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Mass and Energy

Mass and Energy. Beta Factor. Relativity matters when speeds are close to that of light. v > 0.1 c v / c > 0.1 (less than 1% error) The beta factor is often used in relativity to scale values according to the speed of light. Total Energy. Total energy is based on kinetic energy.

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Mass and Energy

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  1. Mass and Energy

  2. Beta Factor • Relativity matters when speeds are close to that of light. • v > 0.1c • v/c > 0.1 (less than 1% error) • The beta factor is often used in relativity to scale values according to the speed of light.

  3. Total Energy • Total energy is based on kinetic energy. • No potential, only kinetic • Classically E = ½ mv2 • With relativity the total energy depends on β. • Check this definition at low speed. • Approximation: • Application:

  4. Low Energy Match • To match kinetic energy with the result at low velocity, the extra term must be subtracted. • The kinetic energy also depends on β.

  5. Rest Energy • The extra term for energy is still there when an object is at rest. • This energy only depends on the mass.

  6. Energy from Mass • The rest energy exists in an object’s inertial frame. • No velocity • No potential • Just mass • Conservation of energy implies that this rest energy can be converted to other forms.

  7. Hot House • An average house uses 2 x 1010 J for heating and cooling in one year. • What mass equivalent is that? • Solve for the rest mass. • Use c = 3 x 108 m/s. • m = 2 x 10-7 kg • About 1/10 the mass of a human hair

  8. Electron Gun • An electron is accelerated through a potential of 106 V. • Rest energy 0.511 MeV • What is the final speed in units of c? • The rest energy doesn’t change. • Potential to kinetic • γ = 3.0, v = 0.94c

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