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Answer :
Let's solve the problem of finding the mass of the roller coaster using the concept of potential energy. The formula for potential energy (PE) is:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [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 (m).
Given:
- Potential energy [tex]\( PE = 235,200 \, J \)[/tex]
- Height [tex]\( h = 30 \, m \)[/tex]
- Gravitational acceleration [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to find the mass [tex]\( m \)[/tex] of the roller coaster. To do this, we'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, plug the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Perform the multiplication in the denominator:
[tex]\[ g \cdot h = 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
When you calculate that division, you get:
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy in joules (J),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [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 (m).
Given:
- Potential energy [tex]\( PE = 235,200 \, J \)[/tex]
- Height [tex]\( h = 30 \, m \)[/tex]
- Gravitational acceleration [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We need to find the mass [tex]\( m \)[/tex] of the roller coaster. To do this, we'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, plug the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Perform the multiplication in the denominator:
[tex]\[ g \cdot h = 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
When you calculate that division, you get:
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].
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