Answer :
To solve this problem, we need to calculate the mass of the roller coaster using the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy} (PE) = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (usually [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill,
- [tex]\( \text{PE} \)[/tex] is the given potential energy, which is [tex]\( 235,200 \, \text{J} \)[/tex].
Here are the steps to find the mass:
1. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
2. Substitute the given values into the equation:
- [tex]\( \text{PE} = 235,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
3. Calculate the mass:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
4. Perform the multiplication and division:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
From the given options, the correct mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy} (PE) = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (usually [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill,
- [tex]\( \text{PE} \)[/tex] is the given potential energy, which is [tex]\( 235,200 \, \text{J} \)[/tex].
Here are the steps to find the mass:
1. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
2. Substitute the given values into the equation:
- [tex]\( \text{PE} = 235,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
3. Calculate the mass:
[tex]\[ m = \frac{235,200}{9.8 \cdot 30} \][/tex]
4. Perform the multiplication and division:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
From the given options, the correct mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
