Question
a roller coaster with a mass of 800kg is at the top of a hill 50 meters high. what is its gravitational potential energy at the top of the hill?
Answers
GPT-4o mini
The gravitational potential energy (PE) of an object can be calculated using the formula:
\[
PE = m \cdot g \cdot h
\]
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 the reference point (in meters).
Given:
- \( m = 800 \, \text{kg} \)
- \( h = 50 \, \text{m} \)
- \( g \approx 9.81 \, \text{m/s}^2 \)
Now we can substitute the values into the formula:
\[
PE = 800 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 50 \, \text{m}
\]
\[
PE = 800 \cdot 9.81 \cdot 50
\]
\[
PE = 800 \cdot 490.5
\]
\[
PE = 392400 \, \text{J}
\]
Thus, the gravitational potential energy at the top of the hill is **392,400 joules** (or 392.4 kJ).
\[
PE = m \cdot g \cdot h
\]
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 the reference point (in meters).
Given:
- \( m = 800 \, \text{kg} \)
- \( h = 50 \, \text{m} \)
- \( g \approx 9.81 \, \text{m/s}^2 \)
Now we can substitute the values into the formula:
\[
PE = 800 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 50 \, \text{m}
\]
\[
PE = 800 \cdot 9.81 \cdot 50
\]
\[
PE = 800 \cdot 490.5
\]
\[
PE = 392400 \, \text{J}
\]
Thus, the gravitational potential energy at the top of the hill is **392,400 joules** (or 392.4 kJ).