A helicopter of mass 1000 kg rises with a vertical acceleration of `15 ms^(-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 surroundings air :
(c ) force on the helicopter due to the surroundings air :

Explanation

(a) ‘Free body’ : crew and passengers
Force on the system by the floor = F upwards, weight of system = mg downwards, ` therefore F – mg = ma`
` F - 300 xx 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