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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,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We're given:
- [tex]\( PE = 235,200 \, \text{J} \)[/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].
1. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
2. Plug in the known values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
3. Calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
4. Divide the potential energy by the result from step 3 to find the mass:
[tex]\[ m = \frac{235,200}{294} \][/tex]
5. Perform the division:
[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,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
We're given:
- [tex]\( PE = 235,200 \, \text{J} \)[/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].
1. Rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
2. Plug in the known values:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
3. Calculate the denominator:
[tex]\[ 9.8 \cdot 30 = 294 \][/tex]
4. Divide the potential energy by the result from step 3 to find the mass:
[tex]\[ m = \frac{235,200}{294} \][/tex]
5. Perform the division:
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
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