Question

a roller coaster is very similar to a pendulum in terms of kinetic and potential energy. use the illustration below to answer the question. which letter represents the place where the cars would have the most kinetic energy? a b c d

Explanation:

Kinetic energy (KE) is related to motion, and potential energy (PE) is related to position (height, for a roller coaster). The formula for gravitational potential energy is \( PE = mgh \) (where \( m \) is mass, \( g \) is gravity, \( h \) is height), and kinetic energy is \( KE=\frac{1}{2}mv^{2} \) (where \( v \) is velocity). By the law of conservation of energy, \( PE + KE=\text{constant} \) (ignoring non - conservative forces like friction for this basic analysis). So, when height (\( h \)) is the lowest, potential energy (\( PE \)) is the lowest. Since the total mechanical energy (\( PE + KE \)) is constant, the kinetic energy (\( KE \)) will be the highest at the lowest point. Looking at the roller - coaster diagram, point D is the lowest point among A, B, C, and D. At point A, the roller - coaster is moving up, so it has both KE and PE, but PE is increasing as height increases, so KE is less than at the lowest point. At point B, which is the highest point, the roller - coaster is momentarily at rest (or has very low velocity), so KE is minimum and PE is maximum. At point C, the roller - coaster is moving down from B, so it has more KE than at B but less than at the lowest point. At point D, as it is the lowest, PE is minimum, so KE is maximum.

Answer:

D