The
blades of a windmill sweep out a circle of area *A* .
(a) If the wind flows at a velocity *v
* perpendicular to the circle,
what is the mass of the air passing through it in time *t* ? (b) What is the kinetic energy
of the air? (c) Assume that the windmill converts 25% of the wind’s
energy into electrical energy, and that *A
* = 30 m ^{ 2 } ,
*v
* = 36 km/h and the density of air
is 1.2 kg m ^{ –3 } .
What is the electrical power produced?

Area
of the circle swept by the windmill = *A*

Velocity
of the wind = *v*

Density
of air =
*ρ*

**(a)** Volume
of the wind flowing through the windmill per sec = *Av*

Mass
of the
wind flowing through the windmill per sec = *ρ**Av*

Mass
*m*,
of the wind flowing through the windmill in time *t*
= *ρ**Avt*

**(b)** Kinetic
energy of air

**(c)** Area
of the circle swept by the windmill = *A
*= 30 m^{2}

Velocity
of the wind = *v*
= 36 km/h

Density
of air, *ρ*
= 1.2 kg m^{–3}

Electric energy produced = 25% of the wind energy

**
**