Gravity Clouds and rain

Classical Mechanics Level 3

A cluster of clouds at a height 1000 m above the surface of the Earth burst and enough rain fell over an area of 1000000 sq.m. with a depth of 2 cm. How much work has been done in rising the cloud to that height?

DETAILS AND ASSUMPTIONS:

1) Take the acceleration due to gravity as $9.8 m/s^2$

2) Provide your answer in Joules.

3) Take the density of water as 1000 kg per cubic meter.

The answer is 196000000000.

1 solution

Mikhael Glen Lataza
Apr 19, 2015

The volume of the cloud, $V$ is

$V = 10^{6} \times 0.02$

$V = 2 \times 10^{4} m^3$

The total mass of the cloud, $M$ is

$M = \rho V$

$M = 1000 \frac{kg}{m^{3}} \times 2 \times 10^{4} m^{3}$

$M = 2 \times 10^{7} kg$

Work done to move the cloud up at height, $h$ is

$W = Mgh$

$W = 2 \times 10^{7} \times 9.8 \times 1000$

$W = \boxed{1.96 \times 10^{11} J}$

Its annoying to write down 196000000000 :p

Tahsin Ahmed - 6 years, 1 month ago

Thnx for give the solution

apoorva singh - 3 years, 9 months ago

Thanks a ton

Cinda Manuvel - 3 years, 6 months ago

no problem

Mikhael Glen Lataza - 1 year, 2 months ago

Gravity Clouds and rain

The answer is 196000000000.

1 solution

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