Question

this image of a roller coaster is designed to show important information about potential and kinetic energy. one of these labeled pieces of information is incorrect. which information is wrong, and why?

Explanation:

Step1: Recall energy concepts

Gravitational potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). Kinetic energy \(K=\frac{1}{2}mv^{2}\) (where \(v\) is velocity). At the highest point of the roller - coaster, \(h\) is maximum, so \(U\) is maximum (correct as labeled). As the roller - coaster descends, \(h\) decreases, \(v\) increases (so \(K\) increases and \(U\) decreases). At the lowest point of the track (not the point labeled “gravitational potential energy and kinetic energy”), \(h\) is minimum (so \(U\) is minimum) and \(v\) is maximum (so \(K\) is maximum).

Step2: Analyze the incorrect label

The label “gravitational potential energy and kinetic energy” is wrong. At the point where it is labeled, it should be either mainly kinetic (if it's near the bottom of a descent) or mainly potential (if it's near a peak). But the maximum kinetic energy occurs at the lowest point of the roller - coaster track (where the height \(h\) is minimum).

Answer:

The label “gravitational potential energy and kinetic energy” is incorrect. Maximum kinetic energy occurs at the lowest point of the roller - coaster (where height \(h\) is minimum, so gravitational potential energy \(U = mgh\) is minimum and kinetic energy \(K=\frac{1}{2}mv^{2}\) is maximum due to maximum speed \(v\)).