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

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

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

Substitute the given values into the formula:

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

Now, calculate the denominator:

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

Substitute back to solve for [tex]\( m \)[/tex]:

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

Upon performing the division, we find:

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

Therefore, the mass of the roller coaster is [tex]\( 800 \, \text{kg} \)[/tex].

So, the correct answer is [tex]\( \boxed{800 \, \text{kg}} \)[/tex].

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