Final answer:
The boulder undergoes a transformation from gravitational potential energy to kinetic energy while rolling down the mountain and the reverse as it ascends the opposite slope. Friction converts some of its kinetic energy into thermal energy, preventing the boulder from reaching its original height.
Step-by-step explanation:
Energy Transformations of a Rolling Boulder
When a boulder rolls down from the top of a mountain and travels across a valley before rolling partway up an opposite ridge, several energy transformations occur. Initially, the boulder possesses high gravitational potential energy (PE) due to its elevated position. As the boulder rolls down the mountain, this potential energy is converted into kinetic energy (KE), which is the energy of motion.
Upon reaching the valley below, the boulder's kinetic energy is at its maximum because it has descended from its highest potential energy position. As the boulder begins to ascend the opposite slope, its kinetic energy is again converted back into gravitational potential energy. However, the boulder does not reach its original height because some energy is lost due to friction. This friction converts part of the boulder's kinetic energy into thermal energy, which is dissipated into the environment, thus reducing the boulder's ability to climb to an equivalent height from which it originally fell.
The entire process demonstrates the conservation of energy, where energy is neither created nor destroyed but transformed from one form to another. The principal energy conversions are potential energy to kinetic energy as the boulder descends, and kinetic energy to potential energy as it ascends. The energy lost to friction as thermal energy results in the boulder not reaching the same height on the opposite side.