The rotating blades of a hovering helicopter swept out an area of radius 2 m imparting a downward velocity of 8 m/s of the air displaced. Find the mass of a helicopter.

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.

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