What happens if you cut the green rope?

Quick Overview

When the green rope is cut in the setup involving a weight supported by two springs connected in series, the weight surprisingly moves up instead of down.

Key Points: Cutting the green rope causes the weight to move up, contrary to most initial predictions that it would fall or stay the same. The setup involves a weight suspended by two springs connected in series; the green rope is attached to the junction between the two springs. The two other ropes (red and black) connected to the junction are initially slack, carrying no tension. The spring attached to the ceiling (the upper spring) is the one bearing the weight of the object, as the ropes attached to the junction are slack. When the green rope is cut, the tension previously held by the upper spring is instantly transferred to the lower spring, causing the junction point to move upwards, which pulls the weight up slightly. The final resting position of the weight is higher than its initial position because the effective spring constant of the system increases after the slack components are removed.

Context: The video presents a physics demonstration asking observers what will happen to a weight suspended by a system of two springs connected in series, where two additional ropes (one green, one black, and one red) are tied to the junction between the springs. The setup is initially demonstrated, showing the weight hanging, and the reactions of several bystanders are solicited before the experiment is performed using the green rope.

Detailed Analysis

The video explores a counter-intuitive physics problem concerning a weight suspended by two springs connected in series. The system involves a spring attached to a fixed point above, which connects to a junction. From this junction, the weight is suspended by a second spring. Crucially, there are two extra ropes attached at the junction: a black one, which is connected to the lower spring's attachment point, and a red loop attached near the top. The green rope, which is the focus of the question, is also attached to this junction point. Before cutting, the red and black ropes are slack, meaning the entire weight is supported only by the upper spring. When the green rope is cut (0:59), the initial prediction from most onlookers is that the weight will drop or stay the same. However, the actual result is that the weight moves slightly upward (1:04). The explanation provided is that cutting the green rope effectively removes the slack components from the load-bearing path, increasing the system's overall stiffness (or decreasing the effective total stretch). Because the weight was initially supported only by the top spring, removing the green rope (which was attached to a relatively fixed point via the junction) changes the boundary conditions, causing the junction point to snap upward, thus pulling the lower spring—and the weight—to a new, slightly higher equilibrium position.