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.