Relativistic Momentum and Energy · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Energy hiding in mass itself

Science · Quantum & Modern Physics · ages 19-20
Name ______________________   Date ____________

  1. An object with mass sits perfectly still. What energy does it hold?

    • Zero total energy because its speed is zero
    • Only thermal energy, with no rest energy
    • Rest energy equal to m c squared

  2. A particle speeds up toward light speed. What happens to gamma m u?

    • It stays equal to the classical momentum m u
    • It grows past the classical momentum m u
    • It falls below the classical momentum m u

  3. Which statement describes the role of rest energy in energy-releasing nuclear reactions?

    • A decrease in total rest mass supplies kinetic energy or radiation
    • Heating supplies all the output without any decrease in total rest mass
    • Motion supplies all the output without any decrease in total rest mass

  4. How are total energy, momentum, and rest mass tied?

    • E squared = (pc) squared + (m c squared), with the rest term left unsquared
    • E squared = (pc) squared + (m c squared) squared
    • E squared = (pc) squared minus (m c squared) squared

  5. In units with c set to 1, a photon carries energy 4. Type its momentum.

    Answer: ______________

  6. A particle of rest mass m moves at 0.8c. Which row gives its momentum p, total energy E and kinetic energy K? Express p in units of mc and both energies in units of mc squared.

    • p = 4/3; E = 5/3; K = 5/3
    • p = 4/5; E = 5/3; K = 2/3
    • p = 4/3; E = 5/3; K = 2/3

  7. In a fusion reaction, the products' rest masses sum to 2.0 x 10^-29 kg less than the reactants'. With c = 3.0 x 10^8 m/s, how much rest energy is released?

    • 1.8 x 10^-12 J of released energy
    • 6.0 x 10^-21 J of released energy
    • 2.0 x 10^-29 J of released energy

  8. A rocket with enough finite energy could accelerate a massive ship past light speed.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Energy hiding in mass itself W1-mt_zBq87F-j3B-s1

  1. Rest energy equal to m c squared · Even at rest, mass holds m c squared of locked energy.
  2. It grows past the classical momentum m u · Gamma increases with speed, so relativistic momentum exceeds the classical value.
  3. A decrease in total rest mass supplies kinetic energy or radiation · A decrease in the sum of particle rest masses releases rest energy as kinetic energy or radiation. Total energy remains conserved.
  4. E squared = (pc) squared + (m c squared) squared · Square the complete momentum term pc and the complete rest-energy term m c squared, then add them to obtain E squared.
  5. 4 · With E equals p c and c set to 1, momentum equals energy: 4.
  6. p = 4/3; E = 5/3; K = 2/3 · Gamma = 1 / sqrt(1 - 0.64) = 5/3. Therefore p/(mc) = (5/3)(4/5) = 4/3, E/(mc squared) = 5/3 and K/(mc squared) = 2/3.
  7. 1.8 x 10^-12 J of released energy · Released rest energy is the rest-mass decrease times c squared: (2.0 x 10^-29)(9.0 x 10^16) = 1.8 x 10^-12 J.
  8. False · Its energy and momentum would need to become infinite first.
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