Exercise 10.34 Part A What is the angular acceleration of the propeller? Treat t

Question

Exercise 10.34 Part A What is the angular acceleration of the propeller? Treat the propeller as a slender rod. An airplane propeller is 2.68 m in length (from tip to tip) and has a mass of 122 kg When the airplane's engine is first started, it applies a constant torque of 1860 N·m to the propeller, which starts from rest. Hints rad/s Submit My Answers Give Up Incorrect; Try Again; 4 attempts remaining Part B What is the propeller's angular speed after making 5.00 rev? radis Submit My Answers Give Up Part C How much work is done by the engine during the first 5.00 re? Submit My Answers Give Up Part D What is the average power output of the engine during the first 5.00 rev? 0? Pav- Submit My Answers Give Up Part E What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 rev?

Explanation / Answer

Modelling the propeller as a uniform rod,

I = mL²/12 = 122kg * (2.68m)² / 12 = 73.02 kg·m²

A) torque = I

1860 N·m = 73.02kg·m² *

= 25.47 rad/s²

B) ² = 2 = 2 * 25.47rad/s² * (5rev * 2rad/rev) = 1600.45 rad/s²

= 40 rad/s

C) KE = ½I² = ½ * 73.02kg·m² * (40rad/s)² = 58,416 J

so this is the amount of work done by the engine.

D) avg power P = work / time

time t = / = 40rad/s / 25.47rad/s² = 1.57 s

P = 58416 J / 1.57s = 37.2 kW

E) P = * = 1860N·m * 40rad/s = 74.4 kW

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