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Class 10 Class 12
A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s–2.
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.

Given,

Mass of the helicopter, mh = 1000 kg

Mass of the crew and passengers, mp = 300 kg

Total mass of the system, m = 1300 kg

Acceleration of the helicopter, a = 15 m/s

Using Newton’s second law of motion, the reaction force R,

R – mpg = ma

= mp(g + a)

= 300 (10 + 15)

= 300 × 25

= 7500 N

The reaction force will be directed upwards, the helicopter is accelerating vertically upwards.

According to Newton’s third law of motion, the force on the floor by the crew and passengers  = 7500 N, directed downward.

(b)

Using Newton’s second law of motion, the reaction force R’ experienced by the helicopter can be calculated as,

R' - mg = ma

= m(g + a)

= 1300 (10 + 15)

= 1300 × 25

= 32500 N

The reaction force experienced by the helicopter from the surrounding air is acting upward. Hence, as per Newton’s third law of motion, the action of the rotor on the surrounding air will be 32500 N, directed downward.

(c) The force on the helicopter due to the surrounding air is 32500 N, directed upwards.

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