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 v = 36 km/h, A = 30 m2 and the density of the air is 1.2 kg m-3. What is the electrical power produced?

Asked by Pragya Singh | 1 year ago |  151

1 Answer

Solution :-

Area = A

Velocity = V

Density = ρ

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

Mass = ρAv

Mass m through the windmill in time t = ρAvt

(b) kinetic energy = \( \dfrac{1}{2}mv^2\)

\( \dfrac{1}{2}​ (ρAvt)v^2 \)


(c) Area = 30 m2

Velocity = 36 km/h

Density of air \(\)ρ = 1.2 kg m-3

Electric energy = 25 % of wind energy

= \( \dfrac{25}{100}\)​ x kinetic energy

\( \dfrac{1}{8}ρAv^3t\)

Power = \( \dfrac{Electric\;energy}{Time}\)

\( \dfrac{1}{8}\dfrac{\rho Av^{3}t}{t}= \dfrac{1}{8}ρAv^3\)

\( \dfrac{1}{8} \times 1.2 \times 30 \times 10^3\)

= 4.5 x 103 W =4.5 kW

Answered by Pragya Singh | 1 year ago

Related Questions

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. 

(a) How much work does she do against the gravitational force? 

(b) Fat supplies 3.8 × 107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

Class 11 Physics Work, Energy and Power View Answer

A body of mass 0.5 kg travels in a straight line with velocity \( v =ax^\dfrac{3}{2} \) where\( a = 5 m^\dfrac{-1}{2}s^{–1}\) What is the work done by the net force during its displacement from x = 0 to x = 2 m?

Class 11 Physics Work, Energy and Power View Answer

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of0.05 kg s–1. What is the speed of the trolley after the entire sandbag is empty?

Class 11 Physics Work, Energy and Power View Answer

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

Class 11 Physics Work, Energy and Power View Answer

A ball A which is at an angle \( 30^{\circ}\) to the vertical is released and it hits a ball B of same mass which is at rest. Does the ball A rises after collision? The collision is an elastic collision.

The bob A of a pendulum released from 30° to the vertical hits another bob B  of the same mass at rest on a table as shown. How high does the bob

Class 11 Physics Work, Energy and Power View Answer