Question

The roof of an apartment building is 58 meters high. A water tank on the roof has a mass of 38,000 kilograms. What is the potential energy of the water tank?(1 point) Responses 10,799,600 J 10,799,600 J 21,599,200 J 21,599,200 J 2,204,000 J 2,204,000 J 211,672,160 J

Answer 1

The potential energy (PE) of an object at height \( h \) can be calculated using the formula:

\[
PE = mgh
\]

where:
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on Earth),
- \( h \) is the height above ground level (in meters).

For the water tank:
- \( m = 38,000 \, \text{kg} \)
- \( g = 9.81 \, \text{m/s}^2 \)
- \( h = 58 \, \text{m} \)

Now, substituting the values into the formula:

\[
PE = 38,000 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 58 \, \text{m}
\]

Calculating this step-by-step:

1. Calculating the force due to gravity:
\[
38,000 \times 9.81 = 372,780 \, \text{N}
\]

2. Now, calculating the potential energy:
\[
PE = 372,780 \, \text{N} \times 58 \, \text{m} = 21,631,440 \, \text{J}
\]

Rounding up to appropriate significant figures based on the given choices, it appears that \( 21,599,200 \, \text{J} \) is the closest match.

Thus, the potential energy of the water tank is \( \boxed{21,599,200 \, \text{J}} \).