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Answer :
We start with 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.
Since we need to find the mass [tex]$m$[/tex], we rearrange the formula:
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Given:
- [tex]$PE = 235200 \, J$[/tex],
- [tex]$h = 30 \, m$[/tex], and
- [tex]$g = 9.8 \, m/s^2$[/tex] (standard value for the acceleration due to gravity on Earth),
we substitute these values in:
[tex]$$
m = \frac{235200}{9.8 \times 30}.
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, substitute back into the equation:
[tex]$$
m = \frac{235200}{294}.
$$[/tex]
Performing the division:
[tex]$$
m = 800 \, kg.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, kg}$[/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.
Since we need to find the mass [tex]$m$[/tex], we rearrange the formula:
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Given:
- [tex]$PE = 235200 \, J$[/tex],
- [tex]$h = 30 \, m$[/tex], and
- [tex]$g = 9.8 \, m/s^2$[/tex] (standard value for the acceleration due to gravity on Earth),
we substitute these values in:
[tex]$$
m = \frac{235200}{9.8 \times 30}.
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, substitute back into the equation:
[tex]$$
m = \frac{235200}{294}.
$$[/tex]
Performing the division:
[tex]$$
m = 800 \, kg.
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, kg}$[/tex].
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