Chapter 4.3, Problem 31R

To determine

To Find: The hill, on top of which thekinetic energy isgreater for a roller coaster rolling from the top of a hill to the top of a lower hill, considering mechanical energy is constant.

Explanation of Solution

Introduction:Mechanical energyis the sum of the kinetic energy and potential energy of the objects in a system.

Mechanical energyis the summation of the kinetic energy and potential energy of the object.

For a roller coaster rolling from the top of a hill to the top of a lower hill, the roller coaster possesses both potential energies due to its height and kinetic energy due to its motion. At the top of the higher hill, the potential energy is greater than the potential energy at the top of the lower hill due to the greater height.

Consideringthe mechanical energy of the system is constant, the kinetic energy of the roller coaster at the top of the higher hill will be less than that at the top of the lower hill.

Conclusion: Kinetic energy of the roller coaster is greater at the top of the lower hill.