Conservation of mechanical energy accounting for frictional work

Steps:

• Initial mechanical energy at P: KE_P + PE_P = 5 kJ + PE_P
• Final mechanical energy at Q: KE_Q + PE_Q, where PE_Q = PE_P - 50 kJ
• Frictional work dissipates 10 kJ, so KE_Q + PE_Q = (KE_P + PE_P) - 10 kJ
• Substitute: KE_Q + (PE_P - 50) = 5 + PE_P - 10; simplify to KE_Q = 45 kJ

Why B is correct:

• Matches the work-energy theorem: change in mechanical energy equals non-conservative work done (-10 kJ).

Why the others are wrong:

• A ignores frictional loss, yielding 5 - 50 = -45 kJ (impossible).
• C subtracts only PE change from initial KE: 5 - 50 + 100? (misapplies conservation).
• D adds frictional work instead of subtracting: 5 - 50 + 10 + 50? (wrong sign).

Final answer: B