Energy/power A levels physics

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yan_plusheartz
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Relevant formula
: p(out) / p (in) x 100 percent = efficiency
My question
Multiple-choice physics question 18: wind turbine blades sweep 2000 m², 50% efficiency, wind speed 10 m s⁻¹, air density 1.3 kg m⁻³; options A 130 kW, B 650 kW, C 1300 kW, D 2600 kW.


My approach
Handwritten working on white paper: Wind to Electrical, efficiency Elec/Wind x100% = 50%, P = F x v, units kg m s^-2 m s^-1 = kg m^2 s^-3, P = 1.3 x 1000(10)^3 kg m^2 s^-3 = 2600 kW, Elec power = 50/100 x 2600 kW = 1300 kW, But the answer is 650 kW.


But the right answer is 650kW
 
You use P = F x v but you write ##\rho## x Area x v3. Is that the same ?
 
Yeah I understand that it is not exactly the same. But my problem is , I don't have the value for F and v . And the only formula I know for power is force x velocity. So I did it by using the values given to derive a unit which is the same as power. But I can't seem to get the right answer. and I'm not sure whether my approach is correct or not. Can you teach me the correct method?

anyhow, thank you for taking your time to try to solve my question:)
 
Yes I can. You know that power is energy / time ?
How much energy does the wind bring in /time ?
 
If that case, the wind energy is 1/2 m (10)*2 am I right? Problem is , I don't have the value of mass and time :(
 
That is correct. And they give you the area and the wind speed.