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.

A helicopter of mass 1000 kg rises with a vertical acceleration of 15

1.	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.
Answer» Solution :(a) ‘Free body’:CREW and passengers Force on the system by the floor = F upwards, WEIGHT of system = mg DOWNWARDS, ` thereforeF – mg = ma` ` F- 300xx 10 = 300 xx 15` ` F= 7.5 xx 10^3 N ` upward By the Third Law, force on the floor by the crew and passengers = `7.5 xx 10^3 N`downwards. (b) ‘Free body’ :helicopter plus the crew and passengers Force by air on the system = R upwards, weight of system = mg downwards ` THEREFORE R – mg = ma` `R - 1300 xx 10=1300 xx 15` ` R= 3.25 xx 10^4 N `upwards By the Third Law, force (action) on the air by the helicopter = `3.25 xx 10^4 N ` downwards. (c ) `3.25 xx 10^4 N ` upwards