Question

A helicopter of mass 1000 kg rises with a vertical acceleration of 15 ms⁻². The crew and the passenger 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 1

F is the force on helicopter due to the surrounding air

∴ F – (M + m)g = (M + m)a

⇒ F = (M + m)g + (M + m)a

⇒ F = (M + m) (g + a)

⇒ F = (1300) (25) N = 32500 N upwards

Now using newton’s third law, force by helicopter on surrounding air is F downward, i.e. 32500 downwards.

Now if we consider the crew,

⇒ N = m (a + g) = 300 (25)

N = 7500 N upwards.

∴ Force on the floor by the crew is 7500 N downwards.

Answer 2

(a) 7500 N downwards, 

(b) 32500 N downwards, 

(c) 32500 N upward