Question

complete these sentences.
if a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy is
once the roller coaster train gets closer to the bottom of the hill, its kinetic energy increases to 1,100 j, and its potential energy decreases to
when the train reaches the bottom of the track and is traveling along the ground, its kinetic energy is

Explanation:

Step1: Calculate the total energy at the start

The total mechanical energy \(E\) of a system is the sum of kinetic energy \(K\) and potential energy \(U\). So, \(E = K+U\).
Given \(K = 500\space J\) and \(U=1500\space J\), then \(E=500 + 1500=2000\space J\)

Step2: Find the potential energy when kinetic energy is \(1100\space J\)

Since the total energy \(E = 2000\space J\) (conservation of mechanical energy, assuming no non - conservative forces like friction for simplicity) and \(K = 1100\space J\), then \(U=E - K\)
\(U=2000-1100 = 900\space J\)

Step3: Determine the kinetic energy at the bottom

At the bottom of the track (ground level), the potential energy \(U = 0\space J\) (taking ground level as the zero - potential level). Since \(E=K + U\) and \(E = 2000\space J\), \(U = 0\space J\), then \(K=E\)
\(K = 2000\space J\)

Answer:

The total energy is \(2000\space J\), the potential energy is \(900\space J\), and the kinetic energy at the bottom is \(2000\space J\)