An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a consta

BenoguigoliB

BenoguigoliB

Answered question

2021-02-19

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of 1950 Nm to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

Answer & Explanation

izboknil3

izboknil3

Skilled2021-02-21Added 99 answers

a.
apply the formula for Torque T=Iα
where alpha is Angular accleration
I is moment of inertia =ML212
α=TI
α=19501172.082.0812
α=46.22 rads2
b. apply the relation between angular speed and ang accleration
As W2=2αθ
W2=246.22523.14
W2=2902.616
W=53.87radsec
c.apply the formula for Work Done W = 0.5 I W2
W=0.51172.082.0853.8753.8712
W=6.12104 Joules
Power P=TW
so
P=195953.87
P=1.05105 watts
Pin=W/t=1.05 e 5 Watts

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