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]$8,000 \, \text{kg}$[/tex]
D. [tex]$78,400 \, \text{kg}$[/tex]

Answer :

To find the mass of the roller coaster using the potential energy formula, we can follow these steps:

1. Identify the given values:

- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravitational acceleration (g) = [tex]\(9.81 \, \text{m/s}^2\)[/tex] (standard acceleration due to gravity)

2. Use the potential energy formula:

[tex]\[
\text{Potential Energy (PE)} = m \times g \times h
\][/tex]

where [tex]\(m\)[/tex] is the mass we want to find.

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

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

4. Plug in the known values:

[tex]\[
m = \frac{235,200}{9.81 \times 30}
\][/tex]

5. Calculate to find the mass:

To solve this, you divide 235,200 by the product of 9.81 and 30, which gives you approximately 799.18 kg.

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