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Answer :
- The problem provides the potential energy (PE), height (h), and gravity (g) and asks for the mass (m).
- The formula PE = mgh is rearranged to solve for m: $m = \frac{PE}{gh}$.
- Substitute the given values: $m = \frac{235200}{9.8 \times 30}$.
- Calculate the mass: $m = 800 kg$. The final answer is $\boxed{800 kg}$.
### Explanation
1. Understanding the Problem
We are given the potential energy (PE) of a roller coaster, its height (h), and the acceleration due to gravity (g). We need to find the mass (m) of the roller coaster. The formula relating these quantities is PE = mgh.
2. Rearranging the Formula
We need to rearrange the formula to solve for the mass (m). Dividing both sides of the equation PE = mgh by (gh), we get: m = PE / (gh)
3. Substituting the Values
Now, we substitute the given values into the formula: PE = 235,200 J, g = 9.8 m/s², and h = 30 m. m = 235,200 J / (9.8 m/s² * 30 m)
4. Calculating the Mass
Calculating the mass: m = 235,200 / (9.8 * 30) = 235,200 / 294 = 800 kg
5. Final Answer
Therefore, the mass of the roller coaster is 800 kg.
### Examples
Understanding potential energy and how it relates to mass and height is crucial in designing roller coasters. Engineers use these principles to ensure the roller coaster has enough energy to complete the ride safely. For example, knowing the mass of the train and the height of the hills allows them to calculate the potential and kinetic energy at various points, ensuring the ride maintains sufficient speed and doesn't stall or become unsafe.
- The formula PE = mgh is rearranged to solve for m: $m = \frac{PE}{gh}$.
- Substitute the given values: $m = \frac{235200}{9.8 \times 30}$.
- Calculate the mass: $m = 800 kg$. The final answer is $\boxed{800 kg}$.
### Explanation
1. Understanding the Problem
We are given the potential energy (PE) of a roller coaster, its height (h), and the acceleration due to gravity (g). We need to find the mass (m) of the roller coaster. The formula relating these quantities is PE = mgh.
2. Rearranging the Formula
We need to rearrange the formula to solve for the mass (m). Dividing both sides of the equation PE = mgh by (gh), we get: m = PE / (gh)
3. Substituting the Values
Now, we substitute the given values into the formula: PE = 235,200 J, g = 9.8 m/s², and h = 30 m. m = 235,200 J / (9.8 m/s² * 30 m)
4. Calculating the Mass
Calculating the mass: m = 235,200 / (9.8 * 30) = 235,200 / 294 = 800 kg
5. Final Answer
Therefore, the mass of the roller coaster is 800 kg.
### Examples
Understanding potential energy and how it relates to mass and height is crucial in designing roller coasters. Engineers use these principles to ensure the roller coaster has enough energy to complete the ride safely. For example, knowing the mass of the train and the height of the hills allows them to calculate the potential and kinetic energy at various points, ensuring the ride maintains sufficient speed and doesn't stall or become unsafe.
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