Exercise 10.34 An airplane propeller is 2.48 m in length (from tip to tip) and h

Question

Exercise 10.34

An airplane propeller is 2.48 m in length (from tip to tip) and has a mass of 157 kg . When the airplane's engine is first started, it applies a constant torque of 1860 Nm to the propeller, which starts from rest.

Part A

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

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Part B

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

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Part C

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

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Part D

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

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Part E

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

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Explanation / Answer

given,

length = 2.48 m

mass = 157 kg

torque = 1860 Nm

moment of inertia of the rod = (1 / 12) * m * l^2

moment of inertia of the rod = (1 / 12) * 157 * 2.48^2

moment of inertia of the rod = 80.4677 kg.m^2

torque = I * acceleration

1860 = 80.4677 * acceleration

acceleration = 23.114 rad/sec^2

distance = 5 rev or 31.4159 radians

v^2 = u^2 + 2as

v^2 = 0 + 2 * 23.114 * 31.4159

v = 38.11 rad/sec

angular speed after 5 rev = 38.11 rad/sec

work = 0.5 * I * w^2

work = 0.5 * 80.4677 * 38.22^2

work done during first 5 rev = 58773.34 J

v = u + at

38.22 = 0 + 23.114 * t

t = 1.65 sec

power = work / time

power = 58773.34 / 1.65

average power output = 35620.2 W

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