Question

1. the image below shows a roller coaster ascending the steepest hill of the ride. what is happening to the potential and kinetic energy at this point?

the kinetic energy is increasing, and the potential energy is decreasing.

Explanation:

Step1: Analyze the motion of the roller - coaster

When the roller - coaster is ascending, its height \(h\) is increasing.

Step2: Recall the formulas for kinetic and potential energy

The formula for kinetic energy is \(K=\frac{1}{2}mv^{2}\) (where \(m\) is mass and \(v\) is velocity), and the formula for gravitational potential energy is \(U = mgh\) (where \(g\) is the acceleration due to gravity and \(h\) is height). As the roller - coaster ascends, its velocity \(v\) is decreasing (since it is going against the force of gravity and the motor is doing work to pull it up, but the main point is the motion).

Step3: Determine the change in energies

Since \(v\) is decreasing, from \(K=\frac{1}{2}mv^{2}\), the kinetic energy \(K\) is decreasing. Since \(h\) is increasing, from \(U=mgh\), the potential energy \(U\) is increasing.

Answer:

The kinetic energy is decreasing and the potential energy is increasing.