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. [tex]8,000 kg[/tex]
D. [tex]78,400 kg[/tex]

Answer :

To solve this problem, we're looking to find the mass of the roller coaster using the formula for potential energy, given by:

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

Where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²), and
- [tex]\( h \)[/tex] is the height of the hill.

We're given:
- [tex]\( PE = 235,200 \)[/tex] Joules,
- [tex]\( h = 30 \)[/tex] meters.

To find the mass [tex]\( m \)[/tex], we need to rearrange the formula:

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

Now, plug in the values:

1. Use the given potential energy: [tex]\( 235,200 \)[/tex] Joules.
2. Use the standard acceleration due to gravity: [tex]\( 9.8 \)[/tex] m/s².
3. Use the height of the hill: [tex]\( 30 \)[/tex] meters.

Calculate:

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

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

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

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