Answer :
To find the mass of the roller coaster using its potential energy, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass [tex]\( m \)[/tex]. To do that, rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
By calculating the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height, given as 30 meters.
We need to solve for the mass [tex]\( m \)[/tex]. To do that, rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
By calculating the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is 800 kg.
