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Answer :
To solve for the mass of the roller coaster, we start with the formula for gravitational potential energy:
$$
PE = mgh
$$
where
- $PE$ is the potential energy,
- $m$ is the mass,
- $g$ is the acceleration due to gravity, and
- $h$ is the height.
We are given:
$$
PE = 235,200 \text{ J}, \quad h = 30 \text{ m}, \quad g = 9.8 \text{ m/s}^2.
$$
The equation can be rearranged to solve for the mass $m$:
$$
m = \frac{PE}{gh}.
$$
Now, substitute the given values into the equation:
$$
m = \frac{235,200}{9.8 \times 30}.
$$
First, calculate 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 $\boxed{800 \text{ kg}}$.
$$
PE = mgh
$$
where
- $PE$ is the potential energy,
- $m$ is the mass,
- $g$ is the acceleration due to gravity, and
- $h$ is the height.
We are given:
$$
PE = 235,200 \text{ J}, \quad h = 30 \text{ m}, \quad g = 9.8 \text{ m/s}^2.
$$
The equation can be rearranged to solve for the mass $m$:
$$
m = \frac{PE}{gh}.
$$
Now, substitute the given values into the equation:
$$
m = \frac{235,200}{9.8 \times 30}.
$$
First, calculate 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 $\boxed{800 \text{ kg}}$.
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