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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height.
We are given:
- The potential energy, [tex]\( PE = 235,200 \, \text{J} \)[/tex],
- The height, [tex]\( h = 30 \, \text{m} \)[/tex].
We're solving for [tex]\( m \)[/tex] (mass), so we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substituting the known values into the formula gives:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
When we calculate this, we find:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Doing the division, the mass [tex]\( m = 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex],
- [tex]\( h \)[/tex] is the height.
We are given:
- The potential energy, [tex]\( PE = 235,200 \, \text{J} \)[/tex],
- The height, [tex]\( h = 30 \, \text{m} \)[/tex].
We're solving for [tex]\( m \)[/tex] (mass), so we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substituting the known values into the formula gives:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
When we calculate this, we find:
[tex]\[ m = \frac{235,200}{294} \][/tex]
Doing the division, the mass [tex]\( m = 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
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