An airplane propeller is 2.58m in length (from tip to tip) and has a mass of 142

Question

An airplane propeller is 2.58m in length (from tip to tip) and has a mass of 142kg . When the airplane's engine is first started, it applies a constant torque of 1910N*m to the propeller, which starts from rest.

Part A

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

a = rad/s2

Part B

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

w = rad/s

Part C

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

W = J

Part D

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

Pav = kW

Part E

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

P = kW

Explanation / Answer

moment of inertia I=ml^2/12=142*2.58^2/12=78.76kg-m2

A)a=T/I=1910/78.76=24.25rad/s2

B)after five revolution v=root(2as)=(2*24.25*5*2*pi)^0.5=39.03rad/s

C)work=KE=1/2*I*w^2=1/2*78.76*39.03^2=59989.16J

D)power=energy/time

now time=w/a=39.03/24.25=1.609s

power=59989.16/1.609=37283.5W

E)final power=T*w=1910*39.03=74547.3W

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.