Mass and Energy

Beta Factor  Relativity matters when speeds are close to that of light. v > 0.1cv > 0.1c v/c > 0.1 (less than 1% error)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. No potential, only kineticNo potential, only kinetic Classically E = ½ mv 2Classically E = ½ mv 2  With relativity the total energy depends on β.  Check this definition at low speed. Approximation: Application:

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.

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

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

Hot House  An average house uses 2 x J for heating and cooling in one year.  What mass equivalent is that?  Solve for the rest mass.  Use c = 3 x 10 8 m/s.  m = 2 x kg About 1/10 the mass of a human hair

Electron Gun  An electron is accelerated through a potential of 10 6 V. Rest energy MeVRest energy MeV  What is the final speed in units of c ?  The rest energy doesn’t change. Potential to kinetic  γ = 3.0, v = 0.94 c