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?
PE = mgh
m = mass
g = 9.8 m/s^2
h = height in meters
PE = mgh
m = mass
g = 9.8 m/s^2
h = height in meters
Answers
GPT-4o mini
To calculate the gravitational potential energy (PE) at the top of the hill, you can use the formula:
\[
PE = mgh
\]
Where:
- \( m \) is the mass (800 kg),
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²),
- \( h \) is the height (50 m).
Plugging in the values:
\[
PE = 800 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 50 \, \text{m}
\]
Now, calculate it step-by-step:
1. Calculate \( g \times h \):
\[
9.8 \, \text{m/s}^2 \times 50 \, \text{m} = 490 \, \text{m}^2/\text{s}^2
\]
2. Now calculate \( m \times (g \times h) \):
\[
800 \, \text{kg} \times 490 \, \text{m}^2/\text{s}^2 = 392000 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\]
This is equivalent to Joules, so:
\[
PE = 392000 \, \text{J}
\]
Thus, the gravitational potential energy at the top of the hill is **392,000 Joules**.
\[
PE = mgh
\]
Where:
- \( m \) is the mass (800 kg),
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²),
- \( h \) is the height (50 m).
Plugging in the values:
\[
PE = 800 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 50 \, \text{m}
\]
Now, calculate it step-by-step:
1. Calculate \( g \times h \):
\[
9.8 \, \text{m/s}^2 \times 50 \, \text{m} = 490 \, \text{m}^2/\text{s}^2
\]
2. Now calculate \( m \times (g \times h) \):
\[
800 \, \text{kg} \times 490 \, \text{m}^2/\text{s}^2 = 392000 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\]
This is equivalent to Joules, so:
\[
PE = 392000 \, \text{J}
\]
Thus, the gravitational potential energy at the top of the hill is **392,000 Joules**.