Answer to Question #5324 in Mechanics | Relativity for Kyle Mitchell

Question #5324
A rain cloud contains 1.73 × 10^7 kg of water vapor.The acceleration of gravity is 9.8 m/s^2 . How long would it take for a 4.9 kW pump to lift the same amount of water to an altitude of 24000 m? Answer in units of years
1
Expert's answer
2011-11-25T10:20:04-0500
Let's find the work needed to do that:
A = m*g*H = 1.73*10^7*9.8*24*10^3 = 406.896*10^10 = 406896*10^7 J.
So, the necessary time is:
T = A/P = 406896*10^7 / 4.9*10^3 = 83040*10^4 s = 13840000 minutes = 230666.(6) hours = 9611.(1) days ≈ 26.332 years.

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