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 can use the formula for potential energy:

[tex]\[ PE = m \cdot g \cdot h \][/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 [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height.

We're given:
- [tex]\( PE = 235,200 \, \text{J} \)[/tex],
- [tex]\( h = 30 \, \text{m} \)[/tex],
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].

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

1. Rearrange the formula to solve for [tex]\( m \)[/tex]:

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

2. Plug in the known values:

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

3. Calculate the denominator:

[tex]\[ 9.8 \cdot 30 = 294 \][/tex]

4. Divide the potential energy by the result from step 3 to find the mass:

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

5. Perform the division:

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

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