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Answer :
To solve this problem, we need to find the mass of the roller coaster using the given potential energy, height of the hill, and the formula for potential energy. Here's a step-by-step solution:
1. Understand the Formula:
The formula for potential energy (PE) is given by:
[tex]\[
\text{PE} = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height.
2. Given Values:
- Potential energy ([tex]\(\text{PE}\)[/tex]): 235,200 Joules
- Height ([tex]\(h\)[/tex]): 30 meters
- Acceleration due to gravity ([tex]\(g\)[/tex]): 9.81 m/s²
3. Rearrange the Formula:
We want to find the mass ([tex]\(m\)[/tex]). Rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[
m = \frac{\text{PE}}{g \cdot h}
\][/tex]
4. Substitute the Known Values:
[tex]\[
m = \frac{235,200}{9.81 \times 30}
\][/tex]
5. Calculate the Mass:
Performing the calculation gives:
[tex]\[
m \approx 799.18 \, \text{kg}
\][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg. Thus, the correct answer is 800 kg.
1. Understand the Formula:
The formula for potential energy (PE) is given by:
[tex]\[
\text{PE} = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height.
2. Given Values:
- Potential energy ([tex]\(\text{PE}\)[/tex]): 235,200 Joules
- Height ([tex]\(h\)[/tex]): 30 meters
- Acceleration due to gravity ([tex]\(g\)[/tex]): 9.81 m/s²
3. Rearrange the Formula:
We want to find the mass ([tex]\(m\)[/tex]). Rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[
m = \frac{\text{PE}}{g \cdot h}
\][/tex]
4. Substitute the Known Values:
[tex]\[
m = \frac{235,200}{9.81 \times 30}
\][/tex]
5. Calculate the Mass:
Performing the calculation gives:
[tex]\[
m \approx 799.18 \, \text{kg}
\][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg. Thus, the correct answer is 800 kg.
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