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A roller coaster with a potential energy of [tex]$235,200 \, J$[/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 :

We start with the formula for potential energy:

[tex]$$
PE = m \cdot g \cdot h
$$[/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.

Given the values:
- [tex]$PE = 235\,200 \,J$[/tex],
- [tex]$g = 9.8 \,m/s^2$[/tex], and
- [tex]$h = 30 \,m$[/tex],

we substitute these values into the equation:

[tex]$$
235\,200 = m \cdot 9.8 \cdot 30.
$$[/tex]

First, calculate the product [tex]$g \cdot h$[/tex]:

[tex]$$
9.8 \cdot 30 = 294.
$$[/tex]

Now, the equation simplifies to:

[tex]$$
235\,200 = m \cdot 294.
$$[/tex]

To solve for [tex]$m$[/tex], divide both sides by [tex]$294$[/tex]:

[tex]$$
m = \frac{235\,200}{294}.
$$[/tex]

Performing the division:

[tex]$$
m = 800.
$$[/tex]

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

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