Two Rubber Bands Hold the Bottle
This is the lesson's own Explore experiment, with the measurements left in. A bottle of water hangs from two identical rubber bands looped over two hooks. Slide the hooks apart and the bottle does not get any heavier — yet both bands stretch further every time. Read the extension against the natural length, read the angle off the protractor, and the tension follows from the elastic law without being assumed.
Como usar esta simulação
- Slide Hooks apart from 4 cm to 26 cm to change the angle without touching the load
- Change the water in the bottle to change the weight the two bands must carry
- Press Record this trial to build the table of angle and extension the lesson asks for
- Use the camera bar to look closely at the hook and its protractor
O que observar
- Opening the hooks increases the angle from the vertical and the extension of both bands
- The weight has not changed, so the extra tension is entirely the angle's doing
- The horizontal components are always equal and opposite — they cancel at every angle
- The check line 2T cos θ = W holds at every setting, to the last decimal place
- Adding water stretches the bands too, but that is the load changing, not the geometry
- At a wide angle the tension in each band can exceed the whole weight of the bottle
A física por trás
Each band can only pull along itself, so only the component of its tension along the vertical does any lifting. With the bands at an angle θ to the vertical, the two horizontal components are equal and opposite and cancel — ΣF_x = 0 — while the two vertical components add to carry the load: 2T cos θ = W. Because cos θ shrinks as θ grows, holding the same weight at a wider angle demands a larger T, and the band stretches until the elastic law T = kx supplies it. The hanging depth is not chosen here: it is solved from the geometry and the elastic law together, so the extension on screen is a measurement in the same sense the real experiment's is.