Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/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.
From the problem, we are given:
- [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex],
- [tex]\( h = 30 \, \text{m} \)[/tex],
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
We need to rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Now, let's plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Based on the options provided:
- 800 kg
- 7.840 kg
- 8,000 kg
- 78,400 kg
The correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( \text{PE} \)[/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.
From the problem, we are given:
- [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex],
- [tex]\( h = 30 \, \text{m} \)[/tex],
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
We need to rearrange the formula to solve for mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
Now, let's plug in the given values:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
Based on the options provided:
- 800 kg
- 7.840 kg
- 8,000 kg
- 78,400 kg
The correct answer is [tex]\( 800 \, \text{kg} \)[/tex].
