Answer :
To find the mass of the roller coaster, we use the formula for potential energy:
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex]),
- [tex]\(h\)[/tex] is the height.
We need to solve for the mass ([tex]\(m\)[/tex]), so we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Given:
- Potential energy ([tex]\(\text{PE}\)[/tex]) = 235,200 Joules,
- Height ([tex]\(h\)[/tex]) = 30 meters,
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s².
Plugging these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now perform the calculation:
1. Multiply [tex]\(9.8\)[/tex] by [tex]\(30\)[/tex] to get [tex]\(294\)[/tex].
2. Divide [tex]\(235,200\)[/tex] by [tex]\(294\)[/tex].
This gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800\)[/tex] kg.
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex]),
- [tex]\(h\)[/tex] is the height.
We need to solve for the mass ([tex]\(m\)[/tex]), so we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Given:
- Potential energy ([tex]\(\text{PE}\)[/tex]) = 235,200 Joules,
- Height ([tex]\(h\)[/tex]) = 30 meters,
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s².
Plugging these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now perform the calculation:
1. Multiply [tex]\(9.8\)[/tex] by [tex]\(30\)[/tex] to get [tex]\(294\)[/tex].
2. Divide [tex]\(235,200\)[/tex] by [tex]\(294\)[/tex].
This gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800\)[/tex] kg.
