# 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 helicopter , m1=1000kg

Mass of the crew & passengers , m2=300kg

Upward acceleration of the helicopter , a = 15m/s2

Total mass of the system, m = 1000+300 = 1300 kg

(a) Reaction force on the floor of helicopter by the crew and passengers is given by:

R = m2(g+a) = 300(10+15) = 7500 N

Reaction force is directed upward, thus the helicopter is accelerating vertically upwards but according to Newton’s 3rd law, the force on the floor of helicopter by crew and passenger will be acting downward and hence equal to the upward force, i.e 7500 N.

(b) Action of rotor of helicopter on surrounding air will be vertically downwards because of mass of helicopter and passenger.

F=(m)(g+a)

=(1300)(10+15)

=1300×25

=32500 N

(c) Force on the helicopter due to surrounding air is the reaction of the force applied by the rotor on the air (By Newton’s 3rd law),

Therefore,

F = 32500 N