Hang a two-stage stack from a spring scale and fly it. Watch what dropping an empty tank does to the speed you get from the same propellant.
Fig 2The rocket equation, on a scaleDrag across the stack, or use the sliderlift-off · 84 t · Δv 0.00 km/s
Needles, hook rod and latches: what movesLow orbit, about 9.4 km/sGhost needle: the same flight the other wayΔv comes from the mass ratio. The first stage burns 60 t and is left carrying 6 t of empty tank. Drop it and the second stage pushes 18 t instead of 24 t, so the same propellant buys far more speed: 8.70 km/s staged against 6.60 km/s carrying the empty tank. Illustrative vehicle; the maths is exact.