College

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 :

To find the mass of the roller coaster, we'll use the formula for potential energy, which is:

[tex]\[ \text{PE} = m \cdot g \cdot h \][/tex]

where:
- [tex]\(\text{PE}\)[/tex] is the potential energy, which is given as 235,200 J (Joules).
- [tex]\(m\)[/tex] is the mass of the roller coaster, which we need to find.
- [tex]\(g\)[/tex] is the acceleration due to gravity, approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex].
- [tex]\(h\)[/tex] is the height of the hill, given as 30 meters.

The formula can be rearranged to solve for mass ([tex]\(m\)[/tex]):

[tex]\[ m = \frac{\text{PE}}{g \cdot h} \][/tex]

By substituting the given values into the equation, we have:

[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \cdot 30 \, \text{m}} \][/tex]

Calculating this gives:

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

[tex]\[ m \approx 800 \, \text{kg} \][/tex]

So, the mass of the roller coaster is approximately [tex]\(800 \, \text{kg}\)[/tex].