Answer :
To solve this problem, we're looking to find the mass of the roller coaster using the formula for potential energy, given by:
[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 9.8 m/s²), and
- [tex]\( h \)[/tex] is the height of the hill.
We're given:
- [tex]\( PE = 235,200 \)[/tex] Joules,
- [tex]\( h = 30 \)[/tex] meters.
To find the mass [tex]\( m \)[/tex], we need to rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
1. Use the given potential energy: [tex]\( 235,200 \)[/tex] Joules.
2. Use the standard acceleration due to gravity: [tex]\( 9.8 \)[/tex] m/s².
3. Use the height of the hill: [tex]\( 30 \)[/tex] meters.
Calculate:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \)[/tex] kg.
[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 9.8 m/s²), and
- [tex]\( h \)[/tex] is the height of the hill.
We're given:
- [tex]\( PE = 235,200 \)[/tex] Joules,
- [tex]\( h = 30 \)[/tex] meters.
To find the mass [tex]\( m \)[/tex], we need to rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
1. Use the given potential energy: [tex]\( 235,200 \)[/tex] Joules.
2. Use the standard acceleration due to gravity: [tex]\( 9.8 \)[/tex] m/s².
3. Use the height of the hill: [tex]\( 30 \)[/tex] meters.
Calculate:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \)[/tex] kg.
