Not Perpetual Motion: Simple Pulley Test Reveals Overlooked Variable in Gravity-Based Energy Models

This submission presents a simple, easily repeatable pulley-based experiment intended as a screening demonstration for examining how gravitational work is interpreted in coupled-mass systems. The setup consists of two containers connected by a rope running over ceiling-mounted pulleys. One container, initially heavier, is raised to a starting height while the lighter container rests on the floor. When released, the heavier container descends while simultaneously lifting the lighter container through an equivalent vertical distance. The motion is documented in real time in the accompanying video.

In conventional analyses based on the three-dimensional work formulation W=F⋅dW = F \cdot dW=F⋅d, the upward motion of the lighter mass is treated as negative work that subtracts from the energy associated with the descending mass. This approach effectively evaluates the system using net displacement. In the demonstrated configuration, however, both masses undergo full gravitational displacement over the same vertical distance, raising the question of whether net-displacement-only accounting adequately represents the physical interactions involved.

The accompanying documents explore this question conceptually and analytically. They examine why the traditional Atwood-machine expression (m1−m2)gh(m_1 - m_2)gh(m1−m2)gh may fail to describe observed system behavior when both masses experience sustained gravitational interaction over time. The author proposes that slowing a falling mass increases the duration over which gravity acts, and that standard work formulations remove this time dependence by definition rather than by empirical necessity.

This version introduces a hypothetical time-inclusive framework in which gravitational action is expressed as:

A4D=F⋅Σd⋅ΔtA_{4D} = F \cdot \Sigma d \cdot \Delta tA4D=F⋅Σd⋅Δt

where Σd\Sigma dΣd represents the sum of all actual distances moved by system components and Δt\Delta tΔt represents the elapsed interaction time. While gravity is the focus of the present experiments, the formulation is presented as a general expression of force acting over distance and time, and may therefore be applicable to other continuous forces that operate over extended durations. This framework is exploratory and unvalidated, and is introduced to encourage discussion and experimental testing rather than to assert general applicability.

No claim of perpetual motion is made. The materials are provided to invite independent replication, theoretical discussion, and critical evaluation. All prior files remain included for context and continuity.