The 12 Mg helicopter is hovering over a lake as the suspended bucket collects 5 m3 of water used to extinguish a fire. Determine the power required by the engine to hold the filled water bucket over the lake. The horizontal blade has a diameter of 14 m. Use rhow = 1000 kg/m3 and rhoa = 1.23 kg/m3

7 MW

Explanation:

mass of helicopter, m = 12 Mg = 12000  

volume of water in bucket, V = 5 m³

diameter of blade, D = 14 m

density of water, d = 1000 kg/m³

density of air, d' = 1.23 kg/m³

The weight of water and the helicopter is balanced by the thrust produced by the rotor blade of the helicopter.

So, force

F = m x g  + V x d x g

F = 12000 x 9.8 + 5 x 1000 x 9.8

F = 166600 N

Let initially the velocity of blade is v

v = 41.96 m/

Power of the helicopter, P = Force x velocity

P = 166600 x 41.96

P = 7 x 10^6 Watt

P = 7 MW

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increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.