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Answer :
To determine the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/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]). We can rearrange the formula to find [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Given values:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Thus, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/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]). We can rearrange the formula to find [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Given values:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Thus, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
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