Answer :
Sure! Let's solve the problem to find the mass of the roller coaster using the potential energy formula.
Formula to use:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
Given:
- Potential Energy ([tex]\( PE \)[/tex]) = 235,200 J (joules),
- Height ([tex]\( h \)[/tex]) = 30 m (meters),
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.81 m/s[tex]\(^2\)[/tex].
Goal:
Find the mass ([tex]\( m \)[/tex]) of the roller coaster.
Steps:
1. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
3. Calculate the product of [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
4. Divide the potential energy by the product from step 3 to find the mass:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
5. Compute the mass:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
The mass of the roller coaster is approximately 800 kg. This fits best with the option provided as 800 kg.
Formula to use:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.
Given:
- Potential Energy ([tex]\( PE \)[/tex]) = 235,200 J (joules),
- Height ([tex]\( h \)[/tex]) = 30 m (meters),
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.81 m/s[tex]\(^2\)[/tex].
Goal:
Find the mass ([tex]\( m \)[/tex]) of the roller coaster.
Steps:
1. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
3. Calculate the product of [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
4. Divide the potential energy by the product from step 3 to find the mass:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
5. Compute the mass:
[tex]\[ m \approx 799.18 \, \text{kg} \][/tex]
The mass of the roller coaster is approximately 800 kg. This fits best with the option provided as 800 kg.
