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?
A. 211,672,160 J
B. 21,599,200 J
C. 10,799,600 J
D. 2,204,000 J

Answer 1

The potential energy (PE) can be calculated using the formula:

\[
PE = mgh
\]

where:
- \( PE \) = potential energy in joules (J)
- \( m \) = mass in kilograms (kg)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height in meters (m)

Given:
- \( m = 38,000 \, \text{kg} \)
- \( h = 58 \, \text{m} \)
- \( g \approx 9.81 \, \text{m/s}^2 \)

Now, substituting the values into the formula:

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

Calculating:

\[
PE = 38,000 \times 9.81 \times 58
\]

First, calculate \( 38,000 \times 9.81 \):

\[
38,000 \times 9.81 = 372,780 \, \text{kg} \cdot \text{m/s}^2
\]

Now multiply this by 58:

\[
372,780 \times 58 = 21,628,440 \, \text{J}
\]

So, the potential energy of the water tank is \( 21,628,440 \, \text{J} \). This value is closest to option B \( 21,599,200 \, \text{J} \).

Therefore, the answer is:

**B. 21,599,200 J**