In a frictionless system, the sum KE + U is constant. If initial KE + U equals 50 J, what is KE_f + U_f?

In a frictionless system, the sum KE + U is constant. If initial KE + U equals 50 J, what is KE_f + U_f?

• A. 10 J
• B. 50 J
• C. 60 J
• D. 0 J

Answer: (B)

In a frictionless system, mechanical energy is conserved: the sum of kinetic energy and potential energy stays the same because only conservative forces do work. If the initial KE plus U is 50 J, then at any later moment KE_f plus U_f must also be 50 J. The individual values of KE and U can swap between each other as the system evolves (one can increase while the other decreases), but their total remains fixed at 50 J. The other numbers would imply gaining or losing energy, which isn’t possible without non-conservative forces like friction.

In a frictionless system, mechanical energy is conserved: the sum of kinetic energy and potential energy stays the same because only conservative forces do work. If the initial KE plus U is 50 J, then at any later moment KE_f plus U_f must also be 50 J. The individual values of KE and U can swap between each other as the system evolves (one can increase while the other decreases), but their total remains fixed at 50 J. The other numbers would imply gaining or losing energy, which isn’t possible without non-conservative forces like friction.