High School

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]P E = m g h[/tex])

A. 800 kg
B. 7840 kg
C. 8000 kg
D. 78,400 kg

Answer :

To find the mass of the roller coaster, we can use the formula for potential energy:

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

where:
- [tex]\( PE \)[/tex] is the potential energy, given as 235,200 Joules,
- [tex]\( m \)[/tex] is the mass (which we are trying to find),
- [tex]\( g \)[/tex] is the acceleration due to gravity, which is approximately 9.8 m/s²,
- [tex]\( h \)[/tex] is the height, given as 30 meters.

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

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

Now, substitute the given values into the formula:

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

Calculating this, we get:

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

[tex]\[ m = 800 \][/tex]

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

Therefore, the correct answer is 800 kg.