# Center of gravity

Say an aircraft without its engines has a mass of 118 tonnes and balances on its rear wheels only. This must mean the center of mass of the aircraft without its engines is directly above the rear wheels. If the 2 engines have a mass of 7.5 tones each and their center of gravity lies 9m ahead of the rear wheels, is it possible to find the center of mass of the whole system?

(If the distance between the front and rear wheels is 28.67m and the overall length of the aircraft is 66.8m)

• I swear this exact same question has been asked before. And it got answers. Are you just resposting the question under a different account? In any case, the answer is yes. Easily. Use a weighted average of the masses weighted on the distance from a datum line. Mar 31, 2022 at 17:54

$$\sum V$$ = total force = 118 + 15 = 133
Distance of the total force to the rear wheel ($$x$$):
$$\sum M$$ about the rear wheel = 0
$$x = 15*9/133 = 1.015 m$$ - the center of the whole mass is located 1.015m to the left of the rear wheel.
You can verify the correctness of this solution by calculating the reactions $$R_R$$ and $$R_L$$ for both systems - 1) two loads on the beam, and 2) one (total) load on the beam, the resulting $$R's$$ should be identical.