According to Einstein's theory of relativity, matter can be converted to energy and energy can be converted to matter. The rest energy of a body is the energy it has by virtue of its mass alone. Thus mass can be regarded as a form of energy. The rest energy of a body is in addition to any KE or PE it might have.
If the mass of a body is mo when it is at rest, its energy is
In this formula c is the velocity of light, whose value is
c = 3.00 x 10^8 m/s = 9.83 x 10^8 ft/s = 186,000 mi/s
The rest mass mo is specified here because the mass of a moving body increases with its velocity. The increase of mass with increasing velocity is significant only at velocities near the velocity of light. (Nothing can move faster than c.) At a velocity of 0.1c, the mass increase is just 0.5 percent. At 0.9999c, however, the mass increase is 7100 percent. Only subatomic particles such as protons and electrons can be given such high velocities.
1. Approximately 4 x 10^9 kg of matter is converted to energy in the sun each second. What is the power output of the sun?
2. How much mass is converted to energy per day in a nuclear power plant operated at a level of 100 MW (100 x 10^6 W)?