Answer :
To solve this problem, we need to find the mass of a roller coaster using the potential energy formula:
[tex]\[ PE = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy, which is given as 235,200 joules (J),
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²),
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters (m).
We want to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now plug in the given values:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 J
- Gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
- Height ([tex]\( h \)[/tex]) = 30 m
Substitute these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/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, which is given as 235,200 joules (J),
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we need to find,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²),
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters (m).
We want to rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now plug in the given values:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 J
- Gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
- Height ([tex]\( h \)[/tex]) = 30 m
Substitute these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is 800 kg.
