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,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We are given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculate the denominator first:
[tex]\[ 9.8 \, \text{m/s}^2 \times 30 \, \text{m} = 294 \, \text{m}^2/\text{s}^2 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, 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,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We are given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculate the denominator first:
[tex]\[ 9.8 \, \text{m/s}^2 \times 30 \, \text{m} = 294 \, \text{m}^2/\text{s}^2 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
