An airplane propeller is 2.68 m in length (from tip to tip) and has a mass of 11

Question

An airplane propeller is 2.68 m in length (from tip to tip) and has a mass of 112 kg . When the airplane's engine is first started, it applies a constant torque of 1890 Nm to the propeller, which starts from rest.

Part B

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

Part C

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

Part D

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

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

length. l=2.68 m

mass, m=112 kg

torque, T=1890 Nm

B)

moment of inertia, I=1/12*m*l^2

I=1/12*112*(2.68)^2

I=67.03 kg.m^2

angular acceleration, alpa=Torque/I

=1890/(67.03)

=28.2 rad/sec^2

angular speed, w=sqrt(2*alpa*theta)

=sqrt(2*28.2*5*2pi)

=42.1 rad/sec

c)

work done=1/2*I*w^2

=1/2*67.03*42.1^2

=59402.32 J

D)

avg power = work/time

here, t=w/alpa

avg power =work*(alpa/w)

=59402.32*(28.2/42.1)

=39789.67 Watt

E)

intantaneous power=Torque*w

=1890*42.1

=79569 Watt

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