Answer :
To find the mass of the roller coaster, we will 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]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
Given:
- Potential Energy ([tex]\( PE \)[/tex]) = [tex]\( 235,200 \, \text{J} \)[/tex],
- Height ([tex]\( h \)[/tex]) = [tex]\( 30 \, \text{m} \)[/tex],
- Acceleration due to gravity ([tex]\( g \)[/tex]) = [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
We need to solve for [tex]\( m \)[/tex]. Rearrange the formula to solve for mass:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. The closest answer to this value from the provided options 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]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
Given:
- Potential Energy ([tex]\( PE \)[/tex]) = [tex]\( 235,200 \, \text{J} \)[/tex],
- Height ([tex]\( h \)[/tex]) = [tex]\( 30 \, \text{m} \)[/tex],
- Acceleration due to gravity ([tex]\( g \)[/tex]) = [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
We need to solve for [tex]\( m \)[/tex]. Rearrange the formula to solve for mass:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex]. The closest answer to this value from the provided options is [tex]\( 800 \, \text{kg} \)[/tex].
