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

21,599,200 J
21,599,200 J

2,204,000 J
2,204,000 J

211,672,160 J
211,672,160 J

10,799,600 J

1 answer

To calculate the potential energy (PE) of the water tank, you can use the formula for gravitational potential energy:

\[ PE = m \cdot g \cdot h \]

where:

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

Given:

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

Now plug in the values:

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

Calculating it step-by-step:

  1. Calculate \( g \cdot h \): \[ 9.81 , \text{m/s}^2 \cdot 58 , \text{m} = 569.98 , \text{m}^2/\text{s}^2 \]

  2. Now multiply by the mass \( m \): \[ PE = 38,000 , \text{kg} \cdot 569.98 , \text{m}^2/\text{s}^2 \approx 21,599,240 , \text{J} \]

So the potential energy of the water tank is approximately \( 21,599,240 , \text{J} \), which can be rounded to \( 21,599,200 , \text{J} \).

The correct answer is:

21,599,200 J