Homework Help: V = 12 m/s to v = 7 m/s

1. Oct 8, 2011

Hafid Iqbal

A 120-V generator is run by a windmill that has blades 2.0 m long. The wind, moving at 12 m/s, is slowed to 7.0 m/s after passing the windmill. The density of air is 1.29 kg/m3. If the system has no losses, what is the largest current the generator can produce?
(Hint : How much energy does the wind lose per second?)

Thank you very much...

2. Oct 8, 2011

SammyS

Staff Emeritus
What have you tried?

Where are you stuck?

We shouldn't try to help until we have seen that you have tried.

3. Oct 8, 2011

Hafid Iqbal

$\Delta \ KE = -\frac{1}{2}.m.(v_2^2-v_1^2)=-\frac{1}{2}.\rho.V.(7^2-12^2)=61.275V$ (V = Volume of air)

$\frac{\tau}{\epsilon} = \frac{N.B.I.A}{N.B.A. \omega} = \frac{I}{ \omega } \ \rightarrow \ \tau= \frac{\epsilon.I}{\omega}=\frac{P}{\omega}$

$\tau=\frac{\Delta KE}{\omega.t} \ = \ \frac{61.275V}{\omega.t}$

And I stuck from that point. Here is my problems :
1. I don't understand what is the use of blades' length
2. How to find volume of air?
3. Is it true angular speed not given?

4. Oct 8, 2011

Staff: Mentor

It could be that they want you to assume that the cross sectional area of the airstream is defined by the span of the blades as they rotate.

5. Oct 9, 2011

Hafid Iqbal

I still can't get the answer.... :(
Anyway, the book says its answer is 77 Ampere

6. Oct 9, 2011

Staff: Mentor

Start with determining the volumetric rate (m3/s) at which air is passing the windmill cross section. Then turn that into mass rate by multiplying by density. What do you get?

7. Oct 10, 2011

Hafid Iqbal

How to find volumetric rate sir? If I multiply it by density, i wiil get mass rate.....

8. Oct 10, 2011

Staff: Mentor

Volume has units of m3. Cross sectional area has units of m2. Velocity has units of m/s...