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Question

A helicopter of mass 1000kg rises with a vertical acceleration of 15m/s2. The crew and the passengers weigh 300kg. Give the magnitude and direction of the

  1. Force on the floor by the crew and passengers.
  2. Action of the rotor of the helicopter on the surrounding air.
  3. Force on the helicopter due to the surrounding air.

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Solution

Step 1. Given data

Mass of the helicopter is, 1000kg
The total mass of crew and passengers is, 300kg
Acceleration of the helicopter, a=15m/s2
The total mass of the system, mt=1300kg

Step 2. Formula used

R-mg=ma

where R is the reaction force on the floor, m mass, a acceleration and gis the acceleration due to gravity

Step 3. Calculate the force exerted on the floor

The reaction force applied by the crew and the passenger on the floor is given by,

R-mg=maR=ma+gR=300×10+15R=7500N

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

Step 4. Calculate the action of the rotor of the helicopter on the surrounding air

The reaction of the rotor to the surrounding air will be due to the mass of the helicopter as well as the passengers.

R'-mtg=mtaR'=mta+gR'=1300×10+15R'=13500N

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

Step 5. Calculate the force on the helicopter due to the surrounding air.

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

Hence,

  1. Force on the floor by the crew and passengers is 7500N.
  2. Action of the rotor of the helicopter on the surrounding air is 32500N.
  3. Force on the helicopter due to the surrounding air is 32500N.

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