Conservation of mechanical energy (ideal case) For an isolated system of moving bodies where only conservative internal forces act (no external work or dissipation), the total mechanical energy of the system:

Introduction / Context:Conservation laws are pillars of mechanics. The total mechanical energy (kinetic + potential) of an isolated system remains constant when only conservative forces (like gravity or ideal springs) act and when non-conservative effects (like friction) are absent.

Given Data / Assumptions:

• System is isolated (no external work input/output).
• Only conservative internal forces are present.
• No energy losses due to friction, air drag, plastic deformation, or heat.

Concept / Approach:Total mechanical energy E is defined as E = K + U, where K is total kinetic energy and U is total potential energy. For conservative forces, work done equals the negative change in potential energy. The work–energy principle and path independence lead to constant E for the entire system.

Step-by-Step Solution:

Verification / Alternative check:Consider two masses connected by an ideal spring on a frictionless surface. As one mass speeds up and the other slows down, K changes, the spring stores/releases U, yet K + U remains constant, validating the principle.

Why Other Options Are Wrong:

• Varies from point to point / Max–min claims: These describe non-conservative scenarios or arbitrary stages; in the ideal conservative case, total energy does not systematically increase or decrease.
• Depends only on mass: Energy depends on both configuration (potential) and motion (kinetic), not mass alone.

Common Pitfalls:Applying energy conservation without checking for non-conservative forces. Always verify isolation and absence of losses before using E = constant.

Final Answer:is constant at every instant