Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [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 are given:
- [tex]\( \text{PE} = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
We can rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Substituting in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/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]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [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 are given:
- [tex]\( \text{PE} = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
We can rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Substituting in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/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].
