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Answer :
To find the mass of the roller coaster, we can use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster that we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height of the hill, which is 30 meters.
Rearrange the formula to solve for the mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this product:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is 800 kg.
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is 235,200 Joules.
- [tex]\( m \)[/tex] is the mass of the roller coaster that we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height of the hill, which is 30 meters.
Rearrange the formula to solve for the mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \times 30 = 294 \][/tex]
Now, divide the potential energy by this product:
[tex]\[ m = \frac{235,200}{294} \][/tex]
[tex]\[ m = 800 \][/tex]
So, the mass of the roller coaster is 800 kg.
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