Question

IF THE TOTAL ENERGY OF THE PARTICLE IS EXACTLY TWICE OF ITS REST ENERGY THEN ITS SPEED IN TERMS OF THE SPEED OF LIGHT C IS

Answer 1

Answer on Question #41067, Mechanics | Kinematics | Dynamics

Question:

IF THE TOTAL ENERGY OF THE PARTICLE IS EXACTLY TWICE OF ITS REST ENERGY THEN ITS SPEED IN TERMS OF THE SPEED OF LIGHT C IS

Answer:

Total energy of the particle equals:

$$E = \frac {m _ {0} c ^ {2}}{\sqrt {1 - \beta^ {2}}}$$

where $c$ is speed of light, $m_0$ is rest mass of particle, $\beta$ is speed in terms the speed of light.

Rest energy equals:

$$E _ {0} = m _ {0} c ^ {2}$$

Therefore:

$$E = 2 E _ {0}$$ $$\frac {m _ {0} c ^ {2}}{\sqrt {1 - \beta^ {2}}} = 2 m _ {0} c ^ {2}$$ $$\sqrt {1 - \beta^ {2}} = \frac {1}{2}$$ $$\beta = \sqrt {1 - \frac {1}{4}} = \frac {\sqrt {3}}{2}$$

Answer: $\frac{\sqrt{3}}{2}$