Question

If an 600 kg roller coaster is at the top of its 60 m high track, it will have a potential energy 352,800 J and a kinetic energy of 0J. This means the mechanical energy is 352,800 J. If the cart drops to a new height 20m, how much kinetic energy does the have now?

Answer 1

In order to determine the kinetic energy of the roller coaster at a height of 20m, take into account that the mechanical energy is constant.

Then, when the roller coaster is at 20m, the sum of the potential energy and the kinetic energy must be equal to 352,800J.

Find the potential energy by using the following formula:

`U=m\cdot g\cdot h`

where,

m: mass = 600kg

g: gravitational acceleration constant = 9.8m/s62

h: height = 20m

Replace the previous values into the formula for U:

`U=(600kg)(9.8(m)/(s^2))(20m)=117600J`

Now, use the following expression for the mechanical energy:

`E=U+K`

where,

E: mechanical energy = 352,800J

U: potential energy = 117,600J

K: kinetic energy = ?

Solve the equation above for K, replace the values of E and U, and simplify:

`\begin{gathered} K=E-U \\ K=352800J-117600J=235200J \end{gathered}`

Hence, the kinetic energy of the roller coaster at 20m is 235,200J