Rest energy is the energy possessed by an object due to its mass when it is at rest. It is given by the equation $E_0 = mc^2$, where $m$ is the rest mass and $c$ is the speed of light in vacuum.
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Rest energy demonstrates the equivalence of mass and energy as proposed by Einstein's theory of relativity.
The formula for rest energy, $E_0 = mc^2$, shows that even a small amount of mass can be converted into a large amount of energy due to the factor of $c^2$ (approximately $9 \times 10^{16} \text{m}^2/\text{s}^2$).
Rest energy is a scalar quantity and does not depend on the object's motion or reference frame.
In nuclear reactions, a small loss in mass results in a significant release of energy, illustrating the concept of rest energy.
Understanding rest energy is crucial for explaining phenomena such as particle-antiparticle annihilation, where two particles destroy each other and convert their rest masses into pure energy.
Review Questions
What equation represents rest energy and what do each of its terms represent?
How does the concept of rest energy support the principle of mass-energy equivalence?
Why does rest energy remain constant regardless of an object's state of motion?
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, which describes how time, length, and relativistic mass change for an object moving relative to an observer.
Mass-Energy Equivalence: A principle stating that mass can be converted into energy and vice versa, encapsulated by Einstein's equation $E = mc^2$.