Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we are trying to find,
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 meters per second squared (m/s²),
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters.
To solve for the mass [tex]\( m \)[/tex], we can rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Let's plug in the values:
1. Substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
2. Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
3. Divide the potential energy by the result from step 2:
[tex]\[ m = \frac{235,200}{294} \][/tex]
4. Perform the division:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass of the roller coaster, which we are trying to find,
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 meters per second squared (m/s²),
- [tex]\( h \)[/tex] is the height of the hill, given as 30 meters.
To solve for the mass [tex]\( m \)[/tex], we can rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Let's plug in the values:
1. Substitute the given values into the formula:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]
2. Calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
3. Divide the potential energy by the result from step 2:
[tex]\[ m = \frac{235,200}{294} \][/tex]
4. Perform the division:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is approximately 800 kg.
