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Question

A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m/s2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the(a) Force on the floor by the crew and passengers.(b) Action of the rotor of the helicopter on the surrounding air.(c) Force on the helicopter due to the surrounding air.

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Solution

Given:
Mass of the helicopter is, 1000kg
The total mass of crew and passengers is, 300kg
Acceleration of the helicopter, a=15m/s2

Total mass of the system, mt=1300kg

(a)
The reaction force applied by the crew and passengers on the floor of the helicopter is given by:
Rmg=ma
=m(g+a)
=300×(10+15)=7500N

So, the force exerted by the passengers on the floor is 7500 N

(b)
The reaction of the rotor on the surrounding air will be due to the mass of the helicopter as well as the passengers.
Rmtg=mta
=mt(g+a)
=1300×(10+15)=32500N

Thus, the reaction force of the rotor on the surrounding air will be 32500 N

(c)
The force on the helicopter due to the surrounding air will be the reaction of the force applied by the rotor on the air. Therefore, its value will be 32500 N.

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