An airplane propeller is 2.38m in length (from tip to tip) and has a mass of 117

Question

An airplane propeller is 2.38m in length (from tip to tip) and has a mass of 117kg. When the airplane's engine is first started, it applies a constant torque of 1930Nm to the propeller, which starts from rest.

(A)What is the angular acceleration of the propeller? Treat the propeller as a slender rod.

(B)What is the propeller's angular speed after making 5.00rev ?

(C)How much work is done by the engine during the first 5.00rev ?

(D)What is the average power output of the engine during the first 5.00rev ?

(E)What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00rev ?

Explanation / Answer

I = ml^2/12 = 55.227 kg-m^2 Torque = I*alpha angular acceleration (alpha) = Torque / I = 1930/55.227 = 34.946 rad/s^2 angular speed after 5 rev angular speed = sqrt(2*34.946*5*2*pi) = 46.85 rad/s work done = .5*I*w^2 = .5*55.227*46.85^2 = 60.632 kJ time taken = 46.85/34.946 = 1.34 sec average power = work done/time = 60.632/1.34 = 45.24 kW Instantaneous Power = F.v

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