Answer :
The potential energy of an object at a height is given by the 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.
We want to solve for the mass [tex]\(m\)[/tex]. Rearranging the formula, we have
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Given that the potential energy [tex]\(PE = 235200 \, J\)[/tex], the height [tex]\(h = 30 \, m\)[/tex], and taking the gravitational acceleration as [tex]\(g = 9.8 \, m/s^2\)[/tex], substitute these values into the formula:
[tex]$$
m = \frac{235200}{9.8 \times 30}.
$$[/tex]
First, calculate the product [tex]\(9.8 \times 30\)[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, divide the potential energy by this product:
[tex]$$
m = \frac{235200}{294} = 800.
$$[/tex]
Thus, the mass of the roller coaster is
[tex]$$
800 \, \text{kg}.
$$[/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 want to solve for the mass [tex]\(m\)[/tex]. Rearranging the formula, we have
[tex]$$
m = \frac{PE}{gh}.
$$[/tex]
Given that the potential energy [tex]\(PE = 235200 \, J\)[/tex], the height [tex]\(h = 30 \, m\)[/tex], and taking the gravitational acceleration as [tex]\(g = 9.8 \, m/s^2\)[/tex], substitute these values into the formula:
[tex]$$
m = \frac{235200}{9.8 \times 30}.
$$[/tex]
First, calculate the product [tex]\(9.8 \times 30\)[/tex]:
[tex]$$
9.8 \times 30 = 294.
$$[/tex]
Now, divide the potential energy by this product:
[tex]$$
m = \frac{235200}{294} = 800.
$$[/tex]
Thus, the mass of the roller coaster is
[tex]$$
800 \, \text{kg}.
$$[/tex]
