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Class 10 Class 12
The blades of a windmill sweep out a circle of area A

(a) If the wind flows at a velocity 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 = 30 m2= 36 km/h and the density of air is 1.2 kg m–3
What is the electrical power produced?

Given,

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 = ρAv

Mass m, of the wind flowing through the windmill in time t = ρAvt

(b) Kinetic energy of air =  mv

=  (ρAvt)v2
= (1/2)ρAv3t

(c) Area of the circle swept by the windmill, = 30 m

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

= () × Kinetic energy of air
=  ρ A v3

Electrical power =

=  ρ A v3t / t
=  ρ A v3
= × 1.2 × 30 × (10)3
= 4.5 kW
425 Views

Define the unit joule.

Work done is said to be one joule if one newton of  force displaces the body through a distance of one meter in the direction of applied  force .
799 Views

Define watt.

Power is said to be one watt if one joule of work is done in one second.
860 Views

What are different units of energy?

The different units of energy are :

(i) Joule
(ii) Erg
(iii) eV
(iv) KWh
(v) Calorie.

804 Views

What is watt?

SI unit of power is Watt.
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Is work a scalar or a vector quantity?

Work is dot product of two vectors. i.e. .

And dot product is a scalar quantity. Therefore, work is a scalar quantity.
1450 Views