A helicopter of m ass 1000 kg rises with a vertical a c c ele ra tio n o f 15 `ms-^(2)` . The crew an d th e passengers weigh 300 kg. Give the magnitude and direction of the,
(a) Force on th e floor by th e 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.

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