# [Solved] A hydroelectric power facility converts the gravitational

A hydroelectric facility converts the gravitational potential energy of water behind a dam to electric energy.

(a) What is the gravitational potential energy relative to the generators of a lake of volume 50.0 km^3 ( mass = 5.00×10^13 kg), given that the lake has an average height of 40.0 m above the generators?

(b) Compare this with the energy stored in a 9-megaton fusion bomb.

(a) **Answer:** The gravitational potential energy of an object is given by the formula:

PE = mgh

where **m** is the mass of the object,

**g** is the acceleration due to gravity (9.8 m/s^2) and

**h** is the height above the reference point.

The mass of the lake is given as 5.00×10^13 kg, and the height above the generators is 40.0 m, so the gravitational potential energy of the lake is:

PE = (5.00×10^13 kg)(9.8 m/s^2)(40.0 m)

= **1.96×10^16 J (Answer)**

b) The energy stored in a 9-megaton fusion bomb is equivalent to 1.38×10^16 joules.

**1.420(Answer)**

It is important to note that the energy from the hydroelectric facility is obtained through a sustainable process, while the energy from the bomb is obtained through a destructive process and is not sustainable.