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Answer :
We start with the formula for gravitational potential energy:
[tex]$$
\text{PE} = mgh,
$$[/tex]
where
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height.
Given that the potential energy is [tex]$235200\,J$[/tex], the height is [tex]$30\,m$[/tex], and the gravitational acceleration is [tex]$9.8\,m/s^2$[/tex], we substitute these values into the equation:
[tex]$$
235200 = m \times 9.8 \times 30.
$$[/tex]
First, calculate the product of [tex]$g$[/tex] and [tex]$h$[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, solve for [tex]$m$[/tex] by dividing both sides of the equation by [tex]$294$[/tex]:
[tex]$$
m = \frac{235200}{294}.
$$[/tex]
Performing the division gives:
[tex]$$
m = 800.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$800\,\text{kg}$[/tex].
[tex]$$
\text{PE} = mgh,
$$[/tex]
where
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height.
Given that the potential energy is [tex]$235200\,J$[/tex], the height is [tex]$30\,m$[/tex], and the gravitational acceleration is [tex]$9.8\,m/s^2$[/tex], we substitute these values into the equation:
[tex]$$
235200 = m \times 9.8 \times 30.
$$[/tex]
First, calculate the product of [tex]$g$[/tex] and [tex]$h$[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, solve for [tex]$m$[/tex] by dividing both sides of the equation by [tex]$294$[/tex]:
[tex]$$
m = \frac{235200}{294}.
$$[/tex]
Performing the division gives:
[tex]$$
m = 800.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$800\,\text{kg}$[/tex].
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