College

A roller coaster with a potential energy of [tex]$235,200 \, \text{J}$[/tex] sits at the top of a 30 m high hill. What is the mass of the roller coaster?

(Formula: [tex]PE = mgh[/tex])

A. 800 kg
B. 7,840 kg
C. 8,000 kg
D. 78,400 kg

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 $\boxed{800 \text{ kg}}$.