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Answer :
To find the mass of the roller coaster, 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.
We need to solve for [tex]$m$[/tex], so we rearrange the formula:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Given:
- [tex]$PE = 235200 \, \text{J}$[/tex],
- [tex]$h = 30 \, \text{m}$[/tex],
- [tex]$g = 9.8 \, \text{m/s}^2$[/tex],
we substitute these values into the equation:
[tex]$$
m = \frac{235200}{9.8 \times 30}
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 30 = 294
$$[/tex]
Now, divide the potential energy by this product:
[tex]$$
m = \frac{235200}{294} = 800 \, \text{kg}
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, \text{kg}}$[/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.
We need to solve for [tex]$m$[/tex], so we rearrange the formula:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Given:
- [tex]$PE = 235200 \, \text{J}$[/tex],
- [tex]$h = 30 \, \text{m}$[/tex],
- [tex]$g = 9.8 \, \text{m/s}^2$[/tex],
we substitute these values into the equation:
[tex]$$
m = \frac{235200}{9.8 \times 30}
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 30 = 294
$$[/tex]
Now, divide the potential energy by this product:
[tex]$$
m = \frac{235200}{294} = 800 \, \text{kg}
$$[/tex]
Thus, the mass of the roller coaster is [tex]$\boxed{800 \, \text{kg}}$[/tex].
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