

Find the speed at which the mass of a particle will be double?

Solution.

The mass of the moving particle is:

$$m = \frac {m _ {0}}{\sqrt {1 - \frac {v ^ {2}}{c ^ {2}}}},$$

where $m_0$ - is the mass of the rest particle, kg;

$v$ - is the speed of the moving particle, m/s;

$c = 299792458 \, \text{m/s} - \text{is the speed of light in vacuum}$

In this case $m = 2 \cdot m_0$ :

$$2 \cdot m _ {0} = \frac {m _ {0}}{\sqrt {1 - \frac {v ^ {2}}{c ^ {2}}}}$$

Find the speed of the moving particle:

$$\begin{array}{l} 2 = \frac {1}{\sqrt {1 - \frac {v ^ {2}}{c ^ {2}}}} \rightarrow \sqrt {1 - \frac {v ^ {2}}{c ^ {2}}} = \frac {1}{2} \rightarrow 1 - \frac {v ^ {2}}{c ^ {2}} = \frac {1}{4} \rightarrow \frac {v ^ {2}}{c ^ {2}} = \frac {3}{4} \rightarrow v ^ {2} = \frac {3}{4} c ^ {2} \rightarrow v = \frac {\sqrt {3}}{2} c = \\ = \frac {\sqrt {3}}{2} \cdot 2 9 9 7 9 2 4 5 8 \approx 2 5 9 6 2 7 8 8 5 \, \text{m/s}; \end{array}$$

Answer: the speed of the moving particle is $\frac{\sqrt{3}}{2} c$ or $259627885 \, \text{m/s}$.