Conservation of Momentum in Helicopter Blade Rotation

A) What is the mass of the helicopter?

B) If the downward velocity of the air is increased to 13m/s, what is the upward acceleration of the helicopter?

Answer:

A) The mass of the helicopter is 0 kg.

B) The upward acceleration of the helicopter is approximately -0.923 m/s^2 when the air has a downward velocity of 13 m/s.

Conservation of momentum plays a crucial role in understanding the dynamics of a hovering helicopter. In the given scenario, the rotating blades of the helicopter sweep out an area of radius 4m, imparting a downward velocity of 12m/s to the air displaced.

A) Mass of the Helicopter

To determine the mass of the helicopter, we can utilize the principle of conservation of momentum. The downward velocity imparted to the air is equal to the mass of the helicopter times the downward velocity of the helicopter. By applying the equation mv = m'v' (where m is the mass of the helicopter, v is the initial velocity, m' is the mass of the air, and v' is the final velocity), we can solve for the mass of the helicopter:

(mass of helicopter)(12 m/s) = (mass of air)(0 m/s)

mass of helicopter = 0 / 12

Therefore, the mass of the helicopter is 0 kg.

B) Upward Acceleration of the Helicopter

To find the upward acceleration of the helicopter when the air has a downward velocity of 13 m/s, we continue to apply the principle of conservation of momentum. The change in momentum of the air is equal to the change in momentum of the helicopter. Using the equation:

(mass of air)(final velocity of air - initial velocity of air) = (mass of helicopter)(final velocity of helicopter - initial velocity of helicopter)

Substitute the given values and solve for the upward acceleration:

(mass of air)(13 m/s) = (mass of helicopter)(-12 m/s)

mass of air/mass of helicopter = (-12 m/s) / (13 m/s)

Thus, the upward acceleration of the helicopter is approximately -0.923 m/s^2.

Understanding concepts like conservation of momentum through practical scenarios like helicopter blade rotation can enhance your knowledge in physics. If you want to delve deeper into the topic of Momentum, you can explore the following resource: [link to additional learning material on Momentum]