Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{PE} = mgh \][/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.
We need to solve for [tex]\(m\)[/tex], the mass of the roller coaster. To do this, rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{gh} \][/tex]
Now, let's plug in the given values:
- Potential energy, [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex]
- Height, [tex]\(h = 30 \, \text{m}\)[/tex]
- Acceleration due to gravity, [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex]
Substitute these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
This gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800 \, \text{kg}\)[/tex].
[tex]\[ \text{PE} = mgh \][/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.
We need to solve for [tex]\(m\)[/tex], the mass of the roller coaster. To do this, rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{gh} \][/tex]
Now, let's plug in the given values:
- Potential energy, [tex]\(\text{PE} = 235,200 \, \text{J}\)[/tex]
- Height, [tex]\(h = 30 \, \text{m}\)[/tex]
- Acceleration due to gravity, [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex]
Substitute these values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294} \][/tex]
This gives us:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(800 \, \text{kg}\)[/tex].
