Answer:
n = 291 people
Explanation:
To solve this interesting problem we are going to take some data from the tables, the density of 7075 aluminum is 2.8 103 kg / m³, the density of 316 stainless steel is 7980 kg / m³, where we have selected one of the most used alloys in for its resistance.
The average mass of a passenger is mo = 80kg and the Boeing 747 aircraft can carry 550 passengers and a crew of 18 people with a length of 70.66 m,
Let's start by calculating the mass of the empty plane and the mass of the passengers
ρ_Al = m_Al / V
m_Al = ρ_Al V
m_passenger= #_pasajeros 80
m_passenger = 550 m₀
The total mass of the plane is
M = m_passengers + m_Al
If the plane is built face to face, the mass of this material is
ρ_Acero = m_steel / V
the total mass of avino is
M = m_pasajeros` + m_steel
As they indicate the total mass of the plane must remain constant
m_passengers + m_Al = m_passengers` + m_steel
let's substitute the values
550 m₀ + 2.8 103 V = n m₀ + 7.98 103 V
where V is the volume of the material used which is the same in both cases
n = 550 mo + (2.8 - 7.98) 103 V = n mo
n = n = 550 + (2.8 - 7.98) 103 V / mo
The calculation of the volume of material used depends on the thickness of the sheet and the resistance of the material, if it assumes that it has the same thickness, e = 1 cm, approximate the volume to the length of the circle by the length of the cylinder by the thickness
V = (2π r) L e
the diameter of the plane approximately the height of the person
d = 1.8 m
V = 2π (1.8 / 2) 70.66 1 10⁻²
V = 3.9957 m³
we substitute
n = 550 - 5.18 10³ (3.9957) / 80
n = 550 - 258.7
n = 291 people
