The Mass of Air Required for a Helicopter to Hover
How is the mass of air needed to produce enough thrust for a helicopter to hover calculated?
During a rescue operation, a 5300-kg helicopter hovers above a fixed point. The helicopter blades send air downward at a speed of 67 m/s. What mass of air must pass through the blades every second to produce enough thrust for the helicopter to hover? Express your answer using two significant figures.
Answer:
The mass of air that must pass through the helicopter blades every second to produce enough thrust for the helicopter to hover is approximately 775 kg/s.
To find the mass of air that must pass through the helicopter blades every second to produce enough thrust for the helicopter to hover, we can use the principle of conservation of momentum.
The downward force exerted by the helicopter blades on the air creates an equal and opposite upward force (thrust) on the helicopter itself. This thrust allows the helicopter to counteract the force of gravity and hover in place.
The thrust force can be calculated using the following equation:
Thrust = Mass flow rate * Velocity
where the mass flow rate is the mass of air passing through the blades per unit time and the velocity is the downward speed at which the air is expelled.
Given data:
Mass of the helicopter, m = 5300 kg
Downward speed of the expelled air, v = 67 m/s
We need to calculate the mass flow rate. To do this, we can rearrange the equation as follows:
Mass flow rate = Thrust / Velocity
The thrust force is equal to the weight of the helicopter, which can be calculated as:
Weight = Mass * acceleration due to gravity
Weight = 5300 kg * 9.8 m/s^2
Weight ≈ 51940 N
Now, we can calculate the mass flow rate:
Mass flow rate = 51940 N / 67 m/s
Mass flow rate ≈ 775 kg/s
In conclusion, the mass of air required for the helicopter to hover is approximately 775 kg/s.