High School

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 :

We start with the formula for gravitational potential energy:

[tex]$$
PE = mgh
$$[/tex]

where
[tex]\( PE \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the acceleration due to gravity, and
[tex]\( h \)[/tex] is the height.

Given [tex]\( PE = 235\,200\,J \)[/tex], [tex]\( g = 9.8\,m/s^2 \)[/tex], and [tex]\( h = 30\,m \)[/tex], we solve for [tex]\( m \)[/tex]:

[tex]$$
m = \frac{PE}{gh}
$$[/tex]

Substitute the given values:

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

First, calculate the denominator:

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

Now, divide the potential energy by this product:

[tex]$$
m = \frac{235\,200}{294} = 800
$$[/tex]

Thus, the mass of the roller coaster is [tex]\( 800\,kg \)[/tex].

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