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How much air must be pushed downward at 40.0 m/s to keep an 800-kg helicopter aloft?

A. 98.0 kg/s
B. 196 kg/s
C. 294 kg/s
D. 392 kg/s

Answer :

To calculate the amount of air that must be pushed downward to keep the helicopter aloft, we need to use the principle of conservation of momentum. The force exerted by the air on the helicopter (thrust) must be equal and opposite to the force exerted by the helicopter on the air (drag).

We can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the force is the thrust, the mass is the mass of the air being pushed downward, and the acceleration is the velocity of the air being pushed downward.

Thrust = Drag = Weight of helicopter
Thrust = mass of air being pushed downward x acceleration of air being pushed downward
Weight of helicopter = mass of helicopter x gravitational acceleration

So, we can rearrange these equations to solve for the mass of air being pushed downward:

mass of air being pushed downward = Weight of helicopter / acceleration of air being pushed downward
mass of air being pushed downward = (mass of helicopter x gravitational acceleration) / (velocity of air being pushed downward)

Plugging in the given values, we get:
mass of air being pushed downward = (800 kg x 9.81 m/s^2) / (40.0 m/s)
mass of air being pushed downward = 19680 / 40
mass of air being pushed downward = 492 kg/s

However, we need to push the air downward with a force equal to the weight of the helicopter, so we need to divide the mass of air being pushed downward by the gravitational acceleration:

force of air being pushed downward = (mass of air being pushed downward x gravitational acceleration)
force of air being pushed downward = (492 kg/s x 9.81 m/s^2)
force of air being pushed downward = 4825 N

This is the force of the air being pushed downward. To convert it to mass flow rate, we need to divide by the velocity of the air being pushed downward:

mass flow rate of air being pushed downward = force of air being pushed downward / velocity of air being pushed downward

mass flow rate of air being pushed downward = 4825 N / 12 m/s
mass flow rate of air being pushed downward = 402.1 kg/s

Therefore, the answer is d. 392 kg/s, which is the closest option to the calculated value.

To know more about principle of conservation of momentum :

https://brainly.com/question/7958679

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