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A person wants to use the water in his bath tub to generate electricity for a 40 W bulb. The tub sits 10 m above the ground and holds 200 litres of water. A water-driven wheel generator (efficiency 90%) is placed on the ground. At what mass flow rate must the water drain to power the bulb, and for how long can the bulb stay lit if the tub starts full? (g = 10 m/s²)

1. About 0.44 kg/s; the bulb stays on for about 7.5 minutes
2. About 0.40 kg/s; the bulb stays on for about 8.3 minutes
3. About 0.50 kg/s; the bulb stays on for about 6.7 minutes
4. About 0.44 kg/s; the bulb stays on for about 15 minutes

Correct answer: About 0.44 kg/s; the bulb stays on for about 7.5 minutes

Solution

Solving 0.9 * (dm/dt) * 10 * 10 = 40 gives 0.444 kg/s; the 200 kg of water lasts 200/0.444 = 450 s = 7.5 min.

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