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 in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
We are given:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 J
- Height ([tex]\( h \)[/tex]) = 30 m
We need to find the mass ([tex]\( m \)[/tex]). Rearranging the formula to solve for mass gives us:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substituting the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this gives:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Thus, the mass of the roller coaster is 800 kg. Therefore, the correct answer is 800 kg.
[tex]\[ PE = m \times g \times h \][/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]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height in meters.
We are given:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 J
- Height ([tex]\( h \)[/tex]) = 30 m
We need to find the mass ([tex]\( m \)[/tex]). Rearranging the formula to solve for mass gives us:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substituting the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
Calculating this gives:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
Thus, the mass of the roller coaster is 800 kg. Therefore, the correct answer is 800 kg.
