Question

An aircraft is coming in for a landing at 300 meters height when the propeller falls off. When it comes off, the propeller has a rotation rate of 20 rev/s, a moment of inertia of 70.0 kg-m^2, and a mass of 200 kg. If air resistance is present and reduces the propeller’s rotational kinetic energy at impact by 30%, what is the propeller’s rotation rate at impact?

a) 14 rev/s
b) 10 rev/s
c) 7 rev/s
d) 20 rev/s

Answer 1

The propeller's rotation rate at impact is approximately 14 rev/s.

Step-by-step explanation:

To find the propeller's rotation rate at impact, we need to consider the change in rotational kinetic energy due to air resistance.

1. First, we calculate the initial rotational energy using the formula:
2. K_initial = (1/2) * I * ω^2
3. Next, we calculate the final rotational energy by reducing the initial energy by 30%:
4. K_final = K_initial - 0.3 * K_initial
5. Finally, we substitute the values into the equation and solve for the final rotation rate:
6. K_final = (1/2) * I * ω_final^2

By rearranging the equation, we find that the final rotation rate is approximately 14 rev/s.