Question

A helicopter of mass 2000 kg rises with a vertical acceleration of 15 ms^–2. The total mass of the crew and passengers is 500 kg. Give the magnitude and direction of the (g = 10 ms^–2)

1. force on the floor of the helicopter by the crew and passengers.
2. action of the rotor of the helicopter on the surrounding air.
3. force on the helicopter due to the surrounding air.

Answer 1

Given, mass of the helicopter (m₁) = 2000 kg

Mass of the crew and passengers m₂ = 500 kg

Acceleration in vertical direction a = 15 m/s² (↑) and g = 10 m/s² (↓) 

a. Force on the floor of the helicopter by the crew and passengers

m₂(g + a) = 500(10 + 15) N

= 500 × 25 N

= 12500 N

b. Action of the rotor of the helicopter on the surrounding air = (m₁ + m₂)(g + a)

= (2000 + 500) × (10 + 15)

= 2500 × 25

= 62500 N (downward)

c. Force on the helicopter due to the surrounding air

= Reaction of force applied by helicopter

= 62500 N (upward)