Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy in joules (235,200 J in this case)
- [tex]\( m \)[/tex] is the mass in kilograms
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²)
- [tex]\( h \)[/tex] is the height in meters (30 m in this case)
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug the values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is 800 kg.
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy in joules (235,200 J in this case)
- [tex]\( m \)[/tex] is the mass in kilograms
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²)
- [tex]\( h \)[/tex] is the height in meters (30 m in this case)
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug the values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is 800 kg.
