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Answer :
To find the mass of the roller coaster, we use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, in joules (J),
- [tex]\( m \)[/tex] is the mass, in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height, in meters (m).
Given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We need to find the mass [tex]\( m \)[/tex]. We'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Next, plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number gives us a mass of approximately [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, in joules (J),
- [tex]\( m \)[/tex] is the mass, in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height, in meters (m).
Given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We need to find the mass [tex]\( m \)[/tex]. We'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Next, plug in the given values:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
Rounding to the nearest whole number gives us a mass of approximately [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is approximately [tex]\( 800 \, \text{kg} \)[/tex].
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