Answer :
To find the mass of the roller coaster at the top of the hill given its potential energy, we can use the potential energy formula:
[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 (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex])
- [tex]\( h \)[/tex] is the height
We want to solve for the mass ([tex]\( m \)[/tex]). To do this, we rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Plugging in the given values:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
Now, substitute these values into the rearranged formula to find the mass:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Carrying out this calculation will give you a mass of [tex]\( 800 \, \text{kg} \)[/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 (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex])
- [tex]\( h \)[/tex] is the height
We want to solve for the mass ([tex]\( m \)[/tex]). To do this, we rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Plugging in the given values:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 30 \, \text{m} \)[/tex]
Now, substitute these values into the rearranged formula to find the mass:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Carrying out this calculation will give you a mass of [tex]\( 800 \, \text{kg} \)[/tex].
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
