Question

A thunderstorm deposits 1.5cm of rain over an area of 25km. The rain fall average height is 2km.
a) What is the total Gravitational Potential Energy of the rain?
b) If the storm last 30min. What is the average power?
c) How did this amount of energy get stored in the storm cloud?

Answer 1

Convert everything to the appropriate units:
\[25km^2 (area)= 2.5x10^7m^2\]\[1.5cm (depth)= 1.5x10^{-2}m\]\[2km (height) = 2x10^3m\]\[30mins = 1.8x10^3s\]
Calculate the volume of the water:
\[V = area * height = (2.5x10^7m^2)(1.5x10^{-2}m) = 3.75x10^5 m^3\]
Find the total mass of the rainwater that fell:
\[Mass_{total} = \frac{1x10^3kg}{m^3} * 3.75x10^5 m^3=3.75x10^8kg\]
Calculate the gravitational potential energy:
\[PE=mgh=(3.75x10^8kg)(9.8 m/s^2)(2x10^3m)=7.35x10^{12}J\]
Calculate the average power:
\[P=\frac{\Delta E}{\Delta t}=\frac{7.35x10^{12}J}{1.8x10^3s}=4.08x10^9 \frac{J}{s}=4.1x10^9 W\]
As far as part C goes the energy stored in the storm cloud should be the same as the gravitational potential energy: 7.35x10^9J

Hopefully this helps and I didn't make any silly mistakes :)

Answer 2

how do you get mass total=(1x10^3)/m^3.
from what information do u get the 1x10^3 and
what formula are u using 'mass total=((1x10^3)/m^3) x 3.75x10^5 m^3

Answer 3

1 cubic meter of water = 1,000kg...that's just a fact that you'll eventually memorize in physics.

As far as the equation goes, I took the knowledge that each cubic meter of water is 1,000kg and multiplied that times the number of cubic meters of water to get the total mass.

Answer 4

oh....thank you very much :) really help me