Answer :
To find 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, given as [tex]\( 235,200 \, \text{Joules} \)[/tex]
- [tex]\( m \)[/tex] is the mass of the roller coaster
- [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, given as [tex]\( 30 \, \text{meters} \)[/tex]
We need to solve for the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substituting the known values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculating:
[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]\[ PE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy, given as [tex]\( 235,200 \, \text{Joules} \)[/tex]
- [tex]\( m \)[/tex] is the mass of the roller coaster
- [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, given as [tex]\( 30 \, \text{meters} \)[/tex]
We need to solve for the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substituting the known values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculating:
[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].
