An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 14
ID: 1600320 • Letter: A
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