An airplane propeller is 2.04 m in length (from tip to tip) and has a mass of 10

Question

An airplane propeller is 2.04 m in length (from tip to tip) and has a mass of 104 kg. When the airplane's engine is first started, it apples a constant torque of 2035 N. m to the propeller, which starts from rest. What is the angular acceleration of the propeller? Model the propeller as a slender rod. What is the propeller's angular speed after making 5.00 revolutions? How much work is done by the engine during the first 5.00 revolutions? What is the average power output of the engine during the first 5.00 revolutions? What is the instantaneous power output of the motor at the propeller has turned through 5.00 revolutions?

Explanation / Answer

the angular acceleration is,

alpha = torque / moment of inertia

= torque / (1/12)ml^2

= 2035 / (1/12)*104*2.04^2

= 56.4 rad/s^2

the angular speed is,

w = sqrt[2*alpha*s]

= sqrt[2*56.4*5*2*pi]

= 75.3 rad/s

the work done is,

W = 0.5Iw^2 = 0.5*[(1/12)ml^2]w^2

= 0.5*[(1/12)*104*2.04*2.04]75.3^2

= 102238.4 J

the average power is,

P = energy/time = energy/[w/alpha] = [102238.4]*56.4/75.3 = 76576.97 W = 76.6 kW

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