Question

An airplane propeller is 2.68 m in length (from tip to tip) and has a mass of 137 kg . When the airplane's engine is first started, it applies a constant torque of 1990 N⋅m to the propeller, which starts from rest.

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

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

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

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

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

Answer #1

I= mL^{2} /12 = 137*2.68^2/12=81.9990667

τ=I* α

α= τ/I = 1990/(81.9990667) = **24.2685689
rad/s ^{2}**

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

θ= 2pi*5 = 10pi

ωf^2 = ωi^2 +2*αθ = 0+2*αθ

ωf = sqrt(2*24.2685689*10*pi)= ** 39.0491889
rad/s**

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

W =τ*θ = 1990*10*pi = **62517.6938
J**

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

ωf = ωi +α*t = 0+α*t

t = ωf/α = 39.0491889/24.2685689 =1.60904374 sec

P = w/t = **62517.6938** /1.60904374 =
**38853.943 Watt**

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

he expression of instantaneous power

P = τ*ωf = 1990*39.0491889 = **77707.8859
Watt**

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