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].
[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].