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

In the problem, you are given:
- Potential Energy (PE) = 235,200 Joules
- Height (h) = 30 meters
- Gravity (g) = 9.8 meters per second squared

We need to solve for the mass (m). The formula rearranges to:

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

Now substituting the values:

[tex]\[ m = \frac{235,200 \, \text{J}}{9.8 \, \text{m/s}^2 \times 30 \, \text{m}} \][/tex]

When you calculate this, you find:

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

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

Therefore, the mass of the roller coaster is 800 kg. The correct answer is 800 kg.