Answer :
We are given the potential energy formula
[tex]$$
PE = m g h,
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass of the roller coaster,
- [tex]$g$[/tex] is the acceleration due to gravity (approximately [tex]$9.8 \, \text{m/s}^2$[/tex]), and
- [tex]$h$[/tex] is the height of the hill.
The problem provides:
- [tex]$PE = 235\,200 \, \text{J}$[/tex],
- [tex]$h = 30 \, \text{m}$[/tex],
- [tex]$g = 9.8 \, \text{m/s}^2$[/tex].
We need to find the mass [tex]$m$[/tex]. Rearranging the formula for [tex]$m$[/tex], we have
[tex]$$
m = \frac{PE}{g \cdot h}.
$$[/tex]
Substitute the given values:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}.
$$[/tex]
First, calculate the product [tex]$g \cdot h$[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, substitute back into the equation:
[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]$$
PE = m g h,
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass of the roller coaster,
- [tex]$g$[/tex] is the acceleration due to gravity (approximately [tex]$9.8 \, \text{m/s}^2$[/tex]), and
- [tex]$h$[/tex] is the height of the hill.
The problem provides:
- [tex]$PE = 235\,200 \, \text{J}$[/tex],
- [tex]$h = 30 \, \text{m}$[/tex],
- [tex]$g = 9.8 \, \text{m/s}^2$[/tex].
We need to find the mass [tex]$m$[/tex]. Rearranging the formula for [tex]$m$[/tex], we have
[tex]$$
m = \frac{PE}{g \cdot h}.
$$[/tex]
Substitute the given values:
[tex]$$
m = \frac{235\,200}{9.8 \times 30}.
$$[/tex]
First, calculate the product [tex]$g \cdot h$[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, substitute back into the equation:
[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].
