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.
Given:
\( PE = 235200 \, \text{J} \)
\( h = 30 \, \text{m} \)
\( g = 9.8 \, \text{m/s}^2 \)
We rearrange the formula to solve for mass \( m \):
$$
m = \frac{PE}{gh}
$$
Plug in the values:
$$
m = \frac{235200}{9.8 \times 30}
$$
First, calculate the denominator:
$$
9.8 \times 30 = 294
$$
Now, divide to find \( m \):
$$
m = \frac{235200}{294} = 800 \, \text{kg}
$$
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.
Given:
\( PE = 235200 \, \text{J} \)
\( h = 30 \, \text{m} \)
\( g = 9.8 \, \text{m/s}^2 \)
We rearrange the formula to solve for mass \( m \):
$$
m = \frac{PE}{gh}
$$
Plug in the values:
$$
m = \frac{235200}{9.8 \times 30}
$$
First, calculate the denominator:
$$
9.8 \times 30 = 294
$$
Now, divide to find \( m \):
$$
m = \frac{235200}{294} = 800 \, \text{kg}
$$
Thus, the mass of the roller coaster is \( \boxed{800 \, \text{kg}} \).
