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 find the mass of the roller coaster, we start with the formula for gravitational potential energy:

[tex]$$
PE = mgh
$$[/tex]

where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height.

We need to solve for [tex]$m$[/tex], so we rearrange the formula:

[tex]$$
m = \frac{PE}{gh}
$$[/tex]

Given:
- [tex]$PE = 235200 \, \text{J}$[/tex],
- [tex]$h = 30 \, \text{m}$[/tex],
- [tex]$g = 9.8 \, \text{m/s}^2$[/tex],

we substitute these values into the equation:

[tex]$$
m = \frac{235200}{9.8 \times 30}
$$[/tex]

First, calculate the product in the denominator:

[tex]$$
9.8 \times 30 = 294
$$[/tex]

Now, divide the potential energy by this product:

[tex]$$
m = \frac{235200}{294} = 800 \, \text{kg}
$$[/tex]

Thus, the mass of the roller coaster is [tex]$\boxed{800 \, \text{kg}}$[/tex].

Other Questions