Question

A small airplane with full fuel tanks, but no occupants or baggage, has a mass of 1.17×103kg and a center of gravity that is 2.58 m behind the nose of the airplane. The pilot’s seat is 2.67 m behind the nose, and the baggage compartment is 4.30 m behind the nose. A 75 kg pilot boards the plane and is the only occupant. If the center of gravity of the airplane with pilot can be no more than 2.76 m behind the nose for in-flight stability, what is the maximum mass that the baggage compartment can hold?

Answer 1

Answer:

141.13636 kg

Explanation:

$m_1$ = Mass of plane = $1.17\times 10^3\ kg$

$m_2$ = Maximum mass that the baggage compartment can hold

$m_3$ = Mass of person = 75 kg

$r_1$ = Distance between pilot and center of gravity

$r_2$ = Distance between baggage and center of gravity

$r_3$ = Distance between center of gravity with pilot and without pilot

As moment of the system is conserved we have the relation

$m_1r_1=m_2r_2+m_3r_3\\\Rightarrow m_2=\dfrac{m_1r_1-m_3r_3}{r_2}\\\Rightarrow m_2=\dfrac{1.17\times 10^3\times (2.76-2.58)-75\times (2.67-2.76)}{4.3-2.76}\\\Rightarrow m_2=141.13636\ kg$

The maximum mass that the baggage compartment can hold is 141.13636 kg