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 = m g h[/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 use the formula for potential energy (PE):

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

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

We need to solve for [tex]\(m\)[/tex], the mass. Rearrange the formula to solve for [tex]\(m\)[/tex]:

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

Now, substitute the given values into the equation:

[tex]\[ m = \frac{235,200}{9.8 \times 30} \][/tex]

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

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

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