Final answer:
The gravitational potential energy of the lake relative to the generators is 1.96 × 10¹⁶ J. The energy stored in the lake is approximately 0.52% of the energy stored in a 9-megaton fusion bomb.
Step-by-step explanation:
The gravitational potential energy of a lake can be calculated using the formula E = mgh, where E is the gravitational potential energy, m is the mass of the lake, g is the acceleration due to gravity, and h is the height of the lake above the generators.
In this case, the mass of the lake is given as 5.00 × 10¹³ kg and the height is 40.0 m above the generators. Assuming the acceleration due to gravity is 9.8 m/s², we can calculate the gravitational potential energy:
E = (5.00 × 10¹³ kg) imes (9.8 m/s²) imes (40.0 m) = 1.96 × 10¹⁶ J
So the gravitational potential energy of the lake relative to the generators is 1.96 × 10¹⁶ J.
To compare this with the energy stored in a 9-megaton fusion bomb, we need to convert the megaton to joules. One ton of TNT is equivalent to 4.18 × 10⁹ J, so a megaton is equivalent to 4.18 × 10¹² J. Therefore, a 9-megaton fusion bomb is equivalent to (9 imes 10⁶) imes (4.18 × 10¹² J) = 3.76 × 10¹⁹ J.
The ratio of gravitational potential energy in the lake to the energy stored in the bomb is calculated as:
ratio = (gravitational potential energy in the lake) / (energy stored in the bomb) = (1.96 × 10¹⁶ J) / (3.76 × 10¹⁹ J) = 0.0052
So the energy stored in the lake is approximately 0.52% of the energy stored in a 9-megaton fusion bomb.