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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]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters.
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 solve for [tex]\( m \)[/tex], which is the mass.
Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Perform the calculations:
1. Multiply [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ 9.81 \cdot 30 = 294.3 \][/tex]
2. Divide the potential energy by the result from step 1:
[tex]\[ m = \frac{235,200}{294.3} \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex].
Among the given options, the closest mass value is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the correct answer is:
[tex]\(800 \, \text{kg}\)[/tex]
[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]\( 9.81 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height in meters.
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 solve for [tex]\( m \)[/tex], which is the mass.
Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \cdot 30} \][/tex]
Perform the calculations:
1. Multiply [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ 9.81 \cdot 30 = 294.3 \][/tex]
2. Divide the potential energy by the result from step 1:
[tex]\[ m = \frac{235,200}{294.3} \approx 799.18 \][/tex]
Therefore, the mass of the roller coaster is approximately [tex]\( 799.18 \, \text{kg} \)[/tex].
Among the given options, the closest mass value is [tex]\( 800 \, \text{kg} \)[/tex]. Therefore, the correct answer is:
[tex]\(800 \, \text{kg}\)[/tex]
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