Energy conservation with friction losses

Steps:

• Trolley starts at X with gravitational potential energy (PE); no initial kinetic energy (KE).
• From X to Y (downhill): PE converts to KE, but friction generates heat, reducing total mechanical energy.
• From Y to Z (uphill): KE converts back to PE, with additional heat from friction causing it to stop short.
• At Z: All mechanical energy dissipated as heat; final PE is less than initial due to total heat loss.

Why D is correct:

• D reflects the law of conservation of energy: total energy (PE + KE + heat) remains constant, with mechanical energy (PE + KE) decreasing to heat in both segments.

Why the others are wrong:

• A: Assumes no friction, violating energy conservation in real systems with losses.
• B: Misrepresents initial energies and omits PE recovery or full heat accounting.
• C: Includes heat only in first segment, ignoring friction losses during uphill motion.

Final answer: D