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Two dams are built to impound a lake; when full, the water reaches the top of each dam. The second dam is twice as tall and twice as wide as the first. By what factor is the total horizontal water force on the second dam greater than on the first? (Ignore atmospheric pressure as it acts on both faces.)
- 2 times
- 4 times
- 8 times
- 16 times
Correct answer: 8 times
Solution
Force on a vertical face = (rho g H / 2) * (H * W) = (rho g W H²)/2. So F is proportional to W * H². Doubling H and W gives factor 2 * 2² = 2 * 4 = 8. Hence the second dam feels 8 times the force.
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