Answer :
We are given the potential energy formula:
[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 that
[tex]\( PE = 235\,200 \, \text{J} \)[/tex],
[tex]\( h = 30 \, \text{m} \)[/tex], and
[tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex],
we need to solve for [tex]\( m \)[/tex]. Rearranging the formula gives:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Substitute the known values into the equation:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}
$$[/tex]
First, evaluate the denominator:
[tex]$$
9.8 \times 30 = 294
$$[/tex]
Now, divide the potential energy by the result:
[tex]$$
m = \frac{235\,200}{294} = 800 \, \text{kg}
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, \text{kg}}$[/tex].
[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 that
[tex]\( PE = 235\,200 \, \text{J} \)[/tex],
[tex]\( h = 30 \, \text{m} \)[/tex], and
[tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex],
we need to solve for [tex]\( m \)[/tex]. Rearranging the formula gives:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Substitute the known values into the equation:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}
$$[/tex]
First, evaluate the denominator:
[tex]$$
9.8 \times 30 = 294
$$[/tex]
Now, divide the potential energy by the result:
[tex]$$
m = \frac{235\,200}{294} = 800 \, \text{kg}
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, \text{kg}}$[/tex].
