Question

a roller coaster with a potential energy of 235,200 j sits at the top of a 30 m high hill. what is the mass of the roller coaster? (formula: pe = mgh)
800 kg
7,840 kg
8,000 kg
78,400 kg

Explanation:

Step1: Recall the potential energy formula

The formula for gravitational potential energy is \( PE = mgh \), where \( PE \) is potential energy, \( m \) is mass, \( g \) is the acceleration due to gravity (we use \( g = 9.8 \, \text{m/s}^2 \) for Earth's surface), and \( h \) is height. We need to solve for \( m \), so we rearrange the formula to \( m=\frac{PE}{gh} \).

Step2: Identify the given values

We know that \( PE = 235200 \, \text{J} \), \( h = 30 \, \text{m} \), and \( g = 9.8 \, \text{m/s}^2 \).

Step3: Substitute the values into the formula

Substitute \( PE = 235200 \), \( g = 9.8 \), and \( h = 30 \) into \( m=\frac{PE}{gh} \):
\[
m=\frac{235200}{9.8\times30}
\]

Step4: Calculate the denominator first

Calculate \( 9.8\times30 = 294 \).

Step5: Divide to find the mass

Now divide \( 235200 \) by \( 294 \):
\[
m=\frac{235200}{294}=800
\]

Answer:

800 kg (corresponding to the first option: 800 kg)