A rain cloud contain 5.37 x 10 to the seventh power kg of water vapor. The acceleration of gravity is 9.81 m/s^2How long would it take for a 1.53kW pump to raise the same amount of water to the...

A rain cloud contain 5.37 x 10 to the seventh power kg of water vapor.

The acceleration of gravity is 9.81 m/s^2

How long would it take for a 1.53kW pump to raise the same amount of water to the cloud's altitude of 1.54 km? Answer in units of s.

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The mass of water to be be pumped=5.37*10^7 kg.

The energy required to raise the mass m=5.37*10^7 kg  to the height of h = 1.54km=1540 meter is = mgh, where g is the acceleration due togravitaty =9.981m/s^2

mgh =5.37*10^7*9.81*1540 J

The energy generation by the 1.53 KW =1.53KW=1530 watt per second

Threfore, the time in seconds the pump could produce the energy to lift the mass of 5.37*10^ 7 kg of water to a height of 15400 metr = 5.37*10^7*9.81*1540/ (1530) seconds.

=530240117.6 seconds.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

Given:

mass of water = m = 5.37 x 10^7 kg

Displacement of water required = s = 1.54 km = 1540 m

Acceleration of gravity = g = 9.81 m/s^2

Power of pump = 1.53 kW = 1530 W

Total work or energy required to raise the water to required height is given by formula:

Work = m*g*s* = (5.37 x 10^7)*9.81*1540 = 811.26738 x 10^12

Time take to do this work is given by the formula:

Time = Work/(Power of pump) = (811.26738 x 10^12)/1530

= 530.2401176 x 10^9 s

Answer:It will take 530.240 x 10^9 s for the pump.

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