3.2 Net Work and Kinetic Energy

Combining Newton’s second law with kinematics for straight-line motion leads to a compact result: net work over a displacement equals the change in kinetic energy. This is not a new law separate from dynamics; it is a repackaging of dynamics that is often easier to apply across finite intervals.

Because only net work appears, multiple forces can be aggregated. A positive pull and negative friction may partially cancel, and the final speed reflects their signed total. This is especially useful in multi-force situations where a full time-based acceleration solution is cumbersome.

Near Earth’s surface, work by gravity depends only on vertical displacement. Horizontal motion contributes nothing to gravity’s work because gravity is perpendicular to that displacement. This is the first hint of path independence and potential energy.

So if two different paths start and end at the same height, gravity does the same work on each path. Path details can still matter for frictional losses, but not for gravitational work itself in this approximation.

The textbook distinguishes two related but different equations. The work-kinetic energy relation tracks how all forces together change kinetic energy: W_net = ΔE_k. A second relation tracks how surroundings change total mechanical energy of a chosen system: ΔE_T = W_ext (for this chapter, with no heat transfer term). Confusing them causes sign errors and missing terms.

Example: for a sliding block treated as the system, friction from the floor is external and can reduce E_T. But if you choose a wider system and track thermal energy as well, total energy remains conserved; only the distribution among stores changes. This viewpoint connects the chapter’s mechanical-energy model to the broader conservation law used later in thermal, electrical, and nuclear contexts.