Answer :
To find the mass of the roller coaster, we can use the formula for potential energy, which is given by:
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy measured in Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster 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.
We are given:
- [tex]\( \text{PE} = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
First, rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
After performing the calculation, you find:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
[tex]\[ \text{PE} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy measured in Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster 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.
We are given:
- [tex]\( \text{PE} = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
First, rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Now plug in the values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
After performing the calculation, you find:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
