Thanks in advance - it went smoothly so I'm hoping I'm right but... usually that's when I've made a big mistake.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

An airplane propeller is 2.08 m (tip to tip) and has a mass of 117 kg. When the engine is first started it applies a constant torque of 1950 N m to the propeller which starts from rest.

a) What is the angular acceleration of the propeller? (model it on a slender rod).

b) What is the propeller's angular speed after 5.00 revolutions?

c) How much work is done during the first 5.00 revolutions by the engine?

d) What is the average power during the first 5.00 revolutions?

e) What is the instantaneous power output of the engine the instant it has completed 5.00 revolutions?

2. Relevant equations

I think this is all of them

I = mL^{2}/12

[tex]\Theta[/tex]_{f}= [tex]\Theta[/tex]_{i}+ [tex]\omega[/tex]t + [tex]\alpha[/tex]t^{2}/2

[tex]\omega[/tex]_{f}= [tex]\omega[/tex]_{i}+ [tex]\alpha[/tex]t

W = [tex]\Delta[/tex]KE = I[tex]\omega[/tex]^{2}/2

P_{avg}= [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2

P_{ins}= [tex]\tau[/tex][tex]\omega[/tex]

3. The attempt at a solution

work that got me to the answers below.

a) 42.2 b) 53.9 rad/sec^{2}c) 1.14 kJ d) 52.6 kW e) 10.5 kW

I = mL^{2}/12 = 117*2.08^{2}/12 = 42.2

a) [tex]\tau[/tex] = 1950 N m = I[tex]\alpha[/tex]

[tex]\alpha[/tex] = 1950/42.2 = 46.2 rad/sec^{2}

b) [tex]\Theta[/tex]_{f}= [tex]\Theta[/tex]_{i}+ [tex]\omega[/tex]t + [tex]\alpha[/tex]t^{2}/2

5*2[tex]\pi[/tex] = 0 + 0 + 46.2t^{2}/2

t = squareroot (20[tex]\pi[/tex]/46.2) = 1.166 seconds

[tex]\omega[/tex]_{f}= [tex]\omega[/tex]_{i}+ [tex]\alpha[/tex]t

= 0 + 46.2*1.166 = 53.9 rad/sec

c) W = [tex]\Delta[/tex]KE = I[tex]\omega[/tex]^{2}/2

= 42.2*53.9/2 = 1.14kJ

d) P_{avg}= [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2 = 1950*53.9/2 = 52.6 kW

e) P_{ins}= [tex]\tau[/tex][tex]\omega[/tex] = 1950*53.9 = 10.5 kW/s

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# Propeller Rotation Problem - Please check

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