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Answer :
To find the mass of the roller coaster given its potential energy, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/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]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We need to find the mass [tex]\( m \)[/tex], so we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
Substitute these into the rearranged formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.81 \cdot 30 = 294.3 \][/tex]
Now divide the potential energy by the result:
[tex]\[ m = \frac{235,200}{294.3} \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex], which matches with the given option [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/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]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We need to find the mass [tex]\( m \)[/tex], so we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
Substitute these into the rearranged formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.81 \cdot 30 = 294.3 \][/tex]
Now divide the potential energy by the result:
[tex]\[ m = \frac{235,200}{294.3} \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex], which matches with the given option [tex]\( 800 \, \text{kg} \)[/tex].
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