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Answer :
To find the mass of the roller coaster, we'll use the formula for potential energy, which is:
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy, which is given as 235,200 J (Joules).
- [tex]\(m\)[/tex] is the mass of the roller coaster, which we need to find.
- [tex]\(g\)[/tex] is the acceleration due to gravity, approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- [tex]\(h\)[/tex] is the height of the hill, given as 30 meters.
The formula can be rearranged to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
By substituting the given values into the equation, we have:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
Calculating this gives:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is approximately [tex]\(800 \, \text{kg}\)[/tex].
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy, which is given as 235,200 J (Joules).
- [tex]\(m\)[/tex] is the mass of the roller coaster, which we need to find.
- [tex]\(g\)[/tex] is the acceleration due to gravity, approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- [tex]\(h\)[/tex] is the height of the hill, given as 30 meters.
The formula can be rearranged to solve for mass ([tex]\(m\)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
By substituting the given values into the equation, we have:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
Calculating this gives:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is approximately [tex]\(800 \, \text{kg}\)[/tex].
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