Answer:
The mass of helicopter is 104.58kg
Explanation:
Given the following parameters;
Mass of helicopter =?
Radius of helicopter blade = 2m
Velocity, V = 8ms^-1
The density of the air = 1.3kgm^-3
Acceleration due to gravity = 10ms^-2
Density = mass/volume...... equation 1
Hence, Mass = density × volume..... equation 2
Area = pie * (radius)²
Area = (22/7×[2]²)
Area = 3.142 × 4 = 12.57m^2
From equation 2;
The mass of air displaced in a seconds = (1.3 × 12.57)V
It then means the momentum of the air increases by 16.341V² in a seconds.
Mass of air displaced in a seconds = 16.341V²
Substituting the value of V, we have;
Weight = 16.341 × 8²
Weight = 16.341 × 64 = 1045.824
The upward force is equal to the weight of the helicopter because it's hovering, thus;
Weight, W = Mass (M) × Acceleration due to gravity (g).
Mass = W/g
Mass = 1045.824/10
Mass = 104.58kg
Therefore, mass of the helicopter in kg is 104.58kg.
