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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 (235,200 J in this case),
- [tex]\( m \)[/tex] is the mass of the roller coaster (what we're trying to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height (30 m in this case).
We need to solve for the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula to:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200 \text{ J}}{9.8 \text{ m/s}² \times 30 \text{ m}} \][/tex]
After performing the calculation, you will find:
[tex]\[ m = 800 \text{ kg} \][/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 (235,200 J in this case),
- [tex]\( m \)[/tex] is the mass of the roller coaster (what we're trying to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height (30 m in this case).
We need to solve for the mass [tex]\( m \)[/tex]. To do this, we rearrange the formula to:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, plug in the values:
[tex]\[ m = \frac{235,200 \text{ J}}{9.8 \text{ m/s}² \times 30 \text{ m}} \][/tex]
After performing the calculation, you will find:
[tex]\[ m = 800 \text{ kg} \][/tex]
So, the mass of the roller coaster is 800 kg.
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