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unscientific
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Homework Statement
Determine the power of a windmill using constants where appropriate.
Homework Equations
P = Fv
K = (1/2)mv2
The Attempt at a Solution
Dynamics Method
P = Fv
In time Δt, Δm amount of wind passes through the windmill, at speed of v.
Δp = vΔm
= v(AρΔx)
Dividing both sides by Δt,
F = Aρv2
P = Fv = Apv3Energy Method
In time Δt, Δm amount of wind passes through the windmill, with KE of (1/2)(Δm)v2 .
Energy Transferred = (1/2)(Δm)v2
= (1/2)(ρAΔx)v2
Dividing both sides by Δt,
Power = (1/2)ρAv3 I've thought a long time about this; both methods make sense, but why are they different? Appreciate any help guys!