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JWDavid
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Thanks in advance - it went smoothly so I'm hoping I'm right but... usually that's when I've made a big mistake.
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?
I think this is all of them
I = mL2/12
[tex]\Theta[/tex]f = [tex]\Theta[/tex]i + [tex]\omega[/tex]t + [tex]\alpha[/tex]t2/2
[tex]\omega[/tex]f = [tex]\omega[/tex]i + [tex]\alpha[/tex]t
W = [tex]\Delta[/tex]KE = I[tex]\omega[/tex]2/2
Pavg = [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2
Pins = [tex]\tau[/tex][tex]\omega[/tex]
work that got me to the answers below.
a) 42.2 b) 53.9 rad/sec2 c) 1.14 kJ d) 52.6 kW e) 10.5 kW
I = mL2/12 = 117*2.082/12 = 42.2
a) [tex]\tau[/tex] = 1950 N m = I[tex]\alpha[/tex]
[tex]\alpha[/tex] = 1950/42.2 = 46.2 rad/sec2
b) [tex]\Theta[/tex]f = [tex]\Theta[/tex]i + [tex]\omega[/tex]t + [tex]\alpha[/tex]t2/2
5*2[tex]\pi[/tex] = 0 + 0 + 46.2t2/2
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) Pavg = [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2 = 1950*53.9/2 = 52.6 kW
e) Pins = [tex]\tau[/tex][tex]\omega[/tex] = 1950*53.9 = 10.5 kW/s
Homework Statement
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?
Homework Equations
I think this is all of them
I = mL2/12
[tex]\Theta[/tex]f = [tex]\Theta[/tex]i + [tex]\omega[/tex]t + [tex]\alpha[/tex]t2/2
[tex]\omega[/tex]f = [tex]\omega[/tex]i + [tex]\alpha[/tex]t
W = [tex]\Delta[/tex]KE = I[tex]\omega[/tex]2/2
Pavg = [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2
Pins = [tex]\tau[/tex][tex]\omega[/tex]
The Attempt at a Solution
work that got me to the answers below.
a) 42.2 b) 53.9 rad/sec2 c) 1.14 kJ d) 52.6 kW e) 10.5 kW
I = mL2/12 = 117*2.082/12 = 42.2
a) [tex]\tau[/tex] = 1950 N m = I[tex]\alpha[/tex]
[tex]\alpha[/tex] = 1950/42.2 = 46.2 rad/sec2
b) [tex]\Theta[/tex]f = [tex]\Theta[/tex]i + [tex]\omega[/tex]t + [tex]\alpha[/tex]t2/2
5*2[tex]\pi[/tex] = 0 + 0 + 46.2t2/2
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) Pavg = [tex]\Delta[/tex]P/2 = [tex]\tau[/tex][tex]\omega[/tex]/2 = 1950*53.9/2 = 52.6 kW
e) Pins = [tex]\tau[/tex][tex]\omega[/tex] = 1950*53.9 = 10.5 kW/s