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Answer :
Sure, let's solve this step-by-step.
The problem gives us the following information:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 Joules
- Height ([tex]\( h \)[/tex]) = 30 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
We need to find the mass ([tex]\( m \)[/tex]) of the roller coaster. The formula for potential energy is:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
To find the mass, we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, we'll plug in the given values:
[tex]\[ m = \frac{235200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \, \text{m/s}^2 \times 30 \, \text{m} = 294 \, \text{m}^2/\text{s}^2 \][/tex]
Now, divide the potential energy by this product:
[tex]\[ m = \frac{235200 \, \text{J}}{294 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \)[/tex] kg.
The problem gives us the following information:
- Potential energy ([tex]\( PE \)[/tex]) = 235,200 Joules
- Height ([tex]\( h \)[/tex]) = 30 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
We need to find the mass ([tex]\( m \)[/tex]) of the roller coaster. The formula for potential energy is:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
To find the mass, we need to rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Now, we'll plug in the given values:
[tex]\[ m = \frac{235200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
First, calculate the denominator:
[tex]\[ 9.8 \, \text{m/s}^2 \times 30 \, \text{m} = 294 \, \text{m}^2/\text{s}^2 \][/tex]
Now, divide the potential energy by this product:
[tex]\[ m = \frac{235200 \, \text{J}}{294 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ m = 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\( 800 \)[/tex] kg.
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