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Answer :
We start with the formula for potential energy:
$$
PE = m \cdot g \cdot h,
$$
where
- $PE$ is the potential energy,
- $m$ is the mass,
- $g$ is the acceleration due to gravity, and
- $h$ is the height.
Given:
- $PE = 235\,200 \, J$,
- $g = 9.8 \, m/s^2$, and
- $h = 30 \, m$.
We need to find the mass $m$. Rearranging the formula for $m$ gives:
$$
m = \frac{PE}{g \cdot h}.
$$
Substitute the given values:
$$
m = \frac{235\,200}{9.8 \times 30}.
$$
First, calculate the product in the denominator:
$$
9.8 \times 30 = 294.
$$
Then, compute the mass:
$$
m = \frac{235\,200}{294} = 800 \, \text{kg}.
$$
Thus, the mass of the roller coaster is $\boxed{800 \, kg}$.
$$
PE = m \cdot g \cdot h,
$$
where
- $PE$ is the potential energy,
- $m$ is the mass,
- $g$ is the acceleration due to gravity, and
- $h$ is the height.
Given:
- $PE = 235\,200 \, J$,
- $g = 9.8 \, m/s^2$, and
- $h = 30 \, m$.
We need to find the mass $m$. Rearranging the formula for $m$ gives:
$$
m = \frac{PE}{g \cdot h}.
$$
Substitute the given values:
$$
m = \frac{235\,200}{9.8 \times 30}.
$$
First, calculate the product in the denominator:
$$
9.8 \times 30 = 294.
$$
Then, compute the mass:
$$
m = \frac{235\,200}{294} = 800 \, \text{kg}.
$$
Thus, the mass of the roller coaster is $\boxed{800 \, kg}$.
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