Relativity Relation Cross Scans

Mass Momentum Energy Three-Row Scan

mass scales ledgers

At fixed speed and gamma, mass scales momentum, total energy, and kinetic energy together.

At fixed speed and gamma, mass scales momentum, total energy, and kinetic energy together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Three kilograms give a twenty-unit momentum

With gamma 5/3, mass 3 kg, and speed 4 m/s, momentum is 20 kg m/s. Total energy is 125 J and kinetic energy is 50 J.

53⋅3⋅4=20K=125 − 75=50\frac{5}{3}\cdot3\cdot4=20\quad K=125\,-\,75=50
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy

Six kilograms double the momentum and energy

Mass 6 kg gives momentum 40 kg m/s, total energy 250 J, and kinetic energy 100 J.

53⋅6⋅4=40K=250 − 150=100\frac{5}{3}\cdot6\cdot4=40\quad K=250\,-\,150=100
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy

Nine kilograms triple the first-row ledgers

Mass 9 kg gives momentum 60 kg m/s, total energy 375 J, and kinetic energy 150 J. The scan changes mass while speed and gamma stay fixed.

53⋅9⋅4=60K=375 − 225=150\frac{5}{3}\cdot9\cdot4=60\quad K=375\,-\,225=150
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy