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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 (in Joules),
- [tex]\( m \)[/tex] is the mass (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
Given:
- Potential energy ([tex]\( PE \)[/tex]) is 235,200 Joules,
- Height ([tex]\( h \)[/tex]) is 30 meters,
- Acceleration due to gravity ([tex]\( g \)[/tex]) is 9.8 m/s².
We need to solve for the mass ([tex]\( m \)[/tex]). Rearranging the formula, we get:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Divide to find the mass:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/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 [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
Given:
- Potential energy ([tex]\( PE \)[/tex]) is 235,200 Joules,
- Height ([tex]\( h \)[/tex]) is 30 meters,
- Acceleration due to gravity ([tex]\( g \)[/tex]) is 9.8 m/s².
We need to solve for the mass ([tex]\( m \)[/tex]). Rearranging the formula, we get:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
Calculate the denominator:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Divide to find the mass:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
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