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 (235,200 Joules),
- [tex]\( m \)[/tex] is the mass of the roller coaster (our unknown),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height (30 meters).
We need to rearrange this formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, we plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
When you calculate this, you get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is 800 kg.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules),
- [tex]\( m \)[/tex] is the mass of the roller coaster (our unknown),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height (30 meters).
We need to rearrange this formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, we plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
When you calculate this, you get:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is 800 kg.
