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Answer :
To solve this problem, we need to find the mass of a roller coaster using the potential energy formula. Let's go through the steps:
1. Understand the given values and formula:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravitational acceleration (g) = 9.8 m/s²
- Formula: [tex]\( PE = m \cdot g \cdot h \)[/tex], where [tex]\( m \)[/tex] is the mass of the roller coaster
2. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
- We need to find the mass, so let's rearrange the formula:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
3. Substitute the known values into the rearranged formula:
[tex]\[
m = \frac{235,200}{9.8 \cdot 30}
\][/tex]
4. Calculate the denominator:
[tex]\[
9.8 \cdot 30 = 294
\][/tex]
5. Calculate the mass:
[tex]\[
m = \frac{235,200}{294}
\][/tex]
[tex]\[
m = 800 \, \text{kg}
\][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex]. The correct answer is 800 kg.
1. Understand the given values and formula:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravitational acceleration (g) = 9.8 m/s²
- Formula: [tex]\( PE = m \cdot g \cdot h \)[/tex], where [tex]\( m \)[/tex] is the mass of the roller coaster
2. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
- We need to find the mass, so let's rearrange the formula:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
3. Substitute the known values into the rearranged formula:
[tex]\[
m = \frac{235,200}{9.8 \cdot 30}
\][/tex]
4. Calculate the denominator:
[tex]\[
9.8 \cdot 30 = 294
\][/tex]
5. Calculate the mass:
[tex]\[
m = \frac{235,200}{294}
\][/tex]
[tex]\[
m = 800 \, \text{kg}
\][/tex]
Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex]. The correct answer is 800 kg.
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