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Q5.21: NCERT Physics - Part 1 WORK, ENERGY AND POWER 5.21 Solution: The blades of a windmill sweep out a circle of area A. (a) If…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently substitute the wind velocity directly in km/h into the kinetic energy formula without converting it to m/s, leading to a power calculation error by a factor of 3.6 squared. Always ensure velocity is in SI units (m/s) before applying $P = \frac{1}{2}\rho A v^3$ or similar energy-based power equations.
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 the windmill converts 25% of the wind's energy into electrical energy, and that A = 30 m_, v = 36 km/h and the density of air is 1.2 kg m__. What is the electrical power produced?
Step-by-Step Verified Solution
**Answer:** (a) m = _Avt (b) KE = __Av_t (c) P = 4.5 kW
**Step-by-Step Explanation:**
(a) Volume of air passing per second = Av. Mass per second = _Av. In time t: m = _Avt.
(b) KE = _mv_ = __Av_t.
(c) v = 36 km/h = 10 m/s. Power = 0.25 _ __Av_ = 0.25 _ 0.5 _ 1.2 _ 30 _ 1000 = 4500 W = 4.5 kW.
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