Answer :
Sure, let's solve this problem step by step.
We are given:
- Potential energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Acceleration due to gravity (g) = 9.8 meters per second squared
We need to find the mass (m) of the roller coaster.
The formula for potential energy is:
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
We can rearrange this formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
1. Substitute the known values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
2. First, calculate the denominator:
[tex]\[ g \cdot h = 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} = 294 \, \text{m} \cdot \text{m/s}^2 \][/tex]
3. Now, divide the potential energy by the result from step 2:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m} \cdot \text{m/s}^2} \][/tex]
4. Perform the division to find the mass:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\(\boxed{800 \, \text{kg}}\)[/tex].
We are given:
- Potential energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Acceleration due to gravity (g) = 9.8 meters per second squared
We need to find the mass (m) of the roller coaster.
The formula for potential energy is:
[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]
We can rearrange this formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]
1. Substitute the known values into the equation:
[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]
2. First, calculate the denominator:
[tex]\[ g \cdot h = 9.8 \, \text{m/s}^2 \cdot 30 \, \text{m} = 294 \, \text{m} \cdot \text{m/s}^2 \][/tex]
3. Now, divide the potential energy by the result from step 2:
[tex]\[ m = \frac{235,200 \, \text{J}}{294 \, \text{m} \cdot \text{m/s}^2} \][/tex]
4. Perform the division to find the mass:
[tex]\[ m \approx 800 \, \text{kg} \][/tex]
So, the mass of the roller coaster is [tex]\(\boxed{800 \, \text{kg}}\)[/tex].
