Answer :
To find the mass of the roller coaster, we use the formula for potential energy (PE):
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy (235,200 J).
- [tex]\(m\)[/tex] is the mass of the roller coaster (what we're trying to find).
- [tex]\(g\)[/tex] is the acceleration due to gravity, which is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- [tex]\(h\)[/tex] is the height of the hill (30 m).
We need to solve for [tex]\(m\)[/tex], the mass. Rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800 \, \text{kg}\)[/tex].
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\(\text{PE}\)[/tex] is the potential energy (235,200 J).
- [tex]\(m\)[/tex] is the mass of the roller coaster (what we're trying to find).
- [tex]\(g\)[/tex] is the acceleration due to gravity, which is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- [tex]\(h\)[/tex] is the height of the hill (30 m).
We need to solve for [tex]\(m\)[/tex], the mass. Rearrange the formula to solve for [tex]\(m\)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800 \, \text{kg}\)[/tex].
