Work, Power and Energy
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Question : 21
Total: 30
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 thewindmill converts 25% of the wind’s energy into electrical energy, and thatA = 30 m 2 , v = 36 km ∕ h kg m – 3
(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 thewindmill converts 25% of the wind’s energy into electrical energy, and that
Solution:
(a) Volume of wind flowing/second = A v
Mass of air passingt s = A v ρ t
(b) K.E. of air=
m v 2 =
( A v ρ t ) v 2 =
A v 3 ρ t
(c) Electrical energy produced= (
) × K . E . =
×
A v 3 ρ t
Electrical power=
=
A v 3 ρ
P =
× 30 × ( 10 ) 3 × 1.2 = 4500 = 4.5 kW
Mass of air passing
(b) K.E. of air
(c) Electrical energy produced
Electrical power
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