Advertisements
Advertisements
Question
The blades of a windmill sweep out a circle of area 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?
- What is the kinetic energy of the air?
- Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced?
Advertisements
Solution
(a) Volume of wind flowing per second = Av Mass of wind flowing per second = Avρ
Mass of air passing in second = Avρt
(b) Kineic energy of air = `1/2mv^2 = 1/2 (Avrhot)v^2 = 1/2 Av^3rhot`
(c) Electrical energy produced = `25/100 xx 1/2 Av^3 rhot = (Av^3rhot)/8`
Electrical power = `(Av^3rhot)/"8t" = (Av^3rho)/8`
Now
`A = 30m^2`
`v = 36 kmh^(-1) = 36 xx 5/18 ms^(-1) 10 ms^(-1) `
`rho = 1.2 kg ms^(-1)`
∴ Electrical power =`((30xx10xx10xx10xx1.2)/8)W`
`= 4500 W = 4.5 KW`
APPEARS IN
RELATED QUESTIONS
A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
Power P= ............ /time taken.
Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is
The expression of power P is
Name the physical quantity which is measured in calorie. How is it related to the S.I. unit of the quality?
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?.
A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to ______
Two equal masses m1 and m2 are moving along the same straight line with velocities 5 ms-1 and -9 ms-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m1 and m2, respectively.
A bullet of mass 20 g strikes a pendulum of mass 5 kg. The centre of mass of the pendulum rises a vertical distance of 10 cm. If the bullet gets embedded into the pendulum, calculate its initial speed.
A quarter horse power motor runs at a speed of 600 r.p.m. Assuming 40% efficiency, the work done by the motor in one rotation will be
An engine pumps up 200 kg of water through a height of 20 m in 10 seconds. If the efficiency of the engine is 80%. Calculate the power of the engine.
Calculate the power of a crane in watts, which lifts a mass of 100 kg to a height of 10 m in 20s.
A man is throwing bricks of mass 2 kg onto a floor from a height of 2 m. Bricks reach the floor at a speed `2sqrt(10)` m/s. Man throws 10 bricks in a minute. If the power of man is W watt then `3/10` W is equal to ______ W.
Sand is being dropped from a stationary dropper at a rate of 0.5 kgs-1 on a conveyor belt moving with a velocity of 5 ms-1. The power needed to keep belt moving with the same velocity will be ______.
Calculate the power spent by a crane while lifting a load of mass 2000 kg, at velocity of 1.5 ms-1. (g = 10 ms-2)
Name the quantity which is measured in kW.
Name the quantity which is measured in Wh.
Name the quantity which is measured in eV.
