The total mass of an aircraft is 9000 kg. The centre of gravity (cg) position is at 2.0 m from the datum line. The aft limit for cg is at 2.1 m from the datum line.
What mass of cargo must be shifted from the front cargo hold (at 0.8 m from the datum) to the aft hold (at 3.8 m), to move the cg to the aft limit?
Mass of airplane : 9000 kg
(old mass same like new mass as we will only change the location of cargo)
Old CG: 2 m
New CG: 2.1 (aft limit)
Front cargo arm: 0.8 m
Aft cargo arm: 3.8 m
We will remove cargo from front compartment so take (- sign) and we add it to aft compartment take (+ sign)
New mass x New CG = (Old mass x Old CG) ± (mass x arm)
9000 x 2.1 = (9000 x 2) — (cargo x 0.8) + (cargo x 3.8)
18900 = 18000 — 0.8 cargo + 3.8 cargo
900 = 3 cargo
Cargo to be moved = 300 kg
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