Two objects with equal and opposite momenta cancel to zero net momentum, but their energies always add because energy has no direction. The left momentum 15 and right momentum -15 sum to 0 while each object's 125 J gives a total energy of 250 J exactly for the stated toy ledger; real measurements carry momentum resolution, track-fitting error, and energy calibration uncertainty.
A pair can have zero total momentum while retaining positive total energy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Opposite momenta can cancel
The left momentum 15 and right momentum minus 15 add to 0.
15+(−15)=0
Energy still adds
Each object carries 125 J, so total energy is 250 J.