A helicopter stays aloft by pushing large quantities of air downward every second.What mass of air must be pushed downward at 30.0 m/s every second to keep a 1000 kg helicopter aloft?
A) 120 kg
B) 245 kg
C) 327 kg
D) 490 kg

Question

Quizplus · Accepted Answer

The force needed to keep the helicopter aloft is equal to its weight, which is 1000 kg multiplied by the acceleration due to gravity, 9.8 m/s². This gives a total force of 9800 N.

By Newton's third law, every action has an equal and opposite reaction, meaning that the helicopter's rotors must push an equal and opposite amount of air downward every second.

The mass of air pushed downward can be found using the formula F = ma, where F is the force required to keep the helicopter aloft (9800 N), m is the mass of air pushed downward, and a is the downward acceleration of the air (which is the same as the helicopter's upward acceleration).

a = 30.0 m/s² (given)
F = 9800 N (calculated above)
m = F / a = 9800 N ÷ 30.0 m/s² = 326.67 kg ≈ 327 kg

Therefore, the best choice is (C) 327 kg.

A Helicopter Stays Aloft by Pushing Large Quantities of Air