Recovered transmission / 00:17:42
The conveyor did not fail all at once. It paused, followed the belt, then tore free from it again. The transfer route to the engine room is still open, but only if I can tell which part of its motion is a promise and which part is only a momentary habit.
This archive is the working record behind Chapter I — The Failing Conveyor. It is not a list of answers. It is a way to turn a machine’s motion into a conclusion that can survive the next trial.
Log — Describe before explaining
Run the conveyor with its default settings. Do not adjust a control for the first two cycles.
- Sketch the position–time trace.
- Mark every change in the phase label.
- Write a prediction for the force that causes each transition.
“The trace changes slope” is an observation. “Friction disappeared” is an explanation. Do not let the second sentence replace the first.
Problem — Build a force model
The spring force grows as the cargo sled is pulled away from its natural length. While the sled sticks to the belt, static friction changes as needed to match the belt velocity. That arrangement has a boundary:
When this inequality no longer holds, record the time, the phase label and the shape of the trace. Explain why the sled must then move relative to the belt.
Experiment — Change one condition at a time
Investigate the kinetic-friction coefficient . Keep spring constant, mass, belt speed and friction ratio fixed. Run at least five trials.
For each trial, record , the phase sequence, approximate time spent sticking, and one statement supported by the graph. Then repeat using a different belt speed. Which part of your original conclusion remains true?
| Trial | Belt speed | Phase sequence | Observation | Claim and its condition | |
|---|---|---|---|---|---|
| 1 | |||||
| 2 | |||||
| 3 |
Model — Test the SHM claim
Set . The formula panel now identifies a fixed equilibrium at the spring’s natural length. Compare that trace with one from a non-zero-friction trial.
During sliding, if the sign of relative velocity remains unchanged, kinetic friction has constant magnitude. The equation can then be expressed about one shifted equilibrium. This is a local SHM description, not a description of the whole journey. When the relative-velocity sign changes or the sled sticks, the equilibrium changes and that conclusion ends.
Write the strongest accurate version of the claim: “The motion is simple harmonic while …”
Decision — Permit or abort the transfer
The ship log needs a decision, not a slogan. State the physical conditions under which the conveyor’s next segment of motion is predictable enough to use. Then find a parameter setting that violates one of those conditions.
If you cannot state the boundary of your conclusion, you do not yet know whether the transfer is safe.
What remains unknown?
The model assumes constant belt speed, an ideal spring, one-dimensional motion, and perfectly inelastic wall collisions. Which assumption would you test first on the real conveyor? What observation could prove that the simulation has stopped being a useful guide?