Answer :
We start with the formula for potential energy:
[tex]$$
PE = m \cdot g \cdot h
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height.
Given the values:
- [tex]$PE = 235\,200 \,J$[/tex],
- [tex]$g = 9.8 \,m/s^2$[/tex], and
- [tex]$h = 30 \,m$[/tex],
we substitute these values into the equation:
[tex]$$
235\,200 = m \cdot 9.8 \cdot 30.
$$[/tex]
First, calculate the product [tex]$g \cdot h$[/tex]:
[tex]$$
9.8 \cdot 30 = 294.
$$[/tex]
Now, the equation simplifies to:
[tex]$$
235\,200 = m \cdot 294.
$$[/tex]
To solve for [tex]$m$[/tex], divide both sides by [tex]$294$[/tex]:
[tex]$$
m = \frac{235\,200}{294}.
$$[/tex]
Performing the division:
[tex]$$
m = 800.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800\, \text{kg}}$[/tex].
[tex]$$
PE = m \cdot g \cdot h
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height.
Given the values:
- [tex]$PE = 235\,200 \,J$[/tex],
- [tex]$g = 9.8 \,m/s^2$[/tex], and
- [tex]$h = 30 \,m$[/tex],
we substitute these values into the equation:
[tex]$$
235\,200 = m \cdot 9.8 \cdot 30.
$$[/tex]
First, calculate the product [tex]$g \cdot h$[/tex]:
[tex]$$
9.8 \cdot 30 = 294.
$$[/tex]
Now, the equation simplifies to:
[tex]$$
235\,200 = m \cdot 294.
$$[/tex]
To solve for [tex]$m$[/tex], divide both sides by [tex]$294$[/tex]:
[tex]$$
m = \frac{235\,200}{294}.
$$[/tex]
Performing the division:
[tex]$$
m = 800.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800\, \text{kg}}$[/tex].
