Relativistic Energy

• What is the formula for relativistic energy?

  E = (γm)c
• What is the formula for rest energy?

  E = mc^2
• What does the kinetic store represent?

  Energy associated with motion
• What happens when total energy E exceeds rest mass energy?

  Additional energy is in the kinetic store
• What is the formula for kinetic energy in relativistic terms?

  Ek = mc^2 − m0c^2
• What do the variables in the kinetic energy formula represent?

  m is relativistic mass, m0 is rest mass
• How is total energy E expressed in terms of rest mass and kinetic energy?

  E = m0c^2 + Ek
• What happens to total energy as speed approaches the speed of light?

  Total energy increases rapidly
• What does the asymptote on the energy graph indicate?

  Infinite energy is needed to reach light speed
• What are the steps to calculate relativistic kinetic energy for a spacecraft?

  1. List known quantities (rest mass, speed)
  2. Use relevant equations (Newtonian and relativistic)
  3. Calculate Newtonian kinetic energy
  4. Calculate gamma term
  5. Substitute into relativistic kinetic energy equation
  6. Find the difference between kinetic energies
• How is Newtonian kinetic energy calculated?

  Ekn = ½mv²
• What is the calculated Newtonian kinetic energy for the spacecraft?

  9.9 × 10¹⁸ J
• How is the gamma term calculated?

  γ = 1 / √(1 - v²/c²)
• What is the calculated gamma value for the spacecraft?

  1.40
• What is the relativistic kinetic energy calculated for the spacecraft?

  1.6 × 10¹⁹ J
• What is the difference between the two kinetic energies?

  6.1 × 10¹⁸ J
• How does relativistic kinetic energy compare to Newtonian kinetic energy?

  Relativistic kinetic energy is almost twice as large