Question

If an 800 kg roller coaster is at the top of its 50 high trackwill have a potential energy 392,000 J and a energy of This means the total mechanical energy is 392,000 the cart drops down to where its kinetic energy is now 92, 000J how high off the ground is the cart now?

Answer 1

Given data:

* The mass of the roller coaster is m = 800 kg.

* The total mechanical energy is E = 392000 J.

* The kinetic energy at the particular height (let h') is K = 92000 J.

Solution:

The potential energy of the roller coaster at h' is,

`\begin{gathered} U=E-K \\ U=392000-92000 \\ U=300000\text{ J} \end{gathered}`

The potential energy in terms of height and mass is,

`U=\text{mgh}`

where g is the acceleration due to gravity,

Substituting the known values,

`\begin{gathered} 300000=800*9.8* h \\ 300000=7840* h \\ h=(300000)/(7840) \\ h=38.3\text{ m} \end{gathered}`

Thus, the height of the roller coaster from the ground is 38.3 meters.