Answer :
To find the mass of the roller coaster, we use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (which is given as 235,200 Joules),
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (which is given as 30 meters).
We need to solve for the mass ([tex]\( m \)[/tex]). We can rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate the denominator first:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
Then, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
When you perform the division, the mass [tex]\( m \)[/tex] is approximately 799.18 kg.
Based on the options provided:
800 kg
7,840 kg
8,000 kg
78,400 kg
The closest match to our calculated value is 800 kg. Therefore, the mass of the roller coaster is approximately 800 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy (which is given as 235,200 Joules),
- [tex]\( m \)[/tex] is the mass of the roller coaster,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (which is given as 30 meters).
We need to solve for the mass ([tex]\( m \)[/tex]). We can rearrange the formula:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Substitute the known values into the formula:
[tex]\[ m = \frac{235,200}{9.81 \times 30} \][/tex]
Calculate the denominator first:
[tex]\[ 9.81 \times 30 = 294.3 \][/tex]
Then, divide the potential energy by this result:
[tex]\[ m = \frac{235,200}{294.3} \][/tex]
When you perform the division, the mass [tex]\( m \)[/tex] is approximately 799.18 kg.
Based on the options provided:
800 kg
7,840 kg
8,000 kg
78,400 kg
The closest match to our calculated value is 800 kg. Therefore, the mass of the roller coaster is approximately 800 kg.
