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Home » The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time and also the kinetic energy of the air. of the wind energy is converted into electrical energy and and the density of the air is What is the electrical power produced?
The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 \% of the wind energy is converted into electrical energy and \mathrm{v}=36 \mathrm{~km} / \mathrm{h}, \mathbf{A}=30 \mathrm{m}^{2} and the density of the air is 1.2 \mathrm{~kg} \mathrm{~m}^{-3} . What is the electrical power produced?
CBSE | Class 11 | NCERT | Physics | Work, Energy, and Power
The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 \% of the wind energy is converted into electrical energy and \mathrm{v}=36 \mathrm{~km} / \mathrm{h}, \mathbf{A}=30 \mathrm{m}^{2} and the density of the air is 1.2 \mathrm{~kg} \mathrm{~m}^{-3} . What is the electrical power produced?

Area = A

Velocity =\mathrm{V}

Density =\rho

(a) Volume of the wind through the windmill per sec is given by =\mathrm{Av}

Mass is given by =\rho \mathrm{AV}

So,

Mass m through the windmill in time t will be \rho Avt

(b) kinetic energy is given by the relation \frac{1}{2} \mathrm{mv}^{2}

=\frac{1}{2}(\rho \mathrm{Avt}) \mathrm{v}^{2}=\frac{1}{2} \rho \mathrm{Av}^{3} \mathrm{t}

(c) Area is given as 30 \mathrm{~m}^{2}

Velocity is given as 36 \mathrm{~km} / \mathrm{h}

Density of air si given as \rho=1.2 \mathrm{~kg} \mathrm{~m}^{-3}

Electric energy is 25 \% of wind energy

=\frac{25}{100} \mathrm{x} kinetic energy

=\frac{1}{8} \rho \mathrm{Av}^{3} \mathrm{t}

Power =\frac{\text { Electric energy }}{\text { Time }}

=\frac{1}{8} \frac{\rho A v^{3} t}{t}=\frac{1}{8} \quad \rho \mathrm{Av}^{3}

=\frac{1}{8} \times 1.2 \times 30 \times 10^{3}

=4.5 \times 10^{3} \mathrm{~W}=4.5 \mathrm{~kW}

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