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

141.13636 kg

Step-by-step explanation:

`m_1` = Mass of plane =
`1.17* 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=(m_1r_1-m_3r_3)/(r_2)\\\Rightarrow m_2=(1.17* 10^3* (2.76-2.58)-75* (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