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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy} (P) = m \cdot g \cdot h \][/tex]
where:
- [tex]\( P \)[/tex] is the potential energy (in joules),
- [tex]\( m \)[/tex] is the mass (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
We are given:
- [tex]\( P = 235,200 \, \text{J} \)[/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]\[ m = \frac{P}{g \cdot h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now compute the value:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
[tex]\[ \text{Potential Energy} (P) = m \cdot g \cdot h \][/tex]
where:
- [tex]\( P \)[/tex] is the potential energy (in joules),
- [tex]\( m \)[/tex] is the mass (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
We are given:
- [tex]\( P = 235,200 \, \text{J} \)[/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]\[ m = \frac{P}{g \cdot h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Now compute the value:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
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