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 in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters.
Given:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula to solve for mass, we get:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, 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 in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters.
Given:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula to solve for mass, we get:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
