Question

Can 1 kg of stone be converted in to energy according To Einstein mass energy relation?

Answer 1

Answer on Question #63669, Physics / Atomic and Nuclear Physics

Can 1 kg of stone be converted in to energy according To Einstein mass energy relation?

Solution:

Relationship between mass m and energy E:

$$E = m c ^ {2} (1),$$

where $c$ is the speed of light in a vacuum (about $3 \times 10^{8} \, \text{m/s}$)

Stone moves with speed $v$:

$$v = \beta c (2),$$

where $0 < \beta < 1$,

$c$ is the speed of light in a vacuum.

Of (2) $\Rightarrow \beta = \frac{v}{c}$ (3)

Relativistic mass m of stone:

$$m = \frac {m _ {0}}{\sqrt {1 - \beta ^ {2}}} (4),$$

where $m_0$ is the rest mass of stone ($m_0 = 1 \, \text{kg}$)

(4) in (1): $E = \frac{m_0}{\sqrt{1 - \beta^2}} c^2$ (5)

Formula (1) is valid.

Answer:

Yes

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