College

A roller coaster with a potential energy of [tex]$235,200 \, \text{J}$[/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 \, \text{kg}[/tex]
D. [tex]78,400 \, \text{kg}[/tex]

Answer :

Sure! Let's solve the problem of finding the mass of the roller coaster using the given formula for potential energy:

1. Understand the Formula:
The formula for potential energy (PE) is given by:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where [tex]\( PE \)[/tex] is potential energy, [tex]\( m \)[/tex] is mass, [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and [tex]\( h \)[/tex] is height.

2. Identify Given Values:
From the problem, we know:
- [tex]\( PE = 235,200 \, \text{Joules} \)[/tex]
- [tex]\( h = 30 \, \text{meters} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]

3. Rearrange the Formula:
To find the mass [tex]\( m \)[/tex], we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]

4. Substitute the Known Values into the Formula:
[tex]\[
m = \frac{235,200}{9.8 \times 30}
\][/tex]

5. Calculate the Mass:
[tex]\[
m = \frac{235,200}{294} = 800
\][/tex]

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