An airplane propeller is 2.78{m} in length (from tip to tip) and has a mass of 1

Question

An airplane propeller is 2.78{m} in length (from tip to tip) and has a mass of 117{kg} . When the airplane's engine is first started, it applies a constant torque of 1970{ m N * m} to the propeller, which starts from rest. angular acceleration is 26.1 rad/s^2 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

a)I =(1/12)ML2 =(1/12)*117*2.782 =75.35 Kg-m2

T=I=> =1970/75.35 =26.1 rad/s2

b)2 =02+2

2 =2*26.1*(2*5) =1639.9

=1639.9 =40.495 rad/s 40.5 rad/s

c)workdone

W=K =Kf-Ki =(1/2)If2-0 =(1/2)*75.35*40.52 =61794.42J =61.79KJ 61.8KJ

d)average power Pave =W/t

=t =>t =40.5/26.1 =1.55 S

Pave =61794.42/1.55 =39283.07 W or 39.28KW

e)instantaneous power output

P =T =1970*40.5 =79785 W or79.785KW

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