An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 14

Question

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 147 kg . When the airplane's engine is first started, it applies a constant torque of 1980 Nm 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 5.00 rev ?

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

D)What is the average power output of the engine during the first 5.00 rev ? E)What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 rev?

Explanation / Answer

moment of inertia I = ml^2/12

I = 147*2.08^2/12

I = 52.99kg-m2

A) a = T/I

a = 1980/52.99

a = 37.37 rad/s2

B) after five revolution v = sqrt(2as)

v = (2*37.37*5*2*3.14)^0.5

= 48.44 rad/s

C) work=KE=1/2*I*w^2

=(1/2)*52.99*(48.44^2)

= 62168.758 J

D) power = energy/time

now time=w/a

= 48.44/37.37

= 1.296 s

power = 62168.758/1.296

= 47969.72 W

E) final power=T*w

= 1980*48.44

= 95911.2 W

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