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.
35⋅3⋅4=20K=125−75=50
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.
35⋅6⋅4=40K=250−150=100
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.