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Answer :
Sure, let's solve this step-by-step using the formula for potential energy:
Given:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Acceleration due to gravity (g) = 9.8 m/s²
To find the mass (m) of the roller coaster, we use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
We need to isolate the mass (m) in this equation. So we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
Now, perform the calculation step-by-step:
1. First, find the product of [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ g \cdot h = 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} = 294 \, \text{m} \cdot \text{m/s}^2 \][/tex]
2. Now, divide the potential energy by this product:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m} \cdot \text{m/s}^2} \][/tex]
3. Simplify the division:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(\textbf{800 kg}\)[/tex].
Given:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Acceleration due to gravity (g) = 9.8 m/s²
To find the mass (m) of the roller coaster, we use the formula for potential energy:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
We need to isolate the mass (m) in this equation. So we rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]
Substitute the given values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
Now, perform the calculation step-by-step:
1. First, find the product of [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ g \cdot h = 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} = 294 \, \text{m} \cdot \text{m/s}^2 \][/tex]
2. Now, divide the potential energy by this product:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m} \cdot \text{m/s}^2} \][/tex]
3. Simplify the division:
[tex]\[ m = 800 \, \text{kg} \][/tex]
Therefore, the mass of the roller coaster is [tex]\(\textbf{800 kg}\)[/tex].
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