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]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 can use the formula for potential energy:

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

where:
- [tex]\( PE \)[/tex] is the potential energy (235,200 Joules),
- [tex]\( m \)[/tex] is the mass of the roller coaster (our unknown),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height (30 meters).

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

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

Now, we plug in the values:

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

When you calculate this, you get:

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

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

So, the mass of the roller coaster is 800 kg.